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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.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E101-A No.8 pp.1223-1234

- Publication Date
- 2018/08/01

- Publicized

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.E101.A.1223

- Type of Manuscript
- PAPER

- Category
- Coding Theory

Toshihiro NIINOMI

Tokyo City University

Hideki YAGI

the University of Electro-Communications

Shigeichi HIRASAWA

Waseda University

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Toshihiro NIINOMI, Hideki YAGI, Shigeichi HIRASAWA, "On the DS2 Bound for Forney's Generalized Decoding Using Non-Binary Linear Block Codes" in IEICE TRANSACTIONS on Fundamentals,
vol. E101-A, no. 8, pp. 1223-1234, August 2018, doi: 10.1587/transfun.E101.A.1223.

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.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E101.A.1223/_p

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@ARTICLE{e101-a_8_1223,

author={Toshihiro NIINOMI, Hideki YAGI, Shigeichi HIRASAWA, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={On the DS2 Bound for Forney's Generalized Decoding Using Non-Binary Linear Block Codes},

year={2018},

volume={E101-A},

number={8},

pages={1223-1234},

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.},

keywords={},

doi={10.1587/transfun.E101.A.1223},

ISSN={1745-1337},

month={August},}

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TY - JOUR

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

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 1223

EP - 1234

AU - Toshihiro NIINOMI

AU - Hideki YAGI

AU - Shigeichi HIRASAWA

PY - 2018

DO - 10.1587/transfun.E101.A.1223

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E101-A

IS - 8

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - August 2018

AB - 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.

ER -