Coding for a multiple access OR channel: A survey

The signature coding for M active users out of T total users over a multiple access OR channel is considered. The mathematical problem is equivalent to the M-cover-free problem of extremal set theory. We survey the upper and lower bounds on the minimal code word length n(T , M), and present some code constructions. According to the current state of the theory, for 1>M>T 1 2 M2 log M log T n(T , M) 1 ln 2 M2 log T , so there is a huge gap between the upper and lower bounds. Moreover, there is no known construction approaching the upper bound. © 2007 Elsevier B.V. All rights reserved.

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