Related papers: Why We Can Not Surpass Capacity: The Matching Cond…
We consider communication over binary-input memoryless output-symmetric channels using low-density parity-check codes and message-passing decoding. The asymptotic (in the length) performance of such a combination for a fixed number of…
This paper provides simple lower bounds on the number of iterations which is required for successful message-passing decoding of some important families of graph-based code ensembles (including low-density parity-check codes and variations…
In this paper, we prove the existence of capacity achieving linear codes with random binary sparse generating matrices. The results on the existence of capacity achieving linear codes in the literature are limited to the random binary codes…
Recently, a new class of codes, called sparse superposition or sparse regression codes, has been proposed for communication over the AWGN channel. It has been proven that they achieve capacity using power allocation and various forms of…
Low-density parity-check (LDPC) convolutional codes (or spatially-coupled codes) have been shown to approach capacity on the binary erasure channel (BEC) and binary-input memoryless symmetric channels. The mechanism behind this spectacular…
Evaluating the channel capacity is one of many key problems in information theory. In this work we derive rather-mild sufficient conditions under which the capacity is finite and achievable. These conditions are derived for generic,…
We introduce a new approach to proving that a sequence of deterministic linear codes achieves capacity on an erasure channel under maximum a posteriori decoding. Rather than relying on the precise structure of the codes our method exploits…
Low-capacity scenarios have become increasingly important in the technology of the Internet of Things (IoT) and the next generation of wireless networks. Such scenarios require efficient and reliable transmission over channels with an…
Given two independent point processes and a certain rule for matching points between them, what is the fraction of matched points over infinitely long streams? In many application contexts, e.g., secure networking, a meaningful matching…
Recently it was proved that if a linear code is invariant under the action of a doubly transitive permutation group, it achieves the capacity of erasure channel. Therefore, it is of sufficient interest to classify all codes, invariant under…
We consider spatially coupled code ensembles. A particular instance are convolutional LDPC ensembles. It was recently shown that, for transmission over the memoryless binary erasure channel, this coupling increases the belief propagation…
We recently showed in [1] the superiority of certain structured coding matrices ensembles (such as partial row-orthogonal) for sparse superposition codes when compared with purely random matrices with i.i.d. entries, both…
This paper introduces a new approach to proving that a sequence of deterministic linear codes achieves capacity on an erasure channel under maximum a posteriori decoding. Rather than relying on the precise structure of the codes, this…
We present two sequences of ensembles of non-systematic irregular repeat-accumulate codes which asymptotically (as their block length tends to infinity) achieve capacity on the binary erasure channel (BEC) with bounded complexity per…
The problem of mismatched decoding for discrete memoryless channels is addressed. A mismatched cognitive multiple-access channel is introduced, and an inner bound on its capacity region is derived using two alternative encoding methods:…
We consider an ensemble of constant composition codes that are subsets of linear codes: while the encoder uses only the constant-composition subcode, the decoder operates as if the full linear code was used, with the motivation of…
Convolutional low-density parity-check (LDPC) codes (or spatially-coupled codes) have now been shown to achieve capacity on binary-input memoryless symmetric channels. The principle behind this surprising result is the threshold-saturation…
This paper is concerned with a class of low density generator matrix codes (LDGM), called repetition and superposition (RaS) codes, which have been proved to be capacity-achieving over binary-input output-symmetric (BIOS) channels in terms…
This paper concerns non-overlapping codes, block codes motivated by synchronisation and DNA-based storage applications. Most existing constructions of these codes do not account for the restrictions posed by the physical properties of…
We recently proved threshold saturation for spatially coupled sparse superposition codes on the additive white Gaussian noise channel. Here we generalize our analysis to a much broader setting. We show for any memoryless channel that…