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A system and method for encoding information arriving from a host in order to store the coded information in flash memory, the method comprising encoding information arriving from a host for storage at a flash memory location including generating a number of redundancy bytes, the encoding proceeding at an encoding rate which is a function of the number of redundancy bytes generated, the encoding including determining an effective error rate, including an anticipated rate of expected reading errors, for the flash memory location; and selecting the encoding rate as a function of the effective error rate such that the number of redundancy bytes is sufficient to overcome the anticipated rate of expected reading errors with a predetermined degree of certainty.
This application is a National Phase Application of PCT International Application No. PCT/IL2008/001228, entitled “SYSTEMS AND METHODS FOR MULTIPLE CODING RATES IN FLASH DEVICES”, International Filing Date Sep. 17, 2008, published on Apr. 30, 2009 as International Publication No. WO 2009/053961, which in turn claims priority from U.S Provisional Patent Application No. 60/996,027, filed Oct. 25, 2007, U.S Provisional Patent Application No. 60/996,782, filed Dec. 5, 2007, U.S Provisional Patent Application No. 61/006,805, filed Jan. 31, 2008, U.S Provisional Patent Application No. 61/064,853, filed Mar. 31, 2008, U.S Provisional Patent Application No. 61/071,465, filed Apr. 30, 2008, U.S Provisional Patent Application No. 61/071,466, filed Apr. 30, 2008 and US Provisional Patent Application No. 61/129,608 filed Jul. 8, 2008, all of which are incorporated herein by reference in their entirety.
Other co-pending applications include: U.S. Provisional Application No. 60/960,207, filed Sep. 20, 2007 and entitled “Systems and Methods for Coupling Detection in Flash Memory”, U.S. Provisional Application No. 61/071,467, filed Apr. 30, 2008 and entitled “Improved Systems and Methods for Determining Logical Values of Coupled Flash Memory Cells”, U.S. Provisional Application No. 60/960,943, filed Oct. 22, 2007 and entitled “Systems and methods to reduce errors in Solid State Disks and Large Flash Devices” and U.S. Provisional Application No. 61/071,469, filed Apr. 30, 2008 and entitled “Systems and Methods for Averaging Error Rates in Non-Volatile Devices and Storage Systems”, U.S. Provisional Application No. 61/006,120, filed Dec. 19, 2007 and entitled “Systems and Methods for Coping with Multi Stage Decoding in Flash Devices”, U.S. Provisional Application No. 61/071,464, filed Apr. 30, 2008 and entitled “A Decoder Operative to Effect A Plurality of Decoding Stages Upon Flash Memory Data and Methods Useful in Conjunction Therewith”, U.S. Provisional Application No. 61/006,385, filed. Jan. 10, 2008 and entitled “A System for Error Correction Encoder and Decoder Using the Lee Metric and Adapted to Work on Multi-Level Physical Media”, U.S. Provisional Application No. 61/064,995, filed Apr. 8, 2008 and entitled “Systems and Methods for Error Correction and Decoding on Multi-Level Physical Media”, U.S. Provisional Application No. 60/996,948, filed Dec. 12, 2007 and entitled “Low Power BCH/RS Decoding: a Low Power Chien-Search Implementation”, U.S. Provisional Application No. 61/071,487, filed May 1, 2008 and entitled “Chien-Search System Employing a Clock-Gating Scheme to Save Power for Error Correction Decoder and other Applications”, U.S. Provisional Application No. 61/071,468, filed Apr. 30, 2008 and entitled “A Low Power Chien-Search Based BCH/RS Recoding System for Flash Memory, Mobile Communications Devices and Other Applications”, U.S. Provisional Application No. 61/006,806, filed Jan. 31, 2008 and entitled “Systems and Methods for using a Erasure Coding in Flash memory”, U.S. Provisional Application No. 61/071,486, filed May 1, 2008 and entitled “Systems and Methods for Handling Immediate Data Errors in Flash Memory”, U.S. Provisional Application No. 61/006,078, filed Dec. 18, 2007 and entitled “Systems and Methods for Multi Rate Coding in Multi Level Flash Devices”, U.S. Provisional Application No. 61/064,923, filed Apr. 30, 2008 and entitled “Apparatus For Coding At A Plurality Of Rates In Multi-Level Flash Memory Systems, And Methods Useful In Conjunction Therewith”, U.S. Provisional Application No. 61/064,760, filed Mar. 25, 2008 and entitled “Hardware efficient implementation of rounding in fixed-point arithmetic”, U.S. Provisional Application No. 61/071,404, filed Apr. 28, 2008 and entitled “Apparatus and Methods for Hardware-Efficient Unbiased Rounding”, U.S. Provisional Application No. 61/136,234, filed Aug. 20, 2008 and entitled “A Method Of Reprogramming A Non-Volatile Memory Device Without Performing An Erase Operation”, U.S. Provisional Application No. 61/129,414, filed Jun. 25, 2008 and entitled “Improved Programming Speed in Flash Devices Using Adaptive Programming”, and several other co-pending patent applications being filed concurrently (same day).
The present invention relates generally to error correction coding and more particularly to error correction coding of data to be stored in memory such as flash memory.
 “Introduction to Coding Theory”, Ron M. Roth, Cambridge University Press, 2006 5. U.S. Pat. Nos. 5,077,737; 6,781,910; 6,873,543; 6,891,768; 6,914,809; 6,961,890 to Smith; 6,990,012; 7,079,436; 7,149,950; and 7,191,379; Published US Applications 2004015771; 2005172179; 2007226592; and 2007171730; and Published PCT Application No. WO2006013529.
 Multi-level memory systems using error control codes, Hsie-Chia Chang; Chien-Ching Lin; Tien-Yuan Hsiao; Jieh-Tsorng Wu; Ta-Hui Wang, Circuits and Systems, 2004. ISCAS apos; 04. Proceedings of the 2004 International Symposium on Volume 2, Issue, 23-26 May 2004 Page(s): II-393-6 Vol. 2.
 G. Campardo, R. Micheloni, D. Novosel, “CLSI-Design of Non-Volatile Memories”, Springer Berlin Heidelberg New York, 2005.
Bank=Device Back=memory Bank=Flash bank=Several Flash memory chips connected to the same controller and jointly providing a large amount of storage space.
Bit error rate (BER)=a parameter that a flash memory device manufacturer commits to vis a vis its customers, expressing the maximum proportion of wrongly read bits (wrongly read bits/total number of bits) that users of the flash memory device need to expect at any time during the stipulated lifetime of the flash memory device e.g. 10 years.
Block=a set of flash memory device cells which must, due to physical limitations of the flash memory device, be erased together. Also termed erase sector, erase block.
Cell: A component of flash memory that stores one bit of information (in single-level cell devices) or n bits of information (in a multi-level device having 2 exp n levels). Typically, each cell comprises a floating-gate transistor. n may or may not be an integer. “Multi-level” means that the physical levels in the cell are, to an acceptable level of certainty, statistically partitionable into multiple distinguishable regions, plus a region corresponding to zero, such that digital values each comprising multiple bits can be represented by the cell. In contrast, in single-level cells, the physical levels in the cell are assumed to be statistically partitionable into only two regions, one corresponding to zero and one other, non-zero region, such that only one bit can be represented by a single-level cell.
Charge level: the measured voltage of a cell which reflects its electric charge.
Coding Rate=Number of information bits/(Number of information bits+Redundancy bits).
Cycling: Repeatedly writing new data into flash memory cells and repeatedly erasing the cells between each two writing operations.
Decision regions: Regions extending between adjacent decision levels, e.g. if decision levels are 0, 2 and 4 volts respectively, the decision regions are under 0 V, 0 V-2 V, 2V-4 V, and over 4 V.
