Related papers: Multiplicatively Repeated Non-Binary LDPC Codes

Low-Density Parity-Check (LDPC) codes received much attention recently due to their capacity-approaching performance. The iterative message-passing algorithm is a widely adopted decoding algorithm for LDPC codes \cite{Kschischang01}. An…

We consider recursive decoding for Reed-Muller (RM) codes and their subcodes. Two new recursive techniques are described. We analyze asymptotic properties of these algorithms and show that they substantially outperform other decoding…

LDPC (Low Density Parity Check) codes are among the most powerful and widely adopted modern error correcting codes. The iterative decoding algorithms required for these codes involve high computational complexity and high processing…

We propose a new low-density parity-check code construction scheme based on 2-lifts. The proposed codes have an advantage of admitting efficient hardware implementations. With the motivation of designing codes with low error floors, we…

In this paper, we propose a non-uniform windowed decoder for multi-dimensional spatially-coupled LDPC (MD-SC-LDPC) codes over the binary erasure channel. An MD-SC-LDPC code is constructed by connecting together several SC-LDPC codes into…

Recursive decoding techniques are considered for Reed-Muller (RM) codes of growing length $n$ and fixed order $r.$ An algorithm is designed that has complexity of order $n\log n$ and corrects most error patterns of weight up to…

Two methods for constructing quantum LDPC codes are presented. We explain how to overcome the difficulty of finding a set of low weight generators for the stabilizer group of the code. Both approaches are based on some graph representation…

We describe a new parameterized family of symmetric error-correcting codes with low-density parity-check matrices (LDPC). Our codes can be described in two seemingly different ways. First, in relation to Reed-Muller codes: our codes are…

Generalized low-density parity-check (GLDPC) codes, where single parity-check constraints on the code bits are replaced with generalized constraints (an arbitrary linear code), are a promising class of codes for low-latency communication.…

In this paper, we introduce an efficient iterative solver for the joint linear-programming (LP) decoding of low-density parity-check (LDPC) codes and finite-state channels (FSCs). In particular, we extend the approach of iterative…

In this paper, a new method for decoding Low Density Parity Check (LDPC) codes, based on Multi-Layer Perceptron (MLP) neural networks is proposed. Due to the fact that in neural networks all procedures are processed in parallel, this method…

Linear nested codes, where two or more sub-codes are nested in a global code, have been proposed as candidates for reliable multi-terminal communication. In this paper, we consider nested array-based spatially coupled low-density…

In this paper, we propose a new coded computing technique called "substitute decoding" for general iterative distributed computation tasks. In the first part of the paper, we use PageRank as a simple example to show that substitute decoding…

A Bounded-Degree Low-Rank Parity-Check (BD-LRPC) code is a rank-metric code that admits a parity-check matrix whose support is generated by a set of powers of an element. This specific structure of the parity-check matrix was employed to…

We introduce a new family of rank metric codes: Low Rank Parity Check codes (LRPC), for which we propose an efficient probabilistic decoding algorithm. This family of codes can be seen as the equivalent of classical LDPC codes for the rank…

A non-binary (2,v)-regular LDPC code is defined by a parity-check matrix with column weight 2 and row weight v. In this report, we give an ontology-based approach to the optimization for this class of codes. All possible inter-connected…

Low density parity check (LDPC) lattices are obtained from Construction D' and a family of nested binary LDPC codes. We consider an special case of these lattices with one binary LDPC code as underlying code. This special case of LDPC…

In this paper, we discuss a construction of CSS codes derived from pairs of practical irregular LDPC codes. Our design of irregular LDPC codes is based the design written in the standardization of IEEE802.16e. Our research has tried to make…

In this work, we propose the integration of GLDPC codes with short polar-like component codes, termed GLDPC codes with polar component codes (GLDPC-PC). This approach leverages the good distance properties of polar-like codes and mitigates…

Spatially coupled low-density parity-check (SC-LDPC) codes are sparse graph codes that have recently become of interest due to their capacity-approaching performance on memoryless binary input channels. In this paper, we unify all existing…