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Review on Decoding Algorithms Useful in Modified Low Density Parity Check Code for Optical Fibre Communication

Bhavinee U. Parihar, Y. A. Nafde

Published Dec 26, 2013• 0 citations
OpenAlex

Abstract

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.

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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.
Although low-density parity-check (LDPC) code has been proved as a powerful forward error correction code for fibre optic communication, its soft-decoding requires high quantisation resolution which is difficult to achieve for high-speed fibre-optic communication systems. A modification to LDPC decoding algorithms is proposed to effectively improve the performance at quantisation resolution as low as two-bit or one-bit. The good decoding performance of LDPC code for error correction is confirmed by experiment. Compared with the RS(255, 239) code commonly used in optical fibre communication, a Q-factor improvement of 2-dB is obtained in the experiment for an LDPC code with quasi-cyclic structure at the same redundancy as the RS code. Furthermore, the impacts of sampling phase and channel estimation using real data over the decoding performance are analysed.
The increasing popularity of optical communication systems emphasizes the need for effective errorcorrection solutions, including high-efficiency hardware decoder designs and codes with strong performance. Within optical communication networks, Low-Density Parity-Check (LDPC) codes utilizing sparse matrices and decoded through the Bit-Flipping (BF) algorithm, known for its hard iterative decoding approach are extensively utilized. These codes effectively balance decoding complexity with error-correction performance.This paper focuses on comparing the optical performance of LDPC codes with and without the BF decoding algorithm using two simulation software packages: MATLAB and OptiSystem 7.0. The comparison is conducted across different wavelengths and quality factors. Through this study, we evaluate the advantages of LDPC codes in terms of error-rate reduction and enhancing the reliability of optical transmission.
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 are a class of linear block codes with implementable decoders, which provide near-capacity performance on a large set of data-transmission and data-storage channels. LDPC codes were invented by Gallager in his 1960 doctoral dissertation and were mostly ignored during the 35 years that followed. One notable exception is the important work of Tanner in 1981, in which Tanner generalized LDPC codes and introduced a graphical representation of LDPC codes, now called a Tanner graph. The study of LDPC codes was resurrected in the mid 1990s with the work of MacKay, Luby, and others [3–6], who noticed, apparently independently of Gallager's work, the advantages of linear block codes with sparse (low-density) parity-check matrices. This chapter introduces LDPC codes and creates a foundation for further study of LDPC codes in later chapters. We start with the fundamental representations of LDPC codes via parity-check matrices and Tanner graphs. We then learn about the decoding advantages of linear codes that possess sparse parity-check matrices. We will see that this sparseness characteristic makes the code amenable to various iterative decoding algorithms, which in many instances provide near optimal performance. Gallager of course recognized the decoding advantages of such low-density parity-check codes and he proposed a decoding algorithm for the BI-AWGNC and a few others for the BSC. These algorithms have received much scrutiny in the past decade, and are still being studied.
Low Density Parity Check Codes (LDPC) is a class of linear block codes best suited for forward error control in communication systems. When compared with other codes, LDPC codes have significant performance gain, which can be turned to an increase of the coverage range or a reduction of transmission power. Hence a convenient and practical receiver is obtained. The analysis done in this paper is based on the Bit Error Rate of the decoded output. The factors considered for the analysis are multiple code rate, different number of iterations and various decoding schemes. For lower code rate, soft decision decoding and increased number of iterations LDPC codes yields a better performance.
Low Density Parity Check (LDPC) codes are one of the block coding techniques that can approach the Shannon’s limit within a fraction of a decibel for high block lengths. In many digital communication systems, these codes have strong competitors of turbo codes for error control. LDPC codes performance depends on the excellent design of parity check matrix and many diverse research methods have been used by different study groups to evaluate the performance. Unlike many other classes of codes, LDPC codes are already equipped with a fast, probabilistic decoding algorithm. This makes LDPC codes not only attractive from a theoretical point of view, but also very suitable for practical applications. This paper throws hard decision and soft decision algorithm of LDPC. The hard decision algorithm contains Bit flipping algorithm and Soft decoding algorithm contains Sum product algorithm which is used to correct burst error. Sum Product algorithm is also called as belief propagation. Bit flipping and Sum Product algorithms are explained and can be implemented for the generated parity check matrix of (1016x508) for LDPC code with code rate 1/2.