2016/05/17 by Dyachkov, A. G., Polyanskii, N., Shchukin, V. +1
#FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.1605.05363
A binary code is called a superimposed cover-free (s,ℓ)-code if the code is identified by the incidence matrix of a family of finite sets in which no intersection of ℓ sets is covered by the union of s others. A binary code is called a superimposed list-decoding sL-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=ℓ=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,ℓ)-code and list-decoding sL-code based on the ensemble of constant weight binary codes. Also, we establish an upper bound on the rate of superimposed list-decoding sL-code.