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International Journal of Business Intelligents

An Efficient Majority Error Detection in Logic Decoding with Euclidean Geometry Low Density Parity Check (Eg-Ldpc) Codes

M Vengadapathiraj, U. Maheswaran, A. Karunakaran

Published Jun 15, 2016• 0 citations
Publisher
DOI
10.20894/ijbi.105.005.001.024

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In a recent article, a technique was proposed to step up the majority logic decoding of variation set low density parity check codes. This is helpful as majority logic decoding can be implemented serially with trouble-free hardware but requires a huge decoding time. The method detect whether a word has errors in the initial iterations of majority logic decoding, and at what time there are no errors the decoding split ends without completing the rest of the iterations. While the majority words in a memory will be error-free, the average decoding time is significantly reduced. The outcome obtained proves that the technique is also effective for EG-LDPC codes. General simulation results are given to precisely estimate the prospect of error detection for different code sizes and numbers of errors.

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ABSTRACT Error correcting coding has become one essential part in nearly all the modern data transmission and storage systems. Low density parity check (LDPC) codes are a class of linear block code has the superior performance closer to the Shannon’s limit. In this paper two error correcting codes from the family of LDPC codes specifically Euclidean Geometry Low Density Parity Check (EG-LDPC) codes and Nonbinary low density parity check (NB-LDPC) codes are compared in terms of power consumption, number of iterations and other parameters. For better performance of EG-LDPC codes, Maximum Likelihood (ML) Algorithm was proposed. NB-LDPC codes can provide better error correcting performance with an average of 10 to 30 iterations but has high decoding complexity which can be improve by EG-LDPC codes with ML algorithm having only three iterations for detecting and correcting errors. One step majority logic decodable (MLD) codes is a subclass of EG-LDPC codes are used to avoid high decoding complexity. The power Consumed by NB-LDPC codes is 2.729W whereas the power consumed by EG-LDPC codes with ML algorithm is 1.148W. KEYWORDS Euclidean Geometry - Low Density Parity Check code, Maximum Likelihood Algorithm, Non Binary - Low Density Parity Check Code.

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Hard decision decoding of low density parity check (LDPC) codes has potential applications in practical settings like data storage. For this purpose, it is important for the code to have an assured minimum distance and, hence, guaranteed error correction capability. In this paper, we show that with very high probability the guaranteed error correction capability of Euclidean geometry (EG) codes using threshold-optimized, iterative majority logic (ML) decoding is much greater than the usual single iteration ML decoding, making these codes much more attractive for hard decision decoding. For instance, the (262143, 242461, t/spl ges/256) EG code (a (512, 512)-regular LDPC code) can correct t=580 bit errors with probability better than 1-1/spl times/10/sup -58/.

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In a recent article, a technique was proposed to step up the majority logic decoding of variation set low density parity check codes. This is helpful as majority logic decoding can be implemented serially with trouble-free hardware but requires a huge decoding time. The method detect whether a word has errors in the initial iterations of majority logic decoding, and at what time there are no errors the decoding split ends without completing the rest of the iterations. While the majority words in a memory will be error-free, the average decoding time is significantly reduced. The outcome obtained proves that the technique is also effective for EG-LDPC codes. General simulation results are given to precisely estimate the prospect of error detection for different code sizes and numbers of errors.
ABSTRACT Error correcting coding has become one essential part in nearly all the modern data transmission and storage systems. Low density parity check (LDPC) codes are a class of linear block code has the superior performance closer to the Shannon’s limit. In this paper two error correcting codes from the family of LDPC codes specifically Euclidean Geometry Low Density Parity Check (EG-LDPC) codes and Nonbinary low density parity check (NB-LDPC) codes are compared in terms of power consumption, number of iterations and other parameters. For better performance of EG-LDPC codes, Maximum Likelihood (ML) Algorithm was proposed. NB-LDPC codes can provide better error correcting performance with an average of 10 to 30 iterations but has high decoding complexity which can be improve by EG-LDPC codes with ML algorithm having only three iterations for detecting and correcting errors. One step majority logic decodable (MLD) codes is a subclass of EG-LDPC codes are used to avoid high decoding complexity. The power Consumed by NB-LDPC codes is 2.729W whereas the power consumed by EG-LDPC codes with ML algorithm is 1.148W. KEYWORDS Euclidean Geometry - Low Density Parity Check code, Maximum Likelihood Algorithm, Non Binary - Low Density Parity Check Code.
Hard decision decoding of low density parity check (LDPC) codes has potential applications in practical settings like data storage. For this purpose, it is important for the code to have an assured minimum distance and, hence, guaranteed error correction capability. In this paper, we show that with very high probability the guaranteed error correction capability of Euclidean geometry (EG) codes using threshold-optimized, iterative majority logic (ML) decoding is much greater than the usual single iteration ML decoding, making these codes much more attractive for hard decision decoding. For instance, the (262143, 242461, t/spl ges/256) EG code (a (512, 512)-regular LDPC code) can correct t=580 bit errors with probability better than 1-1/spl times/10/sup -58/.