Demapping: basic cell-level reading function in which a digital n-tuple originally received from an outside application is derived from a physical value representing a physical state in the cell having a predetermined correspondence to the digital n-tuple.
Digital value or “logical value”: n-tuple of bits represented by a cell in flash memory capable of generating 2 exp n distinguishable levels of a typically continuous physical value such as charge, where n may or may not be an integer.
Erase cycle: The relatively slow process of erasing a block of cells (erase sector), each block typically comprising more than one page, or, in certain non-flash memory devices, of erasing a single cell or the duration of so doing. An advantage of erasing cells collectively in blocks as in flash memory, rather than individually, is enhanced programming speed: Many cells and typically even many pages of cells are erased in a single erase cycle.
Erase-write cycle: The process of erasing a block of cells (erase sector), each block typically comprising a plurality of pages, and subsequently writing new data into at least some of them. The terms “program” and “write” are used herein generally interchangeably.
Flash memory: Non-volatile computer memory including cells that are erased block by block, each block typically comprising more than one page, but are written into and read from, page by page. Includes NOR-type flash memory, NAND-type flash memory, and PRAM, e.g. Samsung PRAM, inter alia, and flash memory devices with any suitable number of levels per cell, such as but not limited to 2, 4, or 8.
Low cycle-count flash device: A flash device in which space S is reserved for redundancy bytes sufficient in number to support decoding, at a predetermined level of accuracy, of original data stored at locations within the flash device which have been subjected to no more than a low number, c, of cycle counts. The number of redundancy bytes fitting into the space S is not sufficient to support decoding, at the predetermined level of accuracy, of original data stored at locations within the flash device which have been subjected to more than c cycle counts.
Mapping: basic cell-level writing function in which incoming digital n-tuple is mapped to a program level by inducing a program level in the cell, having a predetermined correspondence to the incoming logical value.
Page=A portion, typically 512 or 2048 or 4096 bytes in size, of a flash memory e.g. a NAND or NOR flash memory device. Writing can be performed page by page, as opposed to erasing which can be performed only erase sector by erase sector. A few bytes, typically 16-32 for every 512 data bytes are associated with each page (typically 16, 64 or 128 per page), for storage of error correction information. A typical block may include 32 512-byte pages or 64 2048-byte pages.
Precise read, soft read: Cell threshold voltages are read at a precision (number of bits) greater than the number of Mapping levels (2^n). The terms precise read or soft read are interchangeable. In contrast, in “hard read”, cell threshold voltages are read at a precision (number of bits) smaller than the number of Mapping levels (2^n where n=number of bits per cell).
Present level, Charge level: The amount of charge in the cell. The amount of charge currently existing in a cell, at the present time, as opposed to “program level”, the amount of charge originally induced in the cell (i.e. at the end of programming).
Program level (programmed level, programming level): amount of charge originally induced in a cell to represent a given logical value, as opposed to “present level”.
Reprogrammability (Np): An aspect of flash memory quality. This is typically operationalized by a reprogrammability parameter, also termed herein “Np”, denoting the number of times that a flash memory can be re-programmed (number of erase-write cycles that the device can withstand) before the level of errors is so high as to make an unacceptably high proportion of those errors irrecoverable given a predetermined amount of memory devoted to redundancy. Typically recoverability is investigated following a conventional aging simulation process which simulates or approximates the data degradation effect that a predetermined time period e.g. a 10 year period has on the flash memory device, in an attempt to accommodate for a period of up to 10 years between writing of data in flash memory and reading of the data therefrom.
Resolution: Number of levels in each cell, which in turn determines the number of bits the cell can store; typically a cell with 2^n levels stores n bits. Low resolution (partitioning the window, W, of physical values a cell can assume into a small rather than large number of levels per cell) provides high reliability.
Retention: of original physical levels induced in the cells; retention is typically below 100% resulting in deterioration of original physical levels into present levels.
Retention time: The amount of time that data has been stored in a flash device, typically without, or substantially without, voltage having been supplied to the flash device i.e. the time which elapses between programming of a page and reading of the same page.
Threshold level: the voltage (e.g.) against which the charge level of a cell is measured. For example, a cell may be said to store a particular digital n-tuple D if the charge level or other physical level of the cell falls between two threshold values T.
Certain embodiments of the present invention seek to provide use of variable rate code, depending on the number of program/erase cycles, enabling compact storage when Flash device performs well.
Certain embodiments of the present invention seek to provide use of an additional bank of Flash devices to enable efficient encoding with variable code rates, beyond the allotted redundancy of the device.
Certain embodiments of the present invention seek to provide using a weighted cycle count, depending also on the time passage from the last burst of cycles, as determined by the number of errors counted during the last read.
Certain embodiments of the present invention seek to provide a cycle count indicator stored along with the data on a Flash e.g. with a single encoding/decoding block.
There is thus provided, in accordance with at least one embodiment of the present invention, a method for encoding information arriving from a host in order to store the coded information in flash memory, the method comprising encoding information arriving from a host for storage at a flash memory location including generating a number of redundancy bytes, the encoding proceeding at an encoding rate which is a function of the number of redundancy bytes generated, the encoding including determining an effective error rate, including an anticipated rate of expected reading errors, for the flash memory location; and selecting the encoding rate as a function of the effective error rate such that the number of redundancy bytes is sufficient to overcome the anticipated rate of expected reading errors with a predetermined degree of certainty.
Further in accordance with at least one embodiment of the present invention, the flash memory location comprises a page.
Still further in accordance with at least one embodiment of the present invention, determining comprises determining a rate of expected reading errors assuming reading occurs after a time period T, based on known data on frequency of errors when information is read from a flash memory which has undergone a simulation of effects of passage of the time period T.
Additionally in accordance with at least one embodiment of the present invention, determining comprises reading a stored effective error rate, identifying a time t at which the effective error rate was stored, and updating the effective error rate as a function of the stored effective error rate and the time, to take into account spontaneous recovery of the flash memory location, over time, from effects of some of the program cycles to which the flash memory location has been subjected.
Still further in accordance with at least one embodiment of the present invention, the updating comprises finding, for at least one stored number of program cycles to which the flash memory location was subjected at time t, a number of program cycles to which the flash memory location is subjected currently, after which the rate of errors currently read from the flash memory location equals the rate of errors currently read from the flash memory location which was subjected to the stored number of program cycles at time t.
Further in accordance with at least one embodiment of the present invention, the flash memory device comprises an NROM flash memory device.
Also provided, in accordance with at least one embodiment of the present invention, is a computer having an operating system, a storage unit comprising flash memory, and an operating system/storage unit interface providing interface between the storage unit and the operating system, the operating system being operative to query the storage unit to ascertain locations of bad flash memory portions, the interface including a bad location indicator operative to provide the operating system with an indication of the locations of bad flash memory portions, a flash memory controller operative to receive at least one of read commands, write commands, and status commands from a user, each command associated with a logical address, to translate each logical address into a physical address within the flash memory, and to translate the commands into at least one of read, erase and program instructions for the flash memory, and wherein the flash memory controller is operative to determine an encoding rate having fluctuations and accordingly and responsively to the querying, to declare as bad, at least one portion of the flash memory, which was previously devoted to original data and which, due to the fluctuations, is now devoted to redundancy bytes.
Further in accordance with at least one embodiment of the present invention, identifying a time t at which the effective error rate was stored, comprises associating a timer with the flash memory location, capable of generating a time stamp each time an operation is performed upon the flash memory location and storing at least one time stamp.
Further in accordance with at least one embodiment of the present invention, the operation comprises a flash memory location reading operation.
