N. Polyanskii | Searcharxiv

arXiv2018

Separable Codes for the Symmetric Multiple-Access Channel

A binary matrix is called an s-separable code for the disjunctive multiple-access channel (disj-MAC) if Boolean sums of sets of s columns are all distinct. The well-known issue of the combinatorial coding theory is to obtain upper and lower bounds on the rate of s-separable codes for disj-MAC. In our paper, we generalize the problem and discuss upper and lower bounds on the rate of q-ary s-separable codes for models of noiseless symmetric MAC, i.e., when at each time instant the output signal of MAC is a symmetric function of its s input signals.

cs.IT↗

arXiv2016

Bounds on the rate of disjunctive codes (in Russian)

A binary code is called a superimposed cover-free $(s,\ell)$-code if the code is identified by the incidence matrix of a family of finite sets in which no intersection of $\ell$ sets is covered by the union of $s$ others. A binary code is called a superimposed list-decoding $s_L$-code if the code is identified by the incidence matrix of a family of finite sets in which the union of any $s$ sets can cover not more than $L-1$ other sets of the family. For $L=\ell=1$, both of the definitions coincide and the corresponding binary code is called a superimposed $s$-code. Our aim is to obtain new lower and upper bounds on the rate of the given codes. In particular, we derive lower bounds on the rates of a superimposed cover-free $(s,\ell)$-code and list-decoding $s_L$-code based on the ensemble of constant weight binary codes. Also, we establish an upper bound on the rate of superimposed list-decoding $s_L$-code.

cs.IT↗