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IEICE Technical Report; IEICE Tech. Rep.

On Computing the Weight Distribution of LDPC Convolutional Codes

Masanori Hirotomo, Masakatu Morii

Published Sep 14, 2010• 0 citations
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On asymptotic ensemble weight enumerators of LDPC-like codes

Chung-Li Wang, M.P.C. Fossorier

For LDPC-like codes such as LDPC, GLDPC, and DGLDPC codes, it is well known that the error floor can be caused by the codewords of small weights or stopping sets of small sizes. In this paper, we investigate the computation of asymptotic weight enumerators such that it becomes a convenient tool to determine a good distribution of code ensembles. In addition, by analyzing the first order approximation, we derive a condition to obtain a negative asymptotic growth rate of the codewords of small linear-sized weights, which is an important constraint for distribution optimization. Also the weight enumerators of turbo and repeat-accumulate codes are investigated. Furthermore, we extend our results to nonbinary DGLDPC codes. Generalization to N-layer and convolutional code based LDPC-like codes are also developed.

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In this paper, we propose an efficient method for computing the weight spectrum of LDPC convolutional codes constructed from quasi-cyclic block codes. In the proposed method, we reduce the memory size of their parity-check matrices with the same distance profile as original codes, and apply a forward and backward tree search algorithm to the parity-check matrices of reduced memory. We show numerical results of computing the minimum free distance and the low-part weight spectrum of LDPC convolutional codes of memory about 130.

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In this paper, we propose an efficient method for computing the weight spectrum of LDPC convolutional codes based on circulant matrices of quasi-cyclic codes. In the proposed method, we reduce the memory size of their parity-check matrices with the same distance profile as the original codes, and apply a forward and backward tree search algorithm to the parity-check matrices of reduced memory. We show numerical results of computing the free distance and the low-part weight spectrum of LDPC convolutional codes of memory about 130.

IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences•Jan 1, 2014•0 citations
For LDPC-like codes such as LDPC, GLDPC, and DGLDPC codes, it is well known that the error floor can be caused by the codewords of small weights or stopping sets of small sizes. In this paper, we investigate the computation of asymptotic weight enumerators such that it becomes a convenient tool to determine a good distribution of code ensembles. In addition, by analyzing the first order approximation, we derive a condition to obtain a negative asymptotic growth rate of the codewords of small linear-sized weights, which is an important constraint for distribution optimization. Also the weight enumerators of turbo and repeat-accumulate codes are investigated. Furthermore, we extend our results to nonbinary DGLDPC codes. Generalization to N-layer and convolutional code based LDPC-like codes are also developed.
In this paper, we propose an efficient method for computing the weight spectrum of LDPC convolutional codes constructed from quasi-cyclic block codes. In the proposed method, we reduce the memory size of their parity-check matrices with the same distance profile as original codes, and apply a forward and backward tree search algorithm to the parity-check matrices of reduced memory. We show numerical results of computing the minimum free distance and the low-part weight spectrum of LDPC convolutional codes of memory about 130.
In this paper, we propose an efficient method for computing the weight spectrum of LDPC convolutional codes based on circulant matrices of quasi-cyclic codes. In the proposed method, we reduce the memory size of their parity-check matrices with the same distance profile as the original codes, and apply a forward and backward tree search algorithm to the parity-check matrices of reduced memory. We show numerical results of computing the free distance and the low-part weight spectrum of LDPC convolutional codes of memory about 130.