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Journal of Emerging Technologies and Innovative Research

Performance Evaluation of LDPC decoding Algorithm for GF (2)

D Patel Jigisha, Patel Ruchita Kumari

Published Nov 1, 2014• 0 citations
OpenAlex

Abstract

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.

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Many classes of high-performance Low-density parity check codes are based on parity check matrices composed of permutation sub matrices. The emulation-simulation framework further allows the algorithm and implementation to be iteratively redefined to improve the error floor performance of message passing decoder. Log-Like hood-Ratio (LLR) based Belief-Propagation (BP) algorithm is presented for Low Density Parity Check codes. Numerically accurate representation of check node update computation used in LLR-BP decoding is described. The implementation of Sum-Product algorithm (SPA) within Low Density Parity Check Code (LDPC) decoder is described in this paper and the correction term is used to improve the decoding performance of min-sum algorithm (MSA). Quantization and log-tanh function approximation in sum-product decoder strongly affect which absorbing set dominates in error floor region. For LDPC decoder, bit error rate (BER) decreases with increase in the signal to noise ratio.

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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.
Low Density Parity Check (LDPC) codes have excellent error correcting performance. LDPC codes are one of the block coding techniques and it performs near Shannon limit and recommended for many practical applications. Non-binary LDPC codes extension of binary LDPC in error correcting property especially for short and moderate block length. In many digital communication systems these codes have strong competitors of turbo codes for error control. Low Density Parity Check as it name is suggests that in a parity check matrix (H) consists of very small number of non-zero elements comparing with zero elements. The strength of the LDPC code defines Parity Check Matrix (PCM). LDPC code contains two types of decoding algorithms hard and soft decision algorithm. By comparing with other traditional decoding algorithm FFT based sum product algorithm reduced computation complexity with better decoding performance. In this paper, LDPC codes for FFT based sum product decoding algorithm performances are analysed for various order of Galois Field GF(q) using AWGN channel. Decoding performance measured in terms of symbol error rate which improve with increasing order of Galois field.
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.
Forward error correction code with Low Density Parity Check (LDPC) gives substantial results very close to Shannon limit. This can be achieved when complexity and delay time is unlimited. Thus, it is significant to recognize the limitation of those parameters in the decoding of LDPC. In this research, a study of LDPC performance with three decoding algorithms namely; bit-flipping, log domain, and prob domain are presented. The first one is related to hard decision family while the last two types are the soft decision that follows the sum-product algorithm. A simulation model of a wireless communication system included LDPC are evaluated with the motioned three types of decoding using Matlab Package, version 2018a. The results show that the log domain and prob domain are outperforming the bit-flipping algorithm by a significant amount of Signal to Noise Ratio (SNR). Finally, optimum values of LDPC parameters are chosen according to the achieved results that will give better results are presented.
The Low Density Parity Check (LDPC) are direct codes, which are true block and Shannon Limit codes.These codes are attained least error floors of data bits for data transfer applications used in communication systems.However, the proposed LDPC codes are more beneficial than Turbo codes because of reduction in the decoding complexity and detection of the errors in less cycle time.This results the reduction of decoding time, low decoding latency, complexity and as well as least error floorings in communication, when the transmitted data contains multiple error bits.This paper is proposed to represent the majority logic decoding/detecting of LDPC codes.This paper proposes the Generation of Originator and Parity estimated matrices for the Binary LDPC Codes.Here, the proposed techniques are hard decision decrypting and soft decision decrypting schemes.These schemes uses majority logic decoding based on the data transmission and reception in communication channel.This paper also elaborates the effective calculation of Euclidean distance and algorithm for constructing the LDPC codes.
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.
Many classes of high-performance Low-density parity check codes are based on parity check matrices composed of permutation sub matrices. The emulation-simulation framework further allows the algorithm and implementation to be iteratively redefined to improve the error floor performance of message passing decoder. Log-Like hood-Ratio (LLR) based Belief-Propagation (BP) algorithm is presented for Low Density Parity Check codes. Numerically accurate representation of check node update computation used in LLR-BP decoding is described. The implementation of Sum-Product algorithm (SPA) within Low Density Parity Check Code (LDPC) decoder is described in this paper and the correction term is used to improve the decoding performance of min-sum algorithm (MSA). Quantization and log-tanh function approximation in sum-product decoder strongly affect which absorbing set dominates in error floor region. For LDPC decoder, bit error rate (BER) decreases with increase in the signal to noise ratio.