Related papers: A Simple Proof of Threshold Saturation for Coupled…
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…
This paper is concerned with the design of capacity approaching ensembles of Low-Densiy Parity-Check (LDPC) codes for correlated sources. We consider correlated binary sources where the data is encoded independently at each source through a…
In this paper we consider regular low-density parity-check codes over a binary-symmetric channel in the decoding regime. We prove that up to a certain noise threshold the bit-error probability of the bit-sampling decoder converges in mean…
We present the tree-structure expectation propagation (Tree-EP) algorithm to decode low-density parity-check (LDPC) codes over discrete memoryless channels (DMCs). EP generalizes belief propagation (BP) in two ways. First, it can be used…
The recent success in constructing asymptotically good quantum low-density parity-check (QLDPC) codes makes this family of codes a promising candidate for error-correcting schemes in quantum computing. However, conventional belief…
We consider spatially coupled low-density parity-check codes with finite smoothing parameters. A finite smoothing parameter is important for designing practical codes that are decoded using low-complexity windowed decoders. By optimizing…
We present a mathematical connection between channel coding and compressed sensing. In particular, we link, on the one hand, \emph{channel coding linear programming decoding (CC-LPD)}, which is a well-known relaxation o maximum-likelihood…
Low-density parity-check (LDPC) codes have been used for communication over a two-user Gaussian broadcast channel. It has been shown in the literature that the optimal decoding of such system requires joint decoding of both user messages at…
In this paper, we consider a few iterative decoding schemes for the joint source-channel coding of correlated sources. Specifically, we consider the joint source-channel coding of two erasure correlated sources with transmission over…
Whereas many results are known about thresholds for ensembles of low-density parity-check codes under message-passing iterative decoding, this is not the case for linear programming decoding. Towards closing this knowledge gap, this paper…
Accurate modeling of the correlation between the sources plays a crucial role in the efficiency of distributed source coding (DSC) systems. This correlation is commonly modeled in the binary domain by using a single binary symmetric channel…
Raptor codes are rateless codes that achieve the capacity on the binary erasure channels. However the maximum degree of optimal output degree distribution is unbounded. This leads to a computational complexity problem both at encoders and…
A three terminal relay system with binary erasure channel (BEC) was considered, in which a source forwarded information to a destination with a relay's "assistance". The nested LDGM (Low-density generator-matrix) -LDPC (low-density…
We consider communication over the binary erasure channel (BEC) using low-density parity-check (LDPC) codes and belief propagation (BP) decoding. For fixed numbers of BP iterations, the bit error probability approaches a limit as…
The question whether RM codes are capacity-achieving is a long-standing open problem in coding theory that was recently answered in the affirmative for transmission over erasure channels [1], [2]. Remarkably, the proof does not rely on…
We present a new family of low-density parity-check (LDPC) convolutional codes that can be designed using ordered sets of progressive differences. We study their properties and define a subset of codes in this class that have some desirable…
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…
Identifying the best families of quantum error correction (QEC) codes for near-term experiments is key to enabling fault-tolerant quantum computing. Ideally, such codes should have low overhead in qubit number, high physical error…
We consider spatially-coupled protograph-based LDPC codes for the three terminal erasure relay channel. It is observed that BP threshold value, the maximal erasure probability of the channel for which decoding error probability converges to…
In this paper, we formulate a new problem to cope with the transmission of extra bits over an existing coded transmission link (referred to as coded payload link) without any cost of extra transmission energy or extra bandwidth. This is…