Affine Code for <I>T</I>-User Noisy Multiple-Access Adder Channel

Jun CHENG; Yoichiro WATANABE

Affine Code for T-User Noisy Multiple-Access Adder Channel

Jun CHENG, Yoichiro WATANABE

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Coding scheme for a noisy multiple-access adder channel is proposed. When a T-user δ-decodable affine code C is given a priori, a qT-user λ δ-decodable affine code C^* is produced by using a q q matrix B satisfying BA=λ I_{q q}, e. g. , a Hadamard matrix or a conference matrix. In particular, the case of δ=1 is considered for the practical purposes. A (2n-1)-user uniquely decodable (δ=1) affine code Cⁿ with arbitrary code length n is recursively constructed. When Cⁿ plays a role of C, a q(2n-1)-user λ-decodable affine code C^* is obtained. The code length and the number of users of C^* are more flexible than those of the Wilson's code. The total rate of the λ-decodable code in this paper tends to be higher than that of the λ-decodable code by Wilson as the number of users increases.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E83-A No.3 pp.541-550

Publication Date: 2000/03/25

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Type of Manuscript: PAPER

Category: Coding Theory

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Jun CHENG, Yoichiro WATANABE, "Affine Code for T-User Noisy Multiple-Access Adder Channel" in IEICE TRANSACTIONS on Fundamentals, vol. E83-A, no. 3, pp. 541-550, March 2000, doi: .
Abstract: Coding scheme for a noisy multiple-access adder channel is proposed. When a T-user δ-decodable affine code C is given a priori, a qT-user λ δ-decodable affine code C^* is produced by using a q q matrix B satisfying BA=λ I_{q q}, e. g. , a Hadamard matrix or a conference matrix. In particular, the case of δ=1 is considered for the practical purposes. A (2n-1)-user uniquely decodable (δ=1) affine code Cⁿ with arbitrary code length n is recursively constructed. When Cⁿ plays a role of C, a q(2n-1)-user λ-decodable affine code C^* is obtained. The code length and the number of users of C^* are more flexible than those of the Wilson's code. The total rate of the λ-decodable code in this paper tends to be higher than that of the λ-decodable code by Wilson as the number of users increases.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e83-a_3_541/_p

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@ARTICLE{e83-a_3_541,
author={Jun CHENG, Yoichiro WATANABE, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Affine Code for T-User Noisy Multiple-Access Adder Channel},
year={2000},
volume={E83-A},
number={3},
pages={541-550},
abstract={Coding scheme for a noisy multiple-access adder channel is proposed. When a T-user δ-decodable affine code C is given a priori, a qT-user λ δ-decodable affine code C^* is produced by using a q q matrix B satisfying BA=λ I_{q q}, e. g. , a Hadamard matrix or a conference matrix. In particular, the case of δ=1 is considered for the practical purposes. A (2n-1)-user uniquely decodable (δ=1) affine code Cⁿ with arbitrary code length n is recursively constructed. When Cⁿ plays a role of C, a q(2n-1)-user λ-decodable affine code C^* is obtained. The code length and the number of users of C^* are more flexible than those of the Wilson's code. The total rate of the λ-decodable code in this paper tends to be higher than that of the λ-decodable code by Wilson as the number of users increases.},
keywords={},
doi={},
ISSN={},
month={March},}

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TY - JOUR
TI - Affine Code for T-User Noisy Multiple-Access Adder Channel
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 541
EP - 550
AU - Jun CHENG
AU - Yoichiro WATANABE
PY - 2000
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E83-A
IS - 3
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - March 2000
AB - Coding scheme for a noisy multiple-access adder channel is proposed. When a T-user δ-decodable affine code C is given a priori, a qT-user λ δ-decodable affine code C^* is produced by using a q q matrix B satisfying BA=λ I_{q q}, e. g. , a Hadamard matrix or a conference matrix. In particular, the case of δ=1 is considered for the practical purposes. A (2n-1)-user uniquely decodable (δ=1) affine code Cⁿ with arbitrary code length n is recursively constructed. When Cⁿ plays a role of C, a q(2n-1)-user λ-decodable affine code C^* is obtained. The code length and the number of users of C^* are more flexible than those of the Wilson's code. The total rate of the λ-decodable code in this paper tends to be higher than that of the λ-decodable code by Wilson as the number of users increases.
ER -