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Conference Proceeding..
Low Density Parity Check Code for Burst Error Correction Mrugesh Patel#, Prof.Neeta Chapatwala*
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Post Graduate Student, Department of Electronics & Communication, Sarvajanik College of Engineering & Technology, Surat, Gujarat, India * Assistant Professor, Department of Electronics & Communication, Sarvajanik College of Engineering and Technology, Surat,Gujarat,India #
[email protected]
*
[email protected]
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. Low-Density Parity-Check (LDPC) codes are one of the recent topics in coding theory today. Originally invented more than forty years ago, they have been the focus of many researchers in the last few years and are included in the latest digital video broadcasting via satellite standard (DVB-S2). 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 lights on major parts of LDPC codes like generation of parity check matrix, generator matrix, encoding and decoding process etc. Sum product algorithm which is basically soft decoding algorithm is explained and can be implemented for the generated parity check matrix of 635 x 1270 for LDPC code with code rate 1/2. Keywords - Log Likelihood Ratio (LLR), Low density parity check (LDPC), Sum Product Algorithm (SPA), Check Node (CN), Variable Node (VN)
I.
INTRODUCTION
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, who noticed, apparently independently of Gallager’s work, the advantages of linear block codes with sparse (low-density) parity-check matrices[1]. LDPC codes are linear block codes defined by their sparse parity check matrices. By density, we mean the ratio of the number of ones in the matrix to the number of all elements
NCIET-2013, SRPEC
in the matrix. If for each row (or column) ratio of the number of ones to the length of that row (or column) is equal, then the code is called a regular LDPC code. The low-density condition can be satisfied especially for larger block lengths. LDPC codes that has been proposed by Gallager [6] were regular LDPC codes, that has a constant column and row in their parity check matrices. Shortly after the rediscovery of LDPC codes, a new type of LDPC codes has been introduced, which are called irregular LDPC codes. This type of LDPC codes can have different density rows and columns in its parity check matrices, and they can perform better than regular LDPC. Well designed LDPC codes decoded with iterative decoding based on belief propagation, such as the sum product algorithm (SPA)[1] achieve performance close to the Shannon limit. Ever since their rediscovery, design, construction, decoding, efficient encoding, performance analysis, and applications of these codes in digital communication and storage systems have become focal points of research. Performance of binary LDPC code is degraded when the code word length is small or moderate, or when higher order modulation is used for transmission. LDPC codes designed over Galois Field GF (q>2) (also known as non-binary LDPC codes) have shown great performance for these cases. But decoding complexity increases with q which makes the use of non-binary LDPC (NB-LDPC) codes is limited still today [3]. II.
THEORETICAL BACKGROUND
A) Matrix Representation [1] A low-density parity-check code is a linear block code given by the null space of an m × n parity-check matrix H that has a low density of 1s. A regular LDPC code is a linear block code whose parity-check matrix H has column weight g and row weight r, where r = g (n/m) and g
