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Decoding error probability of random parity-check matrix ensemble over the erasure channel: Decoding error of random PC matrix ensemble over EC: C. H. Chan et al.

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Title: Decoding error probability of random parity-check matrix ensemble over the erasure channel: Decoding error of random PC matrix ensemble over EC: C. H. Chan et al.
Authors: Chan, Chin Hei, Fu, Fang-Wei, Xiong, Maosheng
Source: Designs, Codes & Cryptography; Jan2025, Vol. 93 Issue 1, p51-77, 27p
Subject Terms: PARITY-check matrix, ERROR probability, RANDOM matrices, LINEAR codes, EXPONENTS
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. [ABSTRACT FROM AUTHOR]
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  Data: Decoding error probability of random parity-check matrix ensemble over the erasure channel: Decoding error of random PC matrix ensemble over EC: C. H. Chan et al.
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  Data: Designs, Codes & Cryptography; Jan2025, Vol. 93 Issue 1, p51-77, 27p
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  Data: 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. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Designs, Codes & Cryptography is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s10623-024-01516-5
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      – SubjectFull: PARITY-check matrix
        Type: general
      – SubjectFull: ERROR probability
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      – SubjectFull: RANDOM matrices
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      – SubjectFull: LINEAR codes
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      – TitleFull: Decoding error probability of random parity-check matrix ensemble over the erasure channel: Decoding error of random PC matrix ensemble over EC: C. H. Chan et al.
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              Text: Jan2025
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