A simple trellis based algorithm to compute the equivocation of a transmitted codeword, conditioned on the channel output, is presented.

A systematic convolutional encoder of rate (n-1)/n and maximum memory D generates a code of free distance at most V = D + 2 and, at best, a column distance profile (CDP) of [2,3, .. . , D]. A code is memory maximum distance separable if it possesses this CDP. Applied on a communication channel over which packets are transmitted sequentially and which loses (erases) packets randomly, such a code allows the recovery from any pattern of j erasures in the first j n-packet blocks for jm- 1)/pmand V equal to 3 over GF(pm) and rate (2m-1-1)/2m-1and V equal to 4 over GF(2m) are presented, which provide optimum values of V in their respective cases. A search algorithm is also developed, which produces new codes for V for field sizes 2m≤ 214. Using a complete search version of the algorithm, the maximum value of V, and codes that achieve it, are determined for all code rates ≥ 1/2 and every field size GF(2m) for m ≤ 5 (and for some rates for m = 6).

This paper discusses a new channel model and code design for the reader-to-tag channel in near-field passive radio frequency identification (RFID) systems using inductive coupling as a power transfer mechanism. If the receiver resynchronizes its internal clock each time a bit is detected, the bit-shift channel used previously in the literature to model the reader-to-tag channel needs to be modified. In particular, we propose a discretized Gaussian shift channel as a new channel model in this scenario. We introduce the concept of quantifiable error avoidance, which is much simpler than error correction. The capacity is computed numerically, and we also design some new simple codes for error avoidance on this channel model based on insights gained from the capacity calculations. Finally, some simulation results are presented to compare the proposed codes to the Manchester code and two previously proposed codes for the bit-shift channel model.

In this work, we consider the power spectrum of error-control codes designed for the reader-to-tag channel in near-field passive radio frequency identification (RFID) systems using inductive coupling as a power transfer mechanism. In contrast to previous works, binary phase-shift keying is considered, and the power spectral density is computed for two of the codes (and one runlength constraint) considered in a recent paper by Barbero et al. (Inf. Theory Appl., San Diego, CA, 2011), and for two new codes introduced in this paper. Furthermore, we compute the total power transferred to the tag as a function of the inter-coil separation for different codes (and one runlength constraint).

Inductive coupling is a technique wherein one device (the reader) induces an electrical current in another device (the tag), thereby providing not only power for the tag, but also a communication channel. In this paper, we focus exclusively on the reader-to-tag channel. The first part of this paper presents modulation codes that possess a high minimum and a high average power. This is important, since the tag gets its entire power from the received signal, and the information should be modulated in a way that maximizes the power transferred to the tag. The presented modulation codes compare favorably to codes used in radio frequency identification applications today. The second part of the paper describes modulation codes with some error-correcting capabilities. In fact, most errors in the reader-to-tag channel are due to incorrect timing. Here, we propose to model the timing errors in the reader-to-tag communication channel by a simple bit-shift channel, and we will present optimal (in the sense of maximizing the code rate for a given block length) single bit-shift error-correcting codes for this simple bit-shift channel that also have large average power.

In this work, we will consider coding for a bit-shift channel with applications to inductively coupled channels. Inductive coupling is a technique wherein one device (the reader) induces an electrical current in another device (the tag), thereby providing not only power for the tag, but also a communications channel. Most errors in the reader-to-tag channel are due to incorrect timing. In this work, we propose to model the timing errors in the reader-to-tag communications channel by a simple bit-shift channel. We will present optimal single bit-shift error-correcting codes for this simple bit-shift channel that also have large average power. This is important, since the tag gets its entire power from the received signal, and the information should be modulated in a way that maximizes the power transferred to the tag.

Consider a lossy communication channel for unicast with zero-delay feedback. For this communication scenario, a simple retransmission scheme is optimum with respect to delay. An alternative approach is to use random linear coding in automatic repeat-request (ARQ) mode. We extend the work of Shrader and Ephremides in [1], by deriving an expression for the delay of random linear coding over a field of infinite size. Simulation results for various field sizes are also provided.

The linear information flow (LIF) algorithm and its relatives are the most efficient centralized algorithms known for finding network encoding equations for multicast communication. This paper examines the performance of the LIFE (linear information flow on edges) algorithm on a "real" network, through the use of a simulation model. We present results on the algorithm's ability to encode in a finite field of given cardinality, and on the efficiency of the randomized version of the algorithm.

The aim of this paper is to extend some basic concepts related to the Maximum Likelihood decoding of codes on the Z-channel, which is a particular, but very important, example of an asymmetric channel. We study distance properties of linear codes over the Z-channel, in order to define a suitable metric for the implementation of a Maximum Likelihood decoder on the channel. A combinatorial expression for an approximation on the probability of incorrect Maximum Likelihood decoding is also provided, and comparisons are given to evaluate the tightness of the estimation, when a Hamming code, a Turbo code and an LDPC code are used for communicating over the Z-channel.

This correspondence addresses the problem of finding the network encoding equations for error-free networks with multiple sources and sinks. Previous algorithms could not cope with cyclic networks. Networks that are cyclic in three different senses are considered in this correspondence, and two extensions of the polynomial time Linear Information Flow (LIF) algorithm are presented. The first algorithm will produce the network encoding equations for a network which can be cyclic, unless the actual flow paths form cycles. The second algorithm will work also when the flow paths form simple cycles. Finally an example of a third kind of cyclic network, where the previous algorithms will fail, is given. However, a binary encoding is provided also in this case.

We compute the complete weight hierarchies of all Hermitian codes. The tools used are the arithmetic of Hermitian curves and the order bound on the generalized Hamming weights.

Formulas to compute the first members of the weight hierarchy of a product code are given and proved. Basic patterns for the supports of subcodes in which the minimum cardinalities can be found are presented. Hence, formulas for every term of the hierarchy can be given, and the proof for each case will be a generalization of the proofs shown here.>