List decoding for a multiple access hyperchannel

We obtain bounds on the rate of (optimal) list-decoding codes with a fixed list size $L\ge1$ for a $q$-ary multiple access hyperchannel (MAHC) with $s\ge2$ 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 $L\ge1$ and $q=2$, and also for the nonbinary case $q\ge3$ for $L=1$ only, i.e., for so-called frameproof codes. Constructing upper and lower bounds on the rate for the general case of $L\ge1$ and $q\ge2$ in the present paper is based on a substantial development of methods that we designed earlier for the classical binary disjunctive multiple access channel.