Still further in accordance with at least one embodiment of the present invention, identifying a time t at which the effective error rate was stored comprises reading the flash memory location including quantifying and correcting errors encountered, and estimating the time of last programming as a function of the quantification of errors encountered.
Additionally in accordance with at least one embodiment of the present invention, the effective error rate for an individual flash memory location is stored adjacent the individual flash memory location.
Further in accordance with at least one embodiment of the present invention, the flash memory location comprises a page and the effective error rate for the page is stored within the page.
Further in accordance with at least one embodiment of the present invention, the effective error rate is encoded at a fixed coding rate corresponding to a fixed number of redundancy bytes which is high enough to overcome expected corruptions of the effective error rate.
Still further in accordance with at least one embodiment of the present invention, the encoding, determining and selecting are performed for a plurality of flash memory locations.
Also provided, in accordance with at least one embodiment of the present invention, is high cycle count flash memory apparatus having a cycle count C, the apparatus comprising a set of flash memory devices including at least one low cycle-count flash device having a cycle count c<C storing original data elements, at least one additional flash device sufficient in size to store redundancy bytes sufficient in number to ensure that if information is encoded into the set of flash devices, with redundancy, thereby to generate a set of redundancy bytes, the additional flash device is sufficiently large to store a set of redundancy bytes sufficiently large to enable the information to be decoded at least a predetermined level of accuracy; and apparatus for reading at least one original data element from the low cycle flash memory device, and, in parallel, for reading at least one redundancy byte generated in the course of encoding the original data element, from the additional flash device.
Further in accordance with at least one embodiment of the present invention, the set of flash memory devices includes more than one flash device and the at least one additional flash device stores redundancy bytes for the more than one flash device.
A detailed description of the embodiments referred to above, and other embodiments, follows.
FIG. 17 is a simplified flowchart illustration of a page writing method, operative in accordance with certain embodiments of the present invention.
Today's Flash memory devices store information with a high density of Flash cells with ever smaller dimensions. In addition, Multi-Layer Cells (MLC) store several bits per cell by setting the amount of charge in the cell. The amount of charge is then measured by a detector, as measured by a threshold voltage of the transistor gate. Due to inaccuracies during the programming procedure and charge loss due to time and temperature (also known as retention), the measured levels during a Read operation suffer from detection errors. The small dimensions of the Flash cells result in cells that can store very small amounts of charge, enhancing the effects of inaccuracies due to programming and retention. Thus, new single layer cells (SLC) and multi-level cell devices have significantly increased bit error rate (BER), decreasing the reliability of the device.
Flash devices are organized into (physical) pages. Each page comprises a section allocated for data (512 bytes-4 Kbytes) and a small amount of bytes (16-32 bytes for every 512 data bytes) comprising redundancy and back pointers. The redundancy bytes are used to store error correcting information, for correcting errors which may have occurred e.g. during the page Read. Each Read and Program operation is performed on an entire page. A number of pages are grouped together to form an Erase Block (EB). A page cannot be erased unless the entire erase block which comprises it is erased.
An important measure of a Flash device quality is the number of times (Np) it may be reprogrammed before irrecoverable errors occur. The higher the number of program-erase cycles, the higher the bit error rate. Thus, today's multi-level cell devices can perform around Np=1000 cycles or less before the allocation of 16-32 bytes of redundancy per 512 bytes of data bytes becomes insufficient to correct errors. Single-level cell devices usually perform better but obtain a much lower density, and hence their prices are much higher. Note that following Np program-erase cycles the device is still operational but the bit error rate is higher. Furthermore, in many devices (e.g. NROM Flash devices), this behavior is predictable and it can be shown that the number of redundancy bytes required to correct these errors does not jump rapidly.
One application of Flash devices is solid state disks (SSD) where an array of Flash devices is used as the storage media of a computer hard drive, thus enjoying the fast Read and Access times of Flash chips. In a solid state disk (SSD), several Flash chips are programmed and read simultaneously to increase the Read and Program speeds. For this purpose, solid state disks are arranged into multiple “Banks” that allow parallel read/write operations, each Bank typically comprising a number of Flash devices. The Read/Program performance may be multiplied by the number of Banks, compared with a single Flash chip, as is evident from Reference .
Certain embodiments of the present invention provide for encoding with variable redundancy length, depending on the number of Program/Erase cycles (Np) which have occurred in an erase block. For this purpose, an additional Bank of Flash devices may be added which contains additional space for redundancy and data, beyond that allotted in the Flash pages. Thus, the additional redundancy may facilitate correction of a greater number of errors than is conventional, thereby to provide for a significantly higher number of Program/Erase cycles than is conventional and/or than was originally designed. As the additional Bank is read and programmed in parallel with the other banks, the performance hit is small. Furthermore, as only a small proportion of memory banks is typically added to the existing number of banks, such as for example 1 bank per every 4 banks, the added cost may be much smaller than the cost of replacing multi-level cell with single-level cell devices to increase reliability. In applications or environments where Np is small and no additional redundancy is required, the added bank may be used for data.
a. The Host 10 sends “logical” pages to be programmed on the Flash array 50. The host may comprise a computer such as a personal computer, or an SD card-employing application. b. A Variable Rate Encoder/Decoder 20 encodes the logical pages and adds redundancy e.g. as per the example described in detail below. The amount of redundancy added may for example depend on the rate indication obtained by a Cycle count indicator 40.
c. A Page Interleaver 30 receives a sequence of, say, L encoded pages and simultaneously programs them into the Flash array.
d. The Cycle Count Indicator 40 reads the number of cycles that the erase block has gone through from the flash array and determines, e.g. as per the example described in detail below, an appropriate encoding rate. The cycle count may be stored in the erase block on some of the redundancy bytes of some of the pages in the erase block. Indicator 40 typically also knows how to program the cycle count following erasure of the block and programming of the block's first page.
A read operation may be performed analogously, with the operations reversed.
1. Conventional codes for Flash devices include algebraic codes such as Reed Solomon or BCH e.g. as described in Reference . A suitable method for changing the rate of such a code is to change the length of the data being encoded/decoded while maintaining constant redundancy.
For example, consider a binary BCH code designed for a 2 Kbyte page with a redundancy of 128 bytes. Such a code may be used on some of today's devices with standard redundancy. To code with twice the redundancy, code two IKbyte-batches and add to each a redundancy of 128 bytes. Thus, overall, redundancy of 256 bytes is provided for every 2 Kbytes of data. This approximately doubles the possible magnitude of the input bit error rate. Similarly, the redundancy may be quadrupled by coding over batches of 512 bytes.
2. It may sometimes be more efficient, although less compact, to add an inner convolutional code with several puncturing options and use an Algebraic code as an outer code. The algebraic code may be a standard one such as RS or BCH codes. The inner code may be a convolutional code whose puncturing rate may be a parameter of the code e.g. as described in Reference . FIG. 2 is an example of this type of encoder/decoder. If the initial rate (i.e. the rate derived by the redundancy inherently allotted in each Flash device per page) is used, switches A and B are set to bypass the convolutional encoder/decoder and only the algebraic code may be operative. If lower rates are employed, the parameter f is set according to the cycle count e.g. as described below, and the convolutional code may be used.
For example, consider an outer encoder using a binary BCH code designed for a 2 Kbyte page with a redundancy of 128 bytes. By setting f=4, the convolutional encoder may yield a rate of 4/5 and the overall redundancy may be 640 bytes. 128 bytes may be stored with the data on the same page and the other 512 bytes may be stored separately. By setting a rate of 8/9 is obtained and the overall redundancy is 384 bytes.
