Abstract
We obtain bounds on the rate of (optimal) list-decoding codes with a fixed list size L ≥ 1 for a q-ary multiple access hyperchannel (MAHC) with s ≥ 2 inputs and one output. By definition, an output signal of this channel is the set of symbols of a q-ary alphabet that occur in at least one of the s input signals. For example, in the case of a binary MAHC, where q = 2, an output signal takes values in the ternary alphabet {0, 1, {0, 1}}; namely, it equals 0 (1) if all the s input signals are 0 (1) and equals {0, 1} otherwise. Previously, upper and lower bounds on the code rate for a q-ary MAHC were studied for L ≥ 1 and q = 2, and also for the nonbinary case q ≥ 3 for L = 1 only, i.e., for so-called frameproof codes. Constructing upper and lower bounds on the rate for the general case of L ≥ 1 and q ≥ 2 in the present paper is based on a substantial development of methods that we designed earlier for the classical binary disjunctive multiple access channel.
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Original Russian Text © V.Yu. Shchukin, 2016, published in Problemy Peredachi Informatsii, 2016, Vol. 52, No. 4, pp. 14–30.
The research was carried out at the Institute for Information Transmission Problems of the Russian Academy of Sciences at the expense of the Russian Science Foundation, project no. 14-50-00150.
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Shchukin, V.Y. List decoding for a multiple access hyperchannel. Probl Inf Transm 52, 329–343 (2016). https://doi.org/10.1134/S0032946016040025
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DOI: https://doi.org/10.1134/S0032946016040025