Decision Feedback Scheme with Criterion LR+Th for the Ensemble of Linear Block Codes

Toshihiro NIINOMI
Hideki YAGI
Shigeichi HIRASAWA

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E103-A    No.1    pp.334-345
Publication Date: 2020/01/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.2019EAP1045
Type of Manuscript: PAPER
Category: Coding Theory
decision feedback,  generalized decoding,  linear block code,  DS2 bound,  Shulman-Feder bound,  LR+Th,  

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In decision feedback scheme, Forney's decision criterion (Forney's rule: FR) is optimal in the sense that the Neyman-Pearson's lemma is satisfied. Another prominent criterion called LR+Th was proposed by Hashimoto. Although LR+Th is suboptimal, its error exponent is shown to be asymptotically equivalent to that of FR by random coding arguments. In this paper, applying the technique of the DS2 bound, we derive an upper bound for the error probability of LR+Th for the ensemble of linear block codes. Then we can observe the new bound from two significant points of view. First, since the DS2 type bound can be expressed by the average weight distribution whose code length is finite, we can compare the error probability of FR with that of LR+Th for the fixed-length code. Second, the new bound elucidates the relation between the random coding exponents of block codes and those of linear block codes.