3. An additional option is to build a set of encoders/decoder, each designed for a specific rate. This option may be least compact but may assure the most effective use of the redundancy bytes.
a. The data+redundancy may be stored sequentially over the banks. For example, FIG. 3A is a diagram of a Flash array with 5 banks. In each bank a single page may be used. Following encoding at a rate of 4/5, the first bank contains part of the first encoded page. The second bank contains the remainder of the first page and the beginning of the second encoded page, and so on; the remaining encoded pages are distributed over the banks as shown.
b. The data of each logical page is associated with its own bank and the additional redundancy of all encoded pages is stored in a designated bank. For example, FIG. 3B is a diagram of a Flash array with 5 banks. Banks 1 through 4 store the data and some partial redundancy of the respective encoded pages. Bank 5 contains the rest of the redundancies of each of the encoded pages.
The interleaver 30 of FIG. 1 may additionally be operative to determine the correct page address, bank, and device within a bank, when a read or program operation is performed.
If a constant rate is used, one-to-one addressing is able to translate each “logical” address to a “physical” address. However, if variable rate codes are used, it may be desired to utilize unused memory locations when the redundancy is small. FIG. 5A illustrates a page mapping which is effected subsequent to an encoding process which uses a low rate, i.e. with large redundancy blocks. In contrast, FIG. 5B illustrates a page mapping which is effected subsequent to an encoding process which uses a high rate, i.e. with small redundancy blocks. The compacting of the pages in FIG. 5B creates a page mapping problem between the logical address and its actual address. To overcome the mapping problem, a back pointer may be associated with each page or set of pages (e.g. erase block), which maps the page or set to its logical address. This back pointer may be stored during a program operation as part of the redundancy. Then, during a read or program operation, the interleaver 30 may scan the array 50 to determine the actual address.
Alternatively, the interleaver 30 may read the entire array 50 and fill a table mapping the logical addresses to physical addresses during the initialization of the system. FIG. 4 is a diagram of a page comprising both a back pointer 330 and a cycle count indicator 320 which may be stored as part of the redundancy of the page, along with the actual error correction information 340. The cycle count indicator 320 (Np) may optionally be used to determine the encoder rate during the next programming cycle and the rate during a decoding procedure, in which case, the cycle count may be encoded separately, as described in detail below.
According to certain embodiments of the present invention, as the cycles occur at the erase block level rather than at the individual page level. it may be more efficient to store the cycle counter only once per erase block instead of once per page. If so, a specific location within the erase block may be allocated to store the cycle count (Np) for the entire block. Similarly, as the cycle count affects the encoding rate of the entire block, only one back pointer may be stored for an entire block. For example, a back pointer to the first page in the block may be stored, and no back pointers for any of the remaining pages may be stored; instead, the other pages may be counted out sequentially starting from the back pointer of the first page.
Another result of allowing high rate pages to be compacted over the banks as shown in FIG. 5B may be that as the Flash array is cycled, the encoding may use lower rates and hence, more space may be used, such that the space available in the flash array 50 for actual data may become smaller in time. This may result in addressing problems. For example, at the beginning of life two (say) logical pages may be programmed to the array, first written to the lowest logical address available and the last to the highest logical address. As time progresses, the pages in between the 2 logical addresses are cycled and are programmed with lower rates, hence employing more space, such that it may no longer be possible to program all the addresses that were available at the beginning. To accommodate this possibility, some logical addresses in the array 50 may be marked as “bad blocks” or “unavailable blocks”; to alert the host 10, typically via a suitable controller, that these addresses are not to be used. Alternatively, some pages may be falsely marked as occupied although in fact they contain no data.
For compactness and simplicity, an address space which is believed to be typical at end of life may be pre-designated.
The Cycle Count Indicator 40 reads the cycle count field of an individual Erase Block or page and determines the encoding/decoding rate for the encoder 20 and for the interleaver 30. Cycle Count Indicator 40 also determines the number of cycles to be programmed next.
a. The cycle count indicator 40 may not be encoded along with the data and instead may be encoded separately typically using its own code e.g. a short BCH code, thereby to allow the decoding rate to be determined before reading the page.
b. The cycle count indicator 40 may be encoded with the data using the same encoder/decoder, during the read operation. A suitable encoding technique for this purpose is, for example, the selectably-puncturable inner convolutional code/outer algebraic coding technique described above. The outer, algebraic code may use a short redundancy which fits the data in one page in the Flash device e.g. as per the example described in detail below. The remaining redundancy, which is due to the inner convolution code, may be stored separately. For high rate coding only the outer (algebraic) code may be used whereas for lower rates coding, both the inner and outer codes may be used. The decoding may be performed first based solely on the algebraic code. If the decoding is unsuccessful, the read operation may be repeated with reliance on the inner decoder as well. Whereas this technique may be time consuming for high cycle counts (Np), no additional special encoder may be needed for the cycle count indicator.
Normally, the cycle count for each time an erase block is programmed, is simply an increment of the previous count. However, Flash memory devices, with time, tend to “forget” the number of cycles and improve their bit error rate performance following retention. For example, a Flash which underwent 1000 program/erase cycles within a period of one week may suffer a noticeable deterioration in bit error rate performance following retention. However, a Flash device that underwent 999 program/Erase cycles and only a year later underwent its 1000th cycle may exhibit better bit error rate performance, following additional retention, as compared to the previous flash device which underwent all 1000 cycles in the first week. The time passage from the previous erase block erasure can be estimated on a basis of the cycle counts and the number of errors which occurred during the latest read operation of the oldest page in the erase block. The cycle count (Np) can therefore be set to a lower value if the number of errors is not large, e.g. as per the example described below, thus enabling a higher rate encoding and more compact storage. A cycle counter so programmed is termed below a “weighted” cycle count or “weighted” cycle count indicator.
Weighted cycle count is a parameter characterizing a memory portion such as an erase block which is typically an increasing function of the number of erase-write cycles that memory portion has undergone, and an increasing function of the effective duration of time the memory portion had available to recover from erase-write cycles it has undergone, where the effective duration of time is a function of the length of the time period the memory portion had available to recover from erase-write cycles it has undergone (also termed retirement) and the temperature of the memory portion during that time period.
Computation of the weighted cycle count following a certain period of retirement may or may not be based upon a physical model of the Flash memory device. In  N. Mielke, H. Belgal, I. Kalastrisky, P. Kalavade, A. Kurtz, Q. Meng, N. Righos, and J. Wu, “Flash EEPROM Threshold Instabilities due to Charge Trapping During Program/Erase Cycling”, IEEE Trans. On Device and Materials Reliability, Vol. 4, No. 3, September 2004, the authors propose a model where the fraction of traps which disappear at room temperature during time Tr is given by ∝·log (Tr) for some constant trap dissipation rate which depends on the Flash technology being used and the temperature. Therefore, according to some embodiments of the present invention, as the traps are the main contributors for endurance degradation with cycling and retention (at technologies of <100 nm), the disappearance of traps may be represented by effectively decreasing the weighted cycle count.
In the same paper the authors show that the number of traps grows approximately as the square root of the number of cycles. Therefore, according to some embodiments of the present invention, an effective number of cycles may be approximated by: Cs·(1−∝·log(Tr))2 where Cs is the previous weighted cycle count.
Flash array 50, as shown in FIG. 6, typically comprises L+1 banks of Flash memory devices of which L banks are allocated for data and Bank L+1 is allocated for redundancy. Each Bank comprises M Flash memory devices. Each memory device comprises K Erase Blocks and each Erase Block comprises T pages. At each bank, the erase blocks are numbered serially from 1 to MK. In each erase block, the pages are numbered from 1 to T, resetting at the beginning of each erase block.
