Upper Bounds on the Error Probability for the Ensemble of Linear Block Codes with Mismatched Decoding

Toshihiro NIINOMI
Hideki YAGI
Shigeichi HIRASAWA

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E105-A    No.3    pp.363-371
Publication Date: 2022/03/01
Publicized: 2021/10/08
Online ISSN: 1745-1337
DOI: 10.1587/transfun.2021TAP0001
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Coding Theory
DS2 bound,  ensemble of linear block codes,  mismatched decoding,  regular channel,  single letter exponent,  

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In channel decoding, a decoder with suboptimal metrics may be used because of the uncertainty of the channel statistics or the limitations of the decoder. In this case, the decoding metric is different from the actual channel metric, and thus it is called mismatched decoding. In this paper, applying the technique of the DS2 bound, we derive an upper bound on the error probability of mismatched decoding over a regular channel for the ensemble of linear block codes, which was defined by Hof, Sason and Shamai. Assuming the ensemble of random linear block codes defined by Gallager, we show that the obtained bound is not looser than the conventional bound. We also give a numerical example for the ensemble of LDPC codes also introduced by Gallager, which shows that our proposed bound is tighter than the conventional bound. Furthermore, we obtain a single letter error exponent for linear block codes.

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