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A DESIGN OF PARITY CHECK MATRIX FOR SHORT IRREGULAR LDPC CODES VIA MAGIC SQUARE BASED ALGORITHM

Chutima Prasartkaew, Somsak Choomchuay

Published Jan 1, 2013• 2 citations
OpenAlex

Abstract

This paper presents a construction algorithm for the short block irregular low-density parity-check (LDPC) codes. By applying a magic square theorem as a part of the matrix construction, a newly developed algorithm, the so-called Magic Square Based Algorithm (MSBA), is obtained. The modified array codes are focused on in this study since the reduction of 1s can lead to simple encoding and decoding schemes. Simulation results based on AWGN channels show that with the code rate of 0.8 and SNR 5 dB, the BER of �� �� can

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IEEE Region International Conference on Computational Technologies in Electrical and Electronics Engineering•Jul 1, 2008•7 citations
This paper presents a construction algorithm for the short block irregular low-density parity-check (LDPC) codes. By applying a magic square theorem as a part of the matrix construction, a newly developed algorithm, the so-called Magic Square Based Algorithm (MSBA), is obtained. The modified array codes are focused on in this study since the reduction of 1s can lead to simple encoding and decoding schemes. Simulation results based on AWGN channels show that with the code rate of 0.8 and SNR 5 dB, the BER of �� �� can
This paper presents a construction algorithm for the short block irregular LDPC codes. By applying a magic square theorem as a part of the matrix construction, a newly developed algorithm, the so-called Magic Square Based Algorithm (MSBA), is obtained. The modified array codes are focused on in this study since the reduction of 1s can lead to simple encoding and decoding schemes. Simulation results based on AWGN channels show that with the code rate of 0.8 and SNR = 5 dB, the BER of 10-7can be obtained whilst the number of decoding iteration is relatively low.
In this paper, a combined Low-Density Parity-Check (LDPC) code decoding design method, called modified Block-Type LDPC (B-LDPC), for realistic LDPC coding system architectures is presented. The B-LDPC code, which is a special class of quasi-cyclic LDPC (QC-LDPC), has an efficient encoding algorithm owing to the simple structure of their parity-check matrices. A proposed distribution of irregular parity-check matrix for the modified B-LDPC is developed so that we can obtain an area-efficient decoder design, good error correction performance, and achievable architecture implementation. The modified B-LDPC code decoding utilizes the iterative min-sum algorithm (MSA) and its decoding architecture design employs the non-overlapping operations of bit node unit (BNU) and check node unit (CNU). Different block matrix sizes for parity-check matrix can be adopted so that the modified B-LDPC code decoding improves the throughput without obvious performance degradation.
In this paper, a method for constructing Low-Density Parity-Check (LDPC) codes of good performance in terms of Bit Error Rate (BER) using a computer search algorithm is presented. First, LDPC codes and encoding along with its Tanner graph representation is described. Then, a detailed description of the proposed construction algorithm is given. A Modified Shortest-Path (MSP) Algorithm of lower complexity is applied to obtain a code graph of the desired structure. The proposed algorithm works directly on the parity-check matrix of the LDPC code. The parity-check matrix of the code is constructed column by column subject to the bit-degree and girth constraints. Using the proposed algorithm, both regular and irregular LDPC codes have been constructed. Furthermore, not only have the girth been improved but also the rate of LDPC codes. Finally, by simulation results the constructed codes were shown to perform well over an additive white Gaussian noise (AWGN) channel.
Low-density Parity check codes (LDPC) are gaining interest for high data rate application in both terrestrial and spatial communications which requires low bit error rate. This paper proposes an algorithm through which the best parity check matrix is obtained for irregular low density parity check codes, which reduces the Bit Error Rate ,Frame Error Rate and computational complexity. Tanner graph also called a bipartite graph format in an Low Density Parity Check (LDPC) code design contains many short cycles; it will produce a computational complexity in a code design process and it degrades the code performance. To overcome this effect, we proposed an new algorithm which obtains a best final parity check matrix. Throughout the paper we will give the detailed description of an efficient algorithm proposed. The complexity is studied graphically and analytically. Using proposed algorithm, cycles of length four observed in corresponding matrix are removed. Each matrix is evaluated over a noisy Additive White Gaussian Noise (AWGN) channel. Bit Error rate and Frame error rate is calculated. The results are compared with randomly generated best parity check matrix. Simulation results shows that proposed method successfully overcomes the computational complexity and meets the near Shannon limit.
The common approach for the design of an error correction system is first to construct a code and then to define the hardware structure of the encoder and decoder. However, in the case of LDPC codes (low-density parity-check) such a constructed code is generally not well suited for a hardware implementation. It has been recognized that the code construction and hardware design must be considered jointly to facilitate LDPC decoder and encoder implementation. In this paper, an efficient decoder structure for regular and irregular LDPC codes, based on TDMP (turbo-decoding message passing) scheme is designed first. The decoder has been implemented and verified in an FPGA device. Constraints for the parity check matrix of a code to be suitable for the decoder architecture are defined. Then an algorithm for LDPC parity check matrix construction subject to these constraints is presented. The algorithm aims at improving performance of the code in the low SNR region by employing irregular codes as well as in high SNR region by reducing the number of small Stopping Sets and Trapping Sets in the Tanner graph of the code making use of a computer search technique.