Related papers: Sharp Bounds for Optimal Decoding of Low Density P…
It is known that windowed decoding (WD) can effectively balance the performance and complexity of spatially coupled low-density parity-check (LDPC) codes. In this study, we show that information can propagate in a wave-like manner at a…
An algorithm is proposed to encode low-density parity-check (LDPC) codes into codewords with a non-uniform distribution. This enables power-efficient signalling for asymmetric channels. We show gains of 0.9 dB for additive white Gaussian…
Binary message-passing decoders for low-density parity-check (LDPC) codes are studied by using extrinsic information transfer (EXIT) charts. The channel delivers hard or soft decisions and the variable node decoder performs all computations…
Consider communication over the binary erasure channel BEC using random low-density parity-check codes with finite-blocklength n from `standard' ensembles. We show that large error events is conveniently described within a scaling theory,…
In modern data storage systems, non-binary LDPC codes for recovering from disk failures are increasingly considered strong competitors to MDS codes such as Reed-Solomon codes. Since disk failures can be modeled as erasures, we analyze…
We discuss error floor asympotics and present a method for improving the performance of low-density parity check (LDPC) codes in the high SNR (error floor) region. The method is based on Tanner graph covers that do not have trapping sets…
The connections between variable nodes and check nodes have a great influence on the performance of low-density parity-check (LDPC) codes. Inspired by the unique structure of polar code's generator matrix, we proposed a new method of…
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…
Based on the extended binary image of non-binary LDPC codes, we propose a method for generating extra redundant bits, such as to decreases the coding rate of a mother code. The proposed method allows for using the same decoder, regardless…
In this paper, we focus on the two-user Gaussian interference channel (GIC), and study the Han-Kobayashi (HK) coding/decoding strategy with the objective of designing low-density parity-check (LDPC) codes. A code optimization algorithm is…
The non-binary low-density parity-check (NB-LDPC) codes can offer promising performance advantages but suffer from high decoding complexity. To tackle this challenge, in this paper, we consider NB-LDPC codes over finite fields as codes over…
This article introduces a novel concatenated coding scheme called sparse regression LDPC (SR-LDPC) codes. An SR-LDPC code consists of an outer non-binary LDPC code and an inner sparse regression code (SPARC) whose respective field size and…
A concatenated coding scheme over binary memoryless symmetric (BMS) channels using a polarization transformation followed by outer sub-codes is analyzed. Achievable error exponents and upper bounds on the error rate are derived. The first…
In this paper, the stability condition for low-density parity-check (LDPC) codes on the binary erasure channel (BEC) is extended to generalized LDPC (GLDPC) codes and doublygeneralized LDPC (D-GLDPC) codes. It is proved that, in both cases,…
We present a new class of irregular low-density parity-check (LDPC) codes for moderate block lengths (up to a few thousand bits) that are well-suited for rate-compatible puncturing. The proposed codes show good performance under puncturing…
We define and investigate a notion of entropy for quantum error correcting codes. The entropy of a code for a given quantum channel has a number of equivalent realisations, such as through the coefficients associated with the Knill-Laflamme…
We study LDPC codes for the channel with $2^m$-ary input $\underline{x}\in \mathbb{F}_2^m$ and output $\underline{y}=\underline{x}+\underline{z}\in \mathbb{F}_2^m$. The receiver knows a subspace $V\subset \mathbb{F}_2^m$ from which…
In this paper, we propose a new method to design low-density parity-check Hadamard (LDPC-Hadamard) codes, a type of ultimate-Shannon-limit approaching channel codes. The technique is based on applying Hadamard constraints to the check nodes…
We introduce a thermodynamic (large deviation) formalism for computing error exponents in error-correcting codes. Within this framework, we apply the heuristic cavity method from statistical mechanics to derive the average and typical error…
This thesis includes analysis of disordered spin ensembles corresponding to Exact Cover, a multi-access channel problem, and composite models combining sparse and dense interactions. The satisfiability problem in Exact Cover is addressed…