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

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2 Author(s)
Ruszinko, M. ; Comput. & Autom. Inst., Hungarian Acad. of Sci., Budapest, Hungary ; Vanroose, P.

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)

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Information Theory, IEEE Transactions on  (Volume:43 ,  Issue: 1 )