This report contains revision and extension of some results about RBO from [14]. RBO is a simple and ecient broadcast scheduling of n = 2 k uniform frames for battery powered radio receivers. Each frame contains a key from some arbitrary linearly ordered universe. The broadcast cycle a sequence of frames sorted by the keys and permuted by k-bit reversal is transmitted in a round robin fashion by the broadcaster. At arbitrary time during the transmission, the receiver may start a simple protocol that reports to him all the frames with the keys that are contained in a specied
In practical applications, due to imperfect synchronization between the broadcaster and the receiver, the header should also contain either the time-slot number or its bit reversal -- the index of the frame. To enable changing the contents and the length of the sequence of the transmitted keys by the broadcaster, the header may also include the parameter @math , such that @math is the length of the broadcast cycle, and some bits used to notify the receiver that the that the sequence of keys has been changed. For RBO, these issues have been discussed in @cite_7 .
@cite_7
1802425574 2143229717 2130507035 2142458954
We propose a protocol (called RBO) for broadcasting long streams of single-packet messages over radio channel for tiny, battery powered, receivers. The messages are labeled by the keys from some linearly ordered set. The sender repeatedly broadcasts a sequence of many (possibly millions) of messages, while each receiver is interested in reception of a message with a specified key within this sequence. The transmission is arranged so that the receiver can wake up in arbitrary moment and find the nearest transmission of its searched message. Even if it does not know the position of the message in the sequence, it needs only to receive a small number of (the headers of) other messages to locate it properly. Thus it can save energy by keeping the radio switched off most of the time. We show that bit-reversal permutation has "recursive bisection properties" and, as a consequence, RBO can be implemented very efficiently with only constant number of @math -bit variables, where @math is the total number of messages in the sequence. The total number of the required receptions is at most @math in the model with perfect synchronization. The basic procedure of RBO (computation of the time slot for the next required reception) requires only @math bit-wise operations. We propose implementation mechanisms for realistic model (with imperfect synchronization), for operating systems (such as e.g. TinyOS). Recent advances in miniaturization and low-cost, low-power design have led to active research in large-scale networks of small, wireless, low-power sensors and actuators. Time synchronization is critical in sensor networks for diverse purposes including sensor data fusion, coordinated actuation, and power-efficient duty cycling. Though the clock accuracy and precision requirements are often stricter than in traditional distributed systems, strict energy constraints limit the resources available to meet these goals.We present Reference-Broadcast Synchronization, a scheme in which nodes send reference beacons to their neighbors using physical-layer broadcasts. A reference broadcast does not contain an explicit timestamp; instead, receivers use its arrival time as a point of reference for comparing their clocks. In this paper, we use measurements from two wireless implementations to show that removing the sender's nondeterminism from the critical path in this way produces high-precision clock agreement (1.85 ± 1.28μsec, using off-the-shelf 802.11 wireless Ethernet), while using minimal energy. We also describe a novel algorithm that uses this same broadcast property to federate clocks across broadcast domains with a slow decay in precision (3.68 ± 2.57μsec after 4 hops). RBS can be used without external references, forming a precise relative timescale, or can maintain microsecond-level synchronization to an external timescale such as UTC. We show a significant improvement over the Network Time Protocol (NTP) under similar conditions. Motivated by a problem of transmitting supplemental data over broadcast channels (Birk and Kol, INFOCOM 1998), we study the following coding problem: a sender communicates with n receivers R1,..., Rn. He holds an input x ∈ 0,01l n and wishes to broadcast a single message so that each receiver Ri can recover the bit xi. Each Ri has prior side information about x, induced by a directed graph Grain nodes; Ri knows the bits of a; in the positions j | (i,j) is an edge of G .G is known to the sender and to the receivers. We call encoding schemes that achieve this goal INDEXcodes for 0,1 n with side information graph G. In this paper we identify a measure on graphs, the minrank, which exactly characterizes the minimum length of linear and certain types of nonlinear INDEX codes. We show that for natural classes of side information graphs, including directed acyclic graphs, perfect graphs, odd holes, and odd anti-holes, minrank is the optimal length of arbitrary INDEX codes. For arbitrary INDEX codes and arbitrary graphs, we obtain a lower bound in terms of the size of the maximum acyclic induced subgraph. This bound holds even for randomized codes, but has been shown not to be tight. The time-complexity of deterministic and randomized protocols for achieving broadcast (distributing a message from a source to all other nodes) in arbitrary multi-hop radio networks is investigated. In many such networks, communication takes place in synchronous time-slots. A processor receives a message at a certain time-slot if exactly one of its neighbors transmits at that time-slot. We assume no collision-detection mechanism; i.e., it is not always possible to distinguish the case where no neighbor transmits from the case where several neighbors transmit simultaneously. We present a randomized protocol that achieves broadcast in time which is optimal up to a logarithmic factor. In particular, with probability 1 --E, the protocol achieves broadcast within O((D + log n s) ‘log n) time-slots, where n is the number of processors in the network and D its diameter. On the other hand, we prove a linear lower bound on the deterministic time-complexity of broadcast in this model. Namely, we show that any deterministic broadcast protocol requires 8(n) time-slots, even if the network has diameter 3, and n is known to all processors. These two results demonstrate an exponential gap in complexity between randomization and determinism.