1. Encode 2048 bytes of data—+11 bytes provided for additional information such as cycle count, and add 39*3=117 bytes. To do this, divide the 2048+11 bytes into 3 consecutive sections of 686,686 and 687 bytes. Encode each section separately, thereby to generate 39 bytes of redundancy per section, for a total of 2048+128=2176 bytes. This code can handle bit error rate of 6.5E-4 and at its output produces a bit error rate of 1E-15.
2. Encode 2048 bytes of data—+11 bytes and add 20*39 bytes. This may be effected by dividing the 2048+11 bytes into 20 consecutive sections, the first 19 having 103 bytes and the last one having 102 bytes. Encode each section separately, thereby to generate 39 bytes of redundancy, for a total of 2839 bytes. This code can handle a bit error rate of 3E-3 and at its output produces a bit error rate of 1E-15.
3. Encode 2048 bytes of data—+11 bytes and add 58*39 bytes. This may be effected by dividing the 2048+11 bytes into 58 consecutive sections, the even sections having 35 bytes and the odd sections having 36 bytes. Encode each section separately, thereby to generate 39 bytes of redundancy, for a total of 4321 bytes. This code can handle bit error rate of 5.5E-3 and at its output produces a bit error rate of 1E-15.
FIG. 10 shows an example of how the bit error rates may change as a function of the program erase cycles in a NAND flash device employing 3 bits/cell. It can be seen from the graph of FIG. 10 that for 3 bits/cell specifically, the first strategy may be employed up to Np=3000, followed by the second strategy until Np=5000 and above Np=5000 the third strategy may be employed. An alternative is to switch between the 4 bit/cell configuration and the 3 bit/cell configuration depending on the cycle count. FIG. 8 illustrates a variable rate system including a single NAND Flash device 1200 in accordance with certain embodiments of the present invention. In this system, logical pages may accommodate more than a single physical page as shown in FIG. 7. The system of FIG. 8 typically comprises a uController (1100), a NAND Flash device (1200) and a Host (1000). The system may realize an application such as a USB drive or an SD card; the Host 1000 would then be a PC or an application using SD cards such as a digital camera or an MP3. The Host 1000 sends Read/Write commands to the uController 1100 which translates these read/Write commands to read/program/erase commands on the Flash device 1200. The communication between the host 1000 and uController 1100 may occur through standard protocols such as the SD standard or the USB protocol.
FIG. 9 is a simplified functional block diagram illustration of the uController 1100 of FIG. 8, in accordance with certain embodiments of the present invention. As shown, the uController 1100 comprises an Encoder 1120 and Decoder 1130. Typically, each of these can encode at various selectable rates, e.g. as described above, to produce different amounts of redundancy. A host interface 1110 receives the commands from the host 1000 and responds thereto. The host interface 1110 typically comprises a buffer that stores a logical page to be programmed.
The pages sent by the host 1000 may be smaller than the data length used by the encoder 1120 in which case the host interface 1110 translates the data sizes to those used by encoder 1120. For example, the encoder 1120 may use a constant size of 2048 bytes of data whereas the interface with the host 1000 may occur in chunks of 512 bytes. The interface 1110 may serialize 4 chunks of 512 bytes to obtain the 2048 bytes. If this is not possible, e.g. if not enough chunks have arrived, then the interface 1110 may append to the available chunks, a sequence of zeroes, until a full page of 2048 bytes is obtained.
The NAND interface 1150 connects to the NAND flash 1200 and is operative to send suitable program/erase and read commands to the NAND flash 1200. The NAND interface 1150 typically comprises a program buffer (not shown) the size of a page (say 2048+128 bytes). Each time the program buffer is full, a program command is initiated to a physical page location, previously sent to the NAND interface 1150.
A payload logical page buffer 1170 is typically provided to temporarily hold the data to be programmed. A memory management unit 1140 interfaces with the host interface 1110, the variable rate decoder 1130 and, optionally, with a clock 1160, all as described in detail below. The optional clock (1160) stores time stamps and is provided in those embodiments which utilize effective cycle counts rather than raw cycle counts.
a number of logical pages which are actually allocated to this erase block. Optionally, we may also store a time stamp indicating when the block was last programmed.
OccupyVec: a vector of, say, 32 bits indicating which pages have already been programmed and which pages have not. In the illustrated example, 1=programmed, 0=empty.
The size of the set of logical addresses may be the largest common divider of possible values of #PagesPerBlock stored in the physical block usage table of FIG. 11. For example, if the table of FIG. 11 indicates that there are blocks storing 128, 96 and 64 logical pages then the set of logical addresses may include 32 logical addresses.
The illustrated embodiment and example data are based on the 3-rate algebraic code described above and assume that the Flash array 1200 includes Erase blocks, each comprising 128 physical pages, each including 2048+128 bytes. It is also assumed that the data payload comprises 2048 bytes received from the host 1000 and 11 bytes for cycle counts and back pointers as described above. The rate selected for the encoder 1120 and decoder 1130 depends on the cycles count as described above. Thus, a block may comprise 128, 96 or 64 logical pages, using rate 1, 2 or 3.
If a Block comprises 96 logical pages, each set of 32 logical pages is assumed, in the illustrated example, to be programmed into a set of 42 physical pages such that logical pages 0-31 are mapped to physical pages 0-41, logical pages 32-63 are mapped to physical pages 42-83 and logical pages 64-95 are mapped to physical pages 84-125. If there are 64 logical pages per block, each logical page is mapped to two different physical pages.
Each entry in the Logical page lookup table of FIG. 12 comprises a reference to a set of 32 logical pages. Thus, in order to locate the location of a logical page, the methods of FIGS. 13 and 14 may be followed. FIG. 15 is, then, a suitable “read logical page” operation which may be performed by the uController 1100 of FIG. 8. Regarding a “write logical page” operation, if a logical page was previously programmed, it cannot be replaced without first erasing the physical block which contains it. Also, logical pages are now encoded over several physical pages. Hence, even if a target logical page has not been programmed, an adjacent logical page may have been programmed, in which case it may not be possible to program the target page because it may be partially located on the same physical page allocated to another programmed page. To overcome this problem a block copy and modify operation, e.g. as shown in FIGS. 16A-16D, may be performed, followed by a write operation e.g. as shown in FIG. 17.
It is appreciated that each of the methods shown in the various simplified flowchart illustrations provided herein may include some or all of the steps actually shown, suitably ordered e.g. as shown.
In the illustrated embodiment, logical pages have a uniform, predetermined length. However, due to the variable code rate, each erase block is able to store a different number of logical pages. In the illustrated embodiment, 3 example strategies (not intended to be limiting) are employed, as described above, and the number of logical pages which each erase block is to store is determined as a function of the strategy. In the example described herein, the code rates are such that 128, 96 and 64 logical pages are stored per erase block. Therefore, for example, the number of bytes used to store each logical page when strategy 2 is used, is 2839, as may be seen, e.g. in step 1350 of FIG. 13. The numbers of bytes used to store each logical page when strategies 1 and 3 are used are each of course different. In strategy 1, each physical page stores exactly one logical page in the illustrated example. In strategy 3, each logical page is stored over exactly two physical pages as is evident e.g. from step 1385 in FIG. 13.
