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Decoding error probability of random parity-check matrix ensemble over the erasure channel

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Veröffentlicht in:Designs, Codes, and Cryptography vol. 93, no. 1 (Jan 2025), p. 51
1. Verfasser: Chan, Chin Hei
Weitere Verfasser: Fu, Fang-Wei, Xiong, Maosheng
Veröffentlicht:
Springer Nature B.V.
Schlagworte:
Principles
Probability
Coding theory
Codes
Error correction & detection
Maximum likelihood decoding
Parity
Linear codes
Variance
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Abstract:In this paper we carry out an in-depth study on the average decoding error probability of the random parity-check matrix ensemble over the erasure channel under three decoding principles, namely unambiguous decoding, maximum likelihood decoding and list decoding. We obtain explicit formulas for the average decoding error probabilities of the random parity-check matrix ensemble under these three decoding principles and compute the error exponents. Moreover, for unambiguous decoding, we compute the variance of the decoding error probability of the random parity-check matrix ensemble and the error exponent of the variance, which implies a strong concentration result, that is, roughly speaking, the ratio of the decoding error probability of a random linear code in the ensemble and the average decoding error probability of the ensemble converges to 1 with high probability when the code length goes to infinity.
ISSN:0925-1022
1573-7586
DOI:10.1007/s10623-024-01516-5
Quelle:Advanced Technologies & Aerospace Database