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Yuan LI Hidekazu MURATA Susumu YOSHIDA
This paper discusses a communication system with a multiple-access channel where two users simultaneously send complex-valued signals in the same frequency-band. In this channel, ambiguity in decoding occurs when receiver trying to estimate each users' signal. In order to solve the ambiguity problem, a family of uniquely decodable code is derived in this paper. The uniquely decodable code is designed by using trellis-coded modulation (TCM) pair where the trellis structure of one TCM is a transformation of the other in the pair. It is theoretically proved that, with the proposed coding scheme, the composite received signal can be uniquely decomposed into the two constituent signals for any power ratio and any phase difference between the received two users' signals. Improvement of BER performance over non-uniquely decodable code is illustrated by computer simulation.
Multi-user uniquely decodable (UD) k-ary coding for the multiple-access adder channel is investigated. It is shown that a Tf+g+1-user UD k-ary affine code with code length f+g+1 can be obtained from two Tf-user and Tg-user UD k-ary affine codes. This leads to construct recursively a Tn-user UD k-ary affine code with arbitrary code length n. The total rate of the code tends to be higher than those of all the multi-user UD k-ary codes reported previously as the number of users increases.
Jian-Jun SHI Yoichiro WATANABE
The independence number of one-order graph associated with a linear code is formulated. The formulation is represented by the parameters of the generator matrix.
Jian-Jun SHI Yoichiro WATANABE
A uniquely decodable code pair (C, S) is considered for the two-user binary adder channel. When the first code C is linear, a lower bound of |S| is formulated and a uniquely decodable code pair (C, S) is presented. When a rate R1 of C is less than 1/3, a rate R2of S is greater than the best rate known previously.
Jian-Jun SHI Yoichiro WATANABE
A uniquely decodable code (C1, C2, C3) is investigated for the three-user binary adder channel. The uniquely decodable code is constructed as follows: If C1 is an (n, k) linear code with a generator matrix, C2 is a coset of C1 and C3 is a set of all coset leaders, then the code (C1, C2, C3) is uniquely decodable and its total rate is equal to 1k/n, n2k. This code is easily decodable.
Jian-Jun SHI Yoichiro WATANABE
A uniquely decodable (UD) code pair (C, S) is considered for the two-user binary adder channel. For a class of linear codes C, the maximum independent set of the graph associated with C, which is the second code S, is evaluated. When the rate R1 of C is less than 0.5, there exist UD codes (C, S)'s such that the rate R2 of S exceeds the Khachatrian's and Guo's results in amount.
It is known that the uniquely decodable code pairs (C1, C2) for the two-user binary adder channel relates to the maximum independent set of a graph associated with a binary code. This paper formulates the independence number of a class of graphs associated with binary linear codes, and presents an algorithm of the maximum independent set for those graphs. Uniquely decodable code pairs (C1, C2)'s are produced, where C1 is a linear code and C2 is a maximum independent set of the graph associated with C1. For the given C1, the transmission rate of C2 is higher than that by Khachatrian, which is known as the best result as so far. This is not rather surprising because the code C2 is a maximum independent set in this paper but not be Khachatrian's.