To harness the ever growing capacity and decreasing cost of storage, providing an abstraction of dependable storage in the presence of crash-stop and Byzantine failures is compulsory. We propose a decentralized Reed Solomon coding mechanism with minimum communication overhead. Using a progressive data retrieval scheme, a data collector contacts only the necessary number of storage nodes needed to guarantee data integrity. The scheme gracefully adapts the cost of successful data retrieval to the number of storage node failures. Moreover, by leveraging the Welch-Berlekamp algorithm, it avoids unnecessary computations. Compared to the state-of-the-art decoding scheme, the implementation and evaluation results show that our progressive data retrieval scheme has up to 35 times better computation performance for low Byzantine node rates. Additionally, the communication cost in data retrieval is derived analytically and corroborated by Monte-Carlo simulation results. Our implementation is flexible in that the level of redundancy it provides is independent of the number of data generating nodes, a requirement for distributed storage systems
The basic procedure of RS decoding is shown in Figure . The last step of the decoding procedure involves solving a linear set of equations, and can be made efficient by the use of Vandermonde generator matrices @cite_14 .
@cite_14
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In this letter, we propose a new decoding algorithm based on a soft-input soft-output run-length limited (RLL) decoder in visible light communication (VLC) with on–off keying (OOK) modulation and Reed–Solomon (RS) codes. Conventional RLL codes are used for dimming adjustments in VLC; however, in our receiver model, the posterior probability matrix is produced by the new RLL decoder, and it can be matched as the input of the soft RS decoder to enhance the throughput in the VLC system. A significant advantage of our proposed method is that it leads to the enhancement of bit error rate (BER) and frame error rate (FER) performances without any change in the transmitter in VLC systems. The simulation results show that the majority of the BER and FER performances of our proposed method are better than those of hard-input hard-output RLL decoding and soft-input hard-output RLL decoding methods. In this work, we propose a linear base station (BS) precoding strategy based on switched relaying (SR) processing for downlink multiuser multiple-input multiple-output (MIMO) relay systems. The BS and the MIMO relay station (RS) are both equipped with a codebook of interleaving matrices. For a given channel state information (CSI) the selection function at the BS chooses the optimum interleaving matrix from the codebook based on the maximum sum received signal-to-interference-plus-noise ratio (SINR) or sum rate to design the linear BS precoder. Prior to the payload transmission the BS sends the index corresponding to the selected interleaving matrix to the RS, where the optimum interleaving matrix is selected as the optimum relay processing matrix. The entries of the codebook are randomly generated unitary matrices. Simulation results show that the performance of the proposed techniques is significantly better than prior art in the case of perfect CSI.1 Polar codes, as the first provable capacity-achieving error-correcting codes, have received much attention in recent years. However, the decoding performance of polar codes with traditional successive-cancellation (SC) algorithm cannot match that of the low-density parity-check or Turbo codes. Because SC list (SCL) decoding algorithm can significantly improve the error-correcting performance of polar codes, design of SCL decoders is important for polar codes to be deployed in practical applications. However, because the prior latency reduction approaches for SC decoders are not applicable for SCL decoders, these list decoders suffer from the long-latency bottleneck. In this paper, we propose a multibit-decision approach that can significantly reduce latency of SCL decoders. First, we present a reformulated SCL algorithm that can perform intermediate decoding of 2 b together. The proposed approach, referred as 2-bit reformulated SCL ( 2b-rSCL ) algorithm , can reduce the latency of SCL decoder from ( @math ) to ( @math ) clock cycles without any performance loss. Then, we extend the idea of 2-b-decision to general case, and propose a general decoding scheme that can perform intermediate decoding of any @math bits simultaneously. This general approach, referred as @math -bit reformulated SCL ( @math b-rSCL ) algorithm , can reduce the overall decoding latency to as short as @math cycles. Furthermore, on the basis of the proposed algorithms, very large-scale integration architectures for 2b-rSCL and 4b-rSCL decoders are synthesized. Compared with a prior SCL decoder, the proposed (1024, 512) 2b-rSCL and 4b-rSCL decoders can achieve 21 and 60 reduction in latency, 1.66 and 2.77 times increase in coded throughput with list size 2, and 2.11 and 3.23 times increase in coded throughput with list size 4, respectively. Despite their exceptional error-correcting properties, Reed-Solomon (RS) codes have been overlooked in distributed storage applications due to the common belief that they have poor repair bandwidth: A naive repair approach would require the whole file to be reconstructed in order to recover a single erased codeword symbol. In a recent work, Guruswami and Wootters (STOC'16) proposed a single-erasure repair method for RS codes that achieves the optimal repair bandwidth amongst all linear encoding schemes. Their key idea is to recover the erased symbol by collecting a sufficiently large number of its traces, each of which can be constructed from a number of traces of other symbols. As all traces belong to a subfield of the defining field of the RS code and many of them are linearly dependent, the total repair bandwidth is significantly reduced compared to that of the naive repair scheme. We extend the trace collection technique to cope with multiple erasures.