On the DS2 Bound for Forney's Generalized Decoding Using Non-Binary Linear Block Codes

Niinomi, Toshihiro; Yagi, Hideki; Hirasawa, Shigeichi

doi:10.1587/transfun.e101.a.1223

Cited by 2 publications

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“…However, by choosing g * (y) specified in (26) and the special structure of the ensemble such that P(ℓ) = q −(N−k) , the effect of Jensen's inequality disappears, and indeed the RHS of (30) coincides with the one in (7). Noticing that the RHS of ( 7) is also the intermediate step during deriving Shamai and Sason's DS2 bounds, we can conclude that our upper bound in Corollary 4.1 is not looser than those previous bounds (11)- (13).…”

Section: Optimal G(y) For the Ensemble Of Random Linear Block Codesmentioning

confidence: 57%

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

Niinomi

Yagi

Hirasawa

2022

IEICE Trans. Fundamentals

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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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Section: Optimal G(y) For the Ensemble Of Random Linear Block Codesmentioning

confidence: 57%

“…In this section, we derive the DS2 bound [13] for the HSS ensemble from (7) and discuss how to determine reasonable g(y) via the ensemble of random linear codes.…”

Section: The Ds2 Bound For Hss Ensemblementioning

confidence: 99%