Ilya Vorobyev

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

Hypothesis test for upper bound on the size of random defective set

s

Simulated Annealing Method for Construction of High-Girth QC-LDPC Codes

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 the 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., at each time instant the output signal of MAC is a symmetric function of its

On capacities of the two-user union channel with complete feedback.

s

Bounds for Signature Codes.

input signals.

Floor Scale Modulo Lifting for QC-LDPC codes.

Let 1 ≤ s < t, N ≥ 2 be fixed integers and a complex electronic circuit of size t is said to be an s-active, s ≪ t, and can work as a system block if not more than s elements of the circuit are defective. Otherwise, the circuit is said to be an s-defective and should be replaced by a similar s-active circuit. Suppose that there exists a possibility to run N non-adaptive group tests to check the s-activity of the circuit. As usual, we say that a (disjunctive) group test yields the positive response if the group contains at least one defective element. In this paper, we will interpret the unknown set of defective elements as a random set and discuss upper bounds on the error probability of the hypothesis test for the null hypothesis {H0 : the circuit is s-active} versus the alternative hypothesis {H1 : the circuit is s-defective}. Along with the conventional decoding algorithm based on the known random set of positive responses and disjunctive s-codes, we consider a T-weight decision rule which is based on the simple comparison of a fixed threshold T, 1 ≤ T < N, with the known random number of positive responses p, 0 ≤ p ≤ N.