Specifically, FIG. 14 describes one method for receiving (step 1410) an indication of a logical page, e.g. from a host, and returning the physical page mapped to that logical page. In step 1420, the table of FIG. 12 is accessed, at the record corresponding to the logical page address or the floor value thereof. For example, if the logical page address obtained in step 1410 is 319, the record for which logical page address=288 is accessed. In this record, block#=3 and Firstpagenumber=32. It is appreciated that each record in the table of FIG. 12 refers to a “segment” including a plurality of logical pages (32 logical pages in the illustrated example). So, the record accessed above indicates that the segment to which the current logical page belongs, is stored in erase block 3 starting from logical page 32 within that erase block. The Occupyvec field of the above record indicates whether or not each logical page in the segment to which the record corresponds, is occupied; “1” indicating that the logical page is occupied (also termed herein “allocated”) and “0” indicating that the logical page is unoccupied or unallocated. For example, in the segment in question, the first, third, fourth, fifth and sixth logical pages are occupied, and the second logical page is not (as evident from the fact that the first 6 bits in the OccupyVec field of the record corresponding to logicalPageAdress=288, are 101111 respectively.
If the logical page is not allocated i.e. does not contain data, an “unallocated” indication is returned (step 1440); if it is allocated, the physical address of the logical page in question, within the erase block whose serial number is Block#, is computed (step 1450). One suitable method of performing step 1450 is illustrated in FIG. 13. The output of the method of FIG. 14 includes (step 1460) the block in which the logical page whose address was obtained in step 1410 is stored or is to be stored, the number of the physical page within that block at which the logical page is stored or is to be stored, the number of the byte within that physical page at which the logical page is stored (since the beginning of each logical page generally does not correspond to the beginning of the physical page) and the status of the logical page: either programmed, free or blocked; or unallocated (step 1440).
FIG. 13 is a possible implementation of FIG. 14, step 1450 and comprises a method for finding a physical address of a known logical page on which to write or from which to read, within a known block, all as a function of a previously effected mapping between physical and logical pages. As described above, the block number (Block#) is known. The variables to be obtained in step 1310 may be known e.g. from step 1420 of FIG. 14. In step 1315, the table of FIG. 11 is used to determine how many logical pages are stored in the block (block No. 3) in which the logical page in question resides. The answer, in the illustrated embodiment, may be either 64, 96 or 128; and in fact happens to be 96 as shown in the fourth record of FIG. 11 (which corresponds to block No. 3).
Step 1320 computes remainders after dividing logical addresses by 32. The remainder indicates the position of the logical page within its 32-page section (e.g. logical page 319 is 31st within its section). Therefore, the remainder Stipulates the bit within the OccupyVec vector which pertains to the logical page in question. Step 1320 collects information as to whether the logical page, and the pages just before and after it, are or are not programmed.
The method now typically proceeds according to the number of pages per block which in the illustrated embodiment, may be either 64, 96 or 128. In each case, the byte within the physical page starting from which the logical page is or is to be stored, is computed, and an indication is provided of whether the page is free i.e. both it and its neighbors are unoccupied or unallocated, blocked (i.e. free but with at least one occupied neighbor) or allocated.
Page status may be used in reading. For example, FIG. 15 is a simplified flowchart illustration of a “read logical page” method which may be performed by the uController 1100 of FIG. 8, in accordance with certain embodiments of the present invention. As shown, after a logical page address is obtained e.g. from a host (step 1510) and the physical address of that logical page is located e.g using the method of FIG. 14 (step 1520), the method proceeds depending on whether or not the logical page is found to be programmed. If not, the logical page buffer 1170 in step 1540 is reset (e.g. with zeros). If the logical page is programmed, it is decoded (step 1590), using one of the three (in the illustrated example) code rates, as determined (step 1560) by the number of pages in the block in which the logical page is stored.
Page status may also be used in writing. For example, FIG. 17 is a simplified flowchart illustration of a page writing method, operative in accordance with certain embodiments of the present invention. According to the method of FIG. 17, a copy modify process is used to write on a particular logical page (step 2070), if the physical page storing the logical page and/or at least one of the neighbors of that physical page is found to be programmed (step 2030). In the copy modify process, which may follow the method of FIGS. 16A-16B, the erase block which stores the logical page in question is copied to another location and during the copying procedure the logical page in question is modified to store the new data. The original block is then erased (step 2080). The PagesPerBlock field is then updated depending on the cycle count Np since in the illustrated embodiment, the cycle count determines the code rate, using cut-off points of (say) 3000 and 5000.
Otherwise, i.e. if the physical page storing the logical page and both of its neighbors are unoccupied, the code rate is set (step 2040) depending on the value of the PagesPerBlock field in the table of FIG. 11 and the data is encoded at that rate (step 2050). The encoded data is then programmed into the flash (step 2060), at the appropriate physical address e.g. as determined by the method of FIG. 14.
FIGS. 16A-16B, taken together, form a simplified flowchart illustration of a block copy and modify method, operative in accordance with certain embodiments of the present invention and suitable for implementing the copy-modify step 2070 of FIG. 17. FIG. 16C is a simplified flowchart illustration of a method for performing step 1780 of FIG. 16B, in accordance with certain embodiments of the present invention. FIG. 16D is a simplified flowchart illustration of a method for performing step 1784 of FIG. 16B, in accordance with certain embodiments of the present invention.
It is appreciated that the teachings of the present invention can, for example, be implemented by suitably modifying, or interfacing externally with, flash controlling apparatus. The flash controlling apparatus controls a flash memory array and may comprise either a controller external to the flash array or a microcontroller on-board the flash array or otherwise incorporated therewithin. Examples of flash memory arrays include Samsung's K9XXG08UXM series, Hynix' HY27UK08BGFM Series, Micron's MT29F64G08TAAWP or other arrays such as but not limited to NOR or phase change memory. Examples of controllers which are external to the flash array they control include STMicroelectrocincs's ST7265x microcontroller family, STMicroelectrocincs's ST72681 microcontroller, and SMSC's USB97C242, Traspan Technologies' TS-4811, Chipsbank CBM2090/CBM1190. Examples of commercial IP software for Flash file systems are: Denali's Spectra™ NAND Flash File System, Aarsan's NAND Flash Controller IP Core and Arasan's NAND Flash File System. It is appreciated that the flash controller apparatus need not be NAND-type and can alternatively, for example, be NOR-type or phase change memory-type.
A Flash controlling apparatus, whether external or internal to the controlled flash array, typically includes the following components: a Memory Management/File system, a NAND interface (or other flash memory array interface), a Host Interface (USB, SD or other), error correction circuitry (ECC) typically comprising an Encoder and matching decoder, and a control system managing all of the above.
The present invention may for example interface with or modify, as per any of the embodiments described herein, one, some or all of the above components and particularly the ECC and memory management components. The memory management component, or a functional unit interacting therewith, is, according to certain embodiments of the present invention, able to handle different sizes of encoded pages over more than one physical page.
selecting the encoding rate as a function of said effective error rate such that said number of redundancy bytes is sufficient to overcome said anticipated rate of expected reading errors with a predetermined degree of certainty.
2. The method according to claim 1 wherein said flash memory location comprises a page.
3. The method according to claim 1 wherein said determining comprises determining a rate of expected reading errors assuming reading occurs after a time period T, based on known data on frequency of errors when information is read from a flash memory which has undergone a simulation of effects of passage of said time period T.
4. The method according to claim 1 wherein said determining comprises reading a stored effective error rate, identifying a time t at which said effective error rate was stored, and updating said effective error rate as a function of said stored effective error rate and said time, to take into account spontaneous recovery of the flash memory location, over time, from effects of some of the program cycles to which the flash memory location has been subjected.
5. The method according to claim 4 wherein said updating comprises finding, for at least one stored number of program cycles to which the flash memory location was subjected at time t, a number of program cycles to which the flash memory location is subjected currently, after which the rate of errors currently read from said flash memory location equals the rate of errors currently read from said flash memory location which was subjected to said stored number of program cycles at time t.
