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Linear Programming (LP) decoding of Low-Density Parity-Check (LDPC) codes has attracted much attention in the research community in the past few years. LP decoding has been derived for binary and nonbinary linear codes. However, the most…
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…
It was recently shown that spatial coupling of individual low-density parity-check codes improves the belief-propagation threshold of the coupled ensemble essentially to the maximum a posteriori threshold of the underlying ensemble. We…
This paper considers density evolution for lowdensity parity-check (LDPC) and multi-edge type low-density parity-check (MET-LDPC) codes over the binary input additive white Gaussian noise channel. We first analyze three singleparameter…
The asymptotic iterative decoding performances of low-density parity-check (LDPC) codes using min-sum (MS) and sum-product (SP) decoding algorithms on memoryless binary-input output-symmetric (MBIOS) channels are analyzed in this paper. For…
For any given short code (referred to as the basic code), block Markov superposition transmission (BMST) provides a simple way to obtain predictable extra coding gain by spatial coupling the generator matrix of the basic code. This paper…
In this work, we propose a fully differentiable iterative decoder for quantum low-density parity-check (LDPC) codes. The proposed algorithm is composed of classical belief propagation (BP) decoding stages and intermediate graph neural…
In this paper we consider the generalization of binary spatially coupled low-density parity-check (SC-LDPC) codes to finite fields GF$(q)$, $q\geq 2$, and develop design rules for $q$-ary SC-LDPC code ensembles based on their iterative…
We study a new encoding scheme for lossy source compression based on spatially coupled low-density generator-matrix codes. We develop a belief-propagation guided-decimation algorithm, and show that this algorithm allows to approach the…
A method for estimating the performance of low-density parity-check (LDPC) codes decoded by hard-decision iterative decoding algorithms on binary symmetric channels (BSC) is proposed. Based on the enumeration of the smallest weight error…
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…
Fair-density parity-check (FDPC) codes have been recently introduced demonstrating improved performance compared to low-density parity-check (LDPC) codes standardized in 5G systems particularly in high-rate regimes. In this paper, we…
We consider a distributed learning problem in which the computation is carried out on a system consisting of a master node and multiple worker nodes. In such systems, the existence of slow-running machines called stragglers will cause a…
In this paper we study codes with sparse generator matrices. More specifically, codes with a certain constraint on the weight of all the columns in the generator matrix are considered. The end result is the following. For any binary-input…
For LDPC codes operating over additive white Gaussian noise channels and decoded using message-passing decoders with limited precision, absorbing sets have been shown to be a key factor in error floor behavior. Focusing on this scenario,…
We propose the use of certain low-density generator-matrix (LDGM) codes as syndrome measurement (SM) codes for quantum low-density parity check (QLDPC) codes. We use an efficient progressive-edge-growth-like algorithm to create LDGM SM…
In this paper we study the iterative decoding threshold performance of non-binary spatially-coupled low-density parity-check (NB-SC-LDPC) code ensembles for both the binary erasure channel (BEC) and the binary-input additive white Gaussian…
Forward error correcting (FEC) codes are used in many communication standards with a wide range of re quirements. FEC codes should work close to capacity, achieve low error floors, and have low decoding complexity. In this paper, we propose…
We investigate the use of Gallager's low-density parity-check (LDPC) codes in a broadcast channel, one of the fundamental models in network information theory. Combining linear codes is a standard technique in practical network…
Braided convolutional codes (BCCs) are a class of spatially coupled turbo-like codes that can be described by a $(2,3)$-regular compact graph. In this paper, we introduce a family of $(d_v,d_c)$-regular GLDPC codes with convolutional code…