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IEICE technical report. Information theory

An Algorithm for Computing the Stopping Redundancy of LDPC Codes Using the Probabilistic Method

Yoshiho Konishi, Masanori Hirotomo, Masakatu Morii

Published Sep 4, 2008• 0 citations
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On the binary erasure channel (BEC), the performance of low-density parity-check (LDPC) codes decoded by iterative algorithms is estimated by the small stopping sets in the codes. The size of smallest stopping set is called the stopping distance. Since it depends on the structure of parity-check matrix for the code, we can construct the parity-check matrix by adding dependent rows so that the stopping distance is equal to the minimum distance. The stopping redundancy is defined as the smallest number of rows in such a parity-check matrix. In this paper, we propose a probabilistic algorithm for computing the stopping redundancy of LDPC codes. Additionally, we show numerical results of computing the stopping redundancy of (155,64), (504,252) and (1008,504) LDPC codes.

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On the binary erasure channel, the performance of LDPC codes decoded by iterative algorithms is estimated by small-size stopping sets. We have proposed a probabilistic algorithm for computing the minimum size of stopping sets of LDPC codes. In this paper, we analyze the probability and the complexity of finding the minimum-size stopping sets, and give an error probability of determining the minimum size of stopping sets after processing our algorithm. Additionally, we show the numerical results of computing the minimum size of stopping sets of several LDPC codes. In these result, we could compute the minimum size of stopping sets with high reliability.

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On the binary erasure channel (BEC), the performance of low-density parity-check (LDPC) codes decoded by iterative algorithms is estimated by the small stopping sets in the codes. The size of smallest stopping set is called the stopping distance. Since it depends on the structure of parity-check matrix for the code, we can construct the parity-check matrix by adding dependent rows so that the stopping distance is equal to the minimum distance. The stopping redundancy is defined as the smallest number of rows in such a parity-check matrix. In this paper, we propose a probabilistic algorithm for computing the stopping redundancy of LDPC codes. Additionally, we show numerical results of computing the stopping redundancy of (155,64), (504,252) and (1008,504) LDPC codes.
On the binary erasure channel, the performance of LDPC codes decoded by iterative algorithms is dominated by small-size stopping sets, especially minimal stopping sets. In this paper, we propose a probabilistic algorithm for computing the minimum size of stopping sets of LDPC codes. In this algorithm, we generate efficiently small-size stopping sets by using the relation between small-size stopping sets and low-weight codewords. In numerical experiments, we could compute the minimum size of stopping sets of LDPC codes of length about 500, 1000 and 5000 with high reliability, and could find smaller stopping sets than that found by conventional methods.
On the binary erasure channel, the performance of LDPC codes decoded by iterative algorithms is estimated by small-size stopping sets. We have proposed a probabilistic algorithm for computing the minimum size of stopping sets of LDPC codes. In this paper, we analyze the probability and the complexity of finding the minimum-size stopping sets, and give an error probability of determining the minimum size of stopping sets after processing our algorithm. Additionally, we show the numerical results of computing the minimum size of stopping sets of several LDPC codes. In these result, we could compute the minimum size of stopping sets with high reliability.