IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Online ISSN : 1745-1337
Print ISSN : 0916-8508
Regular Section
On the DS2 Bound for Forney's Generalized Decoding Using Non-Binary Linear Block Codes
Toshihiro NIINOMIHideki YAGIShigeichi HIRASAWA
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2018 Volume E101.A Issue 8 Pages 1223-1234

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Abstract

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.

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© 2018 The Institute of Electronics, Information and Communication Engineers
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