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IEICE Transactions on Communications

LDPC Codes for Communication Systems: Coding Theoretic Perspective

T. Nozaki, Motohiko Isaka

Published Feb 9, 2022• 7 citations
Publisher

Abstract

Low-density parity-check (LDPC) codes are widely used in communication systems for their high error-correcting performance. This survey introduces the elements of LDPC codes: decoding algorithms, code construction, encoding algorithms, and several classes of LDPC codes.
DOI
10.1587/transcom.2021ebi0001

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Introduction In this chapter we introduce low-density parity-check (LDPC) codes, a class of error correction codes proposed by Gallager in his 1962 PhD thesis 12 years after error correction codes were first introduced by Hamming (published in 1950). Both Hamming codes and LDPC codes are block codes: the messages are broken up into blocks to be encoded at the transmitter and similarly decoded as separate blocks at the receiver. While Hamming codes are short and very structured with a known, fixed, error correction ability, LDPC codes are the opposite, usually long and often constructed pseudo-randomly with only a probabilistic notion of their expected error correction performance. The chapter begins by presenting parity bits as a means to detect and, when more than one is employed, to correct errors in digital data. Block error correction codes are described as a linear combination of parity-check equations and thus defined by their parity-check matrix representation. The graphical representation of codes by Tanner graphs is presented and the necessary graph theoretic concepts introduced. In Section 2.4 iterative decoding algorithms are introduced using a hard decision algorithm (bit flipping), so that the topic is developed first without reference to probability theory. Subsequently the sum–product decoding algorithm is presented. This chapter serves as a self-contained introduction to LDPC codes and their decoding. It is intended that the material presented here will enable the reader to implement LDPC encoders and iterative decoders.
Low-Density Parity-Check (LDPC) codes form an important class of error correcting codes for today's communication systems.These codes allow for a highly efficient decoding scheme that is known as message passing decoding.Although so-called random LDPC codes perform close to a theoretical limit derived in coding theory, there is a demand for systematic code design in order to keep the encoding process efficient.This article revisits a collection of geometric constructions with an emphasis on those which are based on triangle free geometries.
Low density parity checking codes (LDPC) are one of the most important issues in coding theory at present. LDPC-code are a type of linear-block LDPC-codes. Channel coding might be considered as the finest conversant and most potent components of cellular communications systems, that was employed for transmitting errors corrections imposed by noise, fading and interfering. LDPC-codes are advanced coding gain, i.e., new area in coding. the performances of LDPC-code are similar to the Shannon-limiting, this led to the usage of decoding in several applications in digital communications systems, like DVB-S2 and WLAN802.1..This paper aims to know what is LDPC,what its application and introduce encoding algorithms that gives rise to a linear encoding time and also show that the regular and irregular LDPC performance and also introduce different methods for decoding LDPC. I discuss in detail LDPC decoding algorithm: bit flipping algorithm, as a type from hard decision .belief propagation algorithm, sum product algorithm and minimum sum algorithm as examples from soft decision .I expect that at least some students or researchers involved in researching LDPC codes would find this paper helpful.
Low-density parity-check (LDPC) codes are linear block codes. It is called low density parity check code because their parity-check matrix contains only a few 1’s in comparison to the amount of 0’s. These codes were first introduced by Gallager. It is a very powerful code for forward error correction system. The presently used LDPC code in optical fibre communication systems is not meeting the requirements of the high speed fibre optics communication systems. So the LDPC code can be modified and with which the quality factor can be improved. This modification is beneficial for the high speed fibre optic communication systems. We present here a comprehensive review of decoding algorithm of modified Low density parity check code useful in Optical fibre communication. BP and the MS decoding algorithms which are modified decoding algorithm are use for a better performance in high speed fibre optic communication.
Recently, low-density parity-check (LDPC) codes have attracted much attention because of their excellent error correcting performance and highly parallelizable decoding scheme. However, the effective VLSI implementation of and LDPC decoder remains a big challenge and is a crucial issue in determining how well we can exploit the benefits of the LDPC codes in the real applications. In this master thesis report, following a error coding background, we describe Low-Density Parity-Check codes and their decoding algorithm, and also requirements and architectures of LPDC decoder implementations.