6. A method according to claim 4 wherein said identifying a time t at which said effective error rate was stored, comprises associating a timer with said flash memory location, capable of generating a time stamp each time an operation is performed upon said flash memory location and storing at least one said time stamp.
7. A method according to claim 6 wherein said operation comprises a flash memory location reading operation.
8. A method according to claim 4 wherein said identifying a time t at which said effective error rate was stored comprises reading said flash memory location including quantifying and correcting errors encountered, and estimating the time of last programming as a function of said quantification of errors encountered.
9. The method according to claim 1 wherein said flash memory device comprises an NROM flash memory device.
10. A method according to claim 1 wherein said effective error rate for an individual flash memory location is stored adjacent said individual flash memory location.
11. A method according to claim 10 wherein said flash memory location comprises a page and said effective error rate for said page is stored within said page.
12. A method according to claim 11 wherein said effective error rate is encoded at a fixed coding rate corresponding to a fixed number of redundancy bytes which is high enough to overcome expected corruptions of said effective error rate.
13. A method according to claim 1 wherein said encoding, determining and selecting are performed for a plurality of flash memory locations.
an encoding rate definer selecting the encoding rate as a function of said effective error rate such that said number of redundancy bytes is sufficient to overcome said anticipated rate of expected reading errors with a predetermined degree of certainty.
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KISANO TRADE & INVEST LIMITED; TRASTECO LTD; VADIM SHULMAN, Appellants, v. DEV LEMSTER; STEEL EQUIPMENT CORP; AKIVA SAPIR; SAPIR ENTITIES -100. No. 13-1759. United States Court of Appeals, Third Circuit.
KISANO TRADE & INVEST LIMITED; TRASTECO LTD; VADIM SHULMAN, Appellants, v. DEV LEMSTER; STEEL EQUIPMENT CORP; AKIVA SAPIR; SAPIR ENTITIES 1-100.
No. 13-1759. United States Court of Appeals, Third Circuit. Argued: October 8, 2013. Opinion Filed: December 12, 2013. Bruce S. Marks, Esq. (Argued), Thomas C. Sullivan, Esq., Maria Temkin, Esq., Marks & Sokolov, 1835 Market Street, 28th Floor, Philadelphia, PA 19103, Counsel for Appellants. Larry K. Elliott, Esq. (Argued), David F. Russey, Esq., Julie W. Vanneman, Esq., Curt Vazquez, Esq., Cohen & Grigsby, 625 Liberty Avenue, Pittsburgh, PA 15222, Counsel for Appellees. Before: FUENTES, GREENBERG and BARRY Circuit Judges.
In June of 2011, Kisano Trade & Invest Limited ("Kisano") and Trasteco Ltd. ("Trasteco"), two companies owned by Vadim Shulman, filed suit in the U.S. District Court for the Western District of Pennsylvania against Dev Lemster and his company, Steel Equipment Corp. The complaint alleged violations of the Racketeer Influenced Corrupt Organizations Act ("RICO"), intentional interference with contract, unjust enrichment, and breach of fiduciary duty. After discovering evidence of what Shulman believed to be fraud perpetrated by his business partner, Akiva Sapir, an amended complaint added Shulman as a plaintiff, Sapir and certain of his entities as defendants, and several claims of fraud. Between then and now, we vacated the grant of a preliminary injunction, and the parties moved forward on Sapir's motions to dismiss the complaint for failure to state a claim and on forum non conveniens grounds, the latter motion offering Israel as an alternative forum. The motions were referred by the District Court to the Magistrate Judge to issue a Report and Recommendation (the "R&R"). The R&R recommended that the action be dismissed on forum non conveniens grounds, reasoning that Israel would be the more appropriate forum, and declined to reach the motion to dismiss for failure to state a claim, leaving that to be addressed, if appropriate, by the Israeli court. The District Court adopted the R&R, and granted the motion to dismiss for forum non conveniens "on the understanding that the case may be refiled in Israel and that the defendants waived certain statute of limitations defenses." (A00060.) Plaintiffs now appeal. We will affirm.
The District Court had jurisdiction pursuant to 28 U.S.C. 1331 and 18 U.S.C. 1964(c), as the underlying claim asserts recovery under RICO. We have jurisdiction pursuant to 28 U.S.C. 1291. "`[W]here the court has considered all relevant public and private interest factors, and where its balancing of these factors is reasonable, its decision deserves substantial deference.'" Lony v. E.I. Du Pont de Nemours & Co., 886 F.2d 628, 631-32 (3d Cir. 1989) ("Lony I") (quoting Piper Aircraft Co. v. Reyno, 454 U.S. 235, 257 (1981)) (alteration in original). Thus, "we do not perform a de novo resolution of forum non conveniens issues," and instead review the District Court's dismissal on grounds of forum non conveniens for an abuse of discretion. Lacey v. Cessna Aircraft Co., 862 F.2d 38, 43 (3d Cir. 1988).
This case, at its core, involves plaintiffs' allegations of numerous claims of fraudthe Warren equipment "fraud," the Trasteco "secret deal," the Kisano "secret deal," the Plama "secret deal," the Veolia "secret deal," and the New York real estate "fraud." The parties, at great length, have set forth those facts that plaintiffs believe, on the one hand, support those claims, and defendants believe, on the other, defeat them. At the end of the day, however, the sole issue before us for review is the dismissal on grounds of forum non conveniens. We, therefore, will refer only to those facts necessary to our analysis of that issue. Although a plaintiff's choice of forum should rarely be disturbed, "[w]hen an alternative forum has jurisdiction to hear the case, and when trial in the plaintiff's chosen forum would `establish . . . oppressiveness and vexation to a defendant . . . out of all proportion to plaintiff's convenience,' or when the `chosen forum [is] inappropriate because of considerations affecting the court's own administrative and legal problems,' the court may, in the exercise of its sound discretion, dismiss the case." Windt v. Qwest Commc'ns Int'l, Inc., 529 F.3d 183, 189 (3d Cir. 2008) (quoting Koster v. (Am.) Lumbermens Mut. Cas. Co., 330 U.S. 518, 524 (1947)) (second alteration in original). We have identified the following four factors to guide a district court's exercise of discretion: (1) the amount of deference to be afforded to plaintiffs' choice of forum; (2) the availability of an adequate alternative forum where defendants are amenable to process and plaintiffs' claims are cognizable; (3) relevant "private interest" factors affecting the convenience of the litigants; and (4) relevant "public interest" factors affecting the convenience of the forum. See id. at 189-90. Private interests to consider include the ease of access to sources of proof; ability to compel witness attendance if necessary; means to view relevant premises and objects; and any other potential obstacle impeding an otherwise easy, costeffective, and expeditious trial. Delta Air Lines, Inc. v. Chimet, S.p.A., 619 F.3d 288, 296 (3d Cir. 2010) (citing Gulf Oil Corp. v. Gilbert, 330 U.S. 501, 508 (1947)). Public interests include administrative difficulties arising from increasingly overburdened courts; local interests in having the case tried at home; desire to have the forum match the law that is to govern the case to avoid conflict of laws problems or difficulty in the application of foreign law; and avoiding unfairly burdening citizens in an unrelated forum with jury duty. Id. (citing Piper Aircraft, 454 U.S. at 241 n.6).
