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

Toshihiro NIINOMI  Hideki YAGI  Shigeichi HIRASAWA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E101-A   No.8   pp.1223-1234
Publication Date: 2018/08/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E101.A.1223
Type of Manuscript: PAPER
Category: Coding Theory
decision feedback,  generalized decoding,  linear block code,  DS2 bound,  Shulman-Feder bound,  

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Recently, Hof et al. extended the type-2 Duman and Salehi (DS2) bound to generalized decoding, which was introduced by Forney, with decision criterion FR. From this bound, they derived two significant bounds. One is the Shulman-Feder bound for generalized decoding (GD) with the binary-input output-symmetric channel. The other is an upper bound for an ensemble of linear block codes, by applying the average complete weight distribution directly to the DS2 bound for GD. For the Shulman-Feder bound for GD, the authors derived a condition under which an upper bound is minimized at an intermediate step and show that this condition yields a new bound which is tighter than Hof et al.'s bound. In this paper, we first extend this result for non-binary linear block codes used over a class of symmetric channels called the regular channel. Next, we derive a new tighter bound for an ensemble of linear block codes, which is based on the average weight distribution.