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

Jun CHENG  Yoichiro WATANABE  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E83-A   No.3   pp.541-550
Publication Date: 2000/03/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Coding Theory
Keyword: 
multiple-access communication,  adder channel,  multi-user code,  affine code,  δ-decodable code,  

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Summary: 
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 BAIq 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.