We first consider whether the District Court abused its discretion in affording plaintiffs' choice of forum a lesser degree of deference than would be accorded a domestic plaintiff. "Ordinarily, a strong presumption of convenience exists in favor of a domestic plaintiff's chosen forum, and this presumption may be overcome only when the balance of the public and private interests clearly favors an alternate forum." Windt, 529 F.3d at 190. When a plaintiff is foreign, however, the choice of a United States forum "deserves less deference." Piper Aircraft, 454 U.S. at 256; see also Sinochem Int'l Co. v. Malaysia Int'l Shipping Corp., 549 U.S. 422, 430 (2007) ("When the plaintiff's choice is not its home forum, . . . the presumption in the plaintiff's favor applies with less force, for the assumption that the chosen forum is appropriate is in such cases less reasonable." (internal quotation marks omitted)). Among other reasons, courts are wary of the potential for foreign plaintiffs to seek jurisdiction in the United States because the laws may be more favorable to their claims. See Piper Aircraft, 454 U.S. at 249 n.15 ("[D]ismissal may be warranted where a plaintiff chooses a particular forum, not because it is convenient, but solely in order to . . . take advantage of favorable law."). Shulman is an Israeli citizen, Kisano is a Cypriot corporation, and Trasteco is a Maltese LLC. Despite their foreign citizenship, they argue that the District Court erred by granting lesser deference to their choice of forum because of the "equal access" provision of a treaty between the United States and Israel which, as relevant here, states: Nationals and companies of either Party shall be accorded national treatment and most-favored-nation treatment with respect to access to the courts of justice and to administrative tribunals and agencies within the territories of the other Party, in all degrees of jurisdiction, both in pursuit and in defense of their rights. (A00553 (U.S.-Isr. Treaty, art. V(1)).) Plaintiffs invoke Blanco v. Banco Industrial de Venezuela, S.A., 997 F.2d 974 (2d Cir. 1993), as essentially their sole support for the proposition that "when a treaty with a foreign nation accords its nationals access to our courts equivalent to that provided American citizens, identical forum non conveniens standards must be applied to such nationals by American courts." Id. at 981. Acknowledging that a United States-Venezuela treaty had an equal access provision, the Second Circuit found that "no discount may be imposed upon the plaintiff's initial choice of a New York forum in this case solely because [plaintiff] is a foreign corporation." Id.
 relevant factor. See Solomon v. Cont'l Am. Life Ins. Co., 472 F.2d 1043, 1047 (3d Cir. 1973). The District Court did not abuse its discretion in finding that plaintiffs did not make a strong showing of convenience and therefore affording lesser deference to their choice of forum.
Having concluded that the District Court did not err in according lesser deference to plaintiffs' choice of forum, we turn to whether it abused its discretion when weighing the private and public interest factors in determining if plaintiffs' chosen forum would cause "oppressiveness and vexation to a defendant . . . out of all proportion to plaintiff's convenience." Koster, 330 U.S. at 524. When seeking dismissal on grounds of forum non conveniens, a defendant must show that the balance of public and private factors "tips decidedly in favor of trial in the foreign forum." Lacey v. Cessna Aircraft Co., 932 F.2d 170, 180 (3d Cir. 1991) ("Lacey II"). As an initial matter, plaintiffs argue that the District Court erred as a matter of law in failing to apply the "oppressiveness and vexation" standard. This argument is without merit. While the R&R did not specifically mention those words, the Magistrate Judge's analysis and the District Court's opinion adopting the R&R clearly reflect that the appropriate standard was applied. Moreover, the District Court, when adopting and supplementing the R&R, explicitly acknowledged this standard when overruling plaintiffs' objection that the Magistrate Judge "faile[ed] to apply the `oppressiveness and vexation' standard." (A00055.) Although the District Court did not engage in a lengthy discussion of "oppressiveness and vexation," its thorough analysis of the private and public interest factors and its findings reflect a correct understanding of the standard and permits our appellate review of the Court's "actual consideration and analysis." Windt, 529 F.3d at 196 (stating that District Court's failure to state correct "oppressiveness and vexation" standard was not error when it correctly applied the standard and permitted meaningful appellate review).
Plaintiffs argue that the District Court abused its discretion in its assessment of the private interest factors. To reiterate, private interests include such things as ease of access to sources of proof, ability to compel witness attendance, and other potential obstacles to a cost-effective and expeditious trial. Delta Air Lines, Inc., 619 F.3d at 296. The parties go through lengthy discussions of the witnesses, their countries of residence, their preferred languages, and the facts to which each may testify. We need not scrutinize all of these materials to perform our function of appellate review, nor was it necessary for the District Court to have done so. See id. at 299-300 ("The Supreme Court has rejected the suggestion that defendants seeking forum non conveniens dismissal must submit affidavits identifying the witnesses they would call and the testimony these would provide if the trial were held in the alternative forum, explaining that such detail is not necessary. Rather, the defendant must provide enough information to enable the District Court to balance the parties' interests." (internal citations and quotation marks omitted)). It suffices to say that Shulman identifies several witnesses located in the United States with knowledge of the various deals, while Sapir identifies nearly twenty witnesses located abroad, the majority of whom live in Israel, the country of residence of both Sapir and Shulman. Sapir contends that Shulman's witnesses in the United States will testify to facts not in dispute, such as the purchase price of the Warren plant and equipment and the fact that $500,000 was never paid to one Bob Stump in connection with this purchase. Rather, Sapir's defense is that Shulman knew the actual purchase price and that the witnesses with information regarding the actual negotiation of the disputed deals are located in Israel or live closer to Israel. Shulman also argues, without any authority, that there are roughly 18,700 pages of documents in English that would need to be translated into Hebrew in an Israeli forum. As noted above, Sapir provided the declaration of an Israeli lawyer, asserting that documents in English need not be translated because Israel courts are typically proficient in English.
The location of the parties, their witnesses, and the availability of evidence favor resolution in Israel. The District Court did not abuse its discretion in concluding that the private interest factors weighed in favor of dismissal.
Plaintiffs also argue that the District Court erred in weighing the public interest factors because it applied the wrong standard, citing Lacey II for the proposition that absent a showing that the private interest factors impose oppressiveness or vexation, a defendant must show the public interest factors weigh heavily in favor of dismissal. Plaintiffs misstate the relevant test: To prevail on a forum non conveniens motion, "the movant must show that the balance of these [private and public interest] factors tips decidedly in favor of trial in the foreign forum." Lacey II, 932 F.2d at 180 (emphasis added). Plaintiffs contend that there is no congestion in the chosen district, that there is a strong federal interest in plaintiffs' choice of forum, that a United States jury has a strong interest in the case, that Pennsylvania law will apply, that the locus of the culpable conduct occurred in Pennsylvania, and that the District Court has already invested substantial resources in the case. As the District Court noted, however, Shulman and Sapir met in Israel, discussed and negotiated the purchase of the Warren plant and equipment in Israel, discussed the coal deals in Israel, and most interactions with each other took place in Israel, Monaco or the Ukraine, not in Pennsylvania (or even in the United States). Other than the actual wire payments and Shulman's law firm, there appears to be no other connection to Pennsylvania, and little else to the United States. The District Court further concluded that there had been no apparent progress made in the case. As to the other factors, the District Court found the choice-of-law issue potentially complicated and did not address it. See id. at 187 n.14 ("[I]n resolving a forum non conveniens motion, the district court is not required to predict what law the foreign court would apply."). It also correctly noted that not every public interest factor need weigh in favor of dismissal. Accordingly, the District Court did not abuse its discretion in finding that public interest factors weighed in favor of dismissal. IV. Conclusion The order of the District Court dismissing the action on forum non conveniens grounds will be affirmed.
risks. The District Court, however, with the competing affidavits of doctors from both sides, declined to conclusively resolve the issue and instead based its decision on other private interests. We do not address it further.
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Derecho de Libre Determinación y Derecho a Decidir: Nueva Soberanía y Derechos Humanos en El Siglo XXI.
Granger Associates vs. Microwave Systems, Inc.

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