How an Erdos-Renyi-type search approach gives an explicit code construction of rate 1 for random access with multiplicity feedback

Authors:
M. Ruszinko;P. Vanroose
Affiliations:
Comput. & Autom. Inst., Hungarian Acad. of Sci., Budapest;-
Venue:
IEEE Transactions on Information Theory
Year:
2006

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Abstract

Pippenger (1981) showed in a probabilistic way that the capacity of a collision channel with multiplicity feedback is one. In this correspondence, using an Erdos-Renyi type search strategy, we settle a long-standing open problem by giving a constructive proof of this result. Moreover, we prove that two different capacity definitions are equivalent, thereby solving a problem posed by Tsybakov (1985)