In this paper, we consider a vector disjunctive channel in which users transmit some binary vectors of length L. We estimate the capacity of this channel and derive a lower bound on this value. In addition, the lower bound is calculated both for the case of the Bernoulli distribution and for an arbitrary distribution for the case when L = 2. It is shown numerically that for L = 2 and the multiplicity of the collision t = 1, the Bernoulli distribution is optimal, i.e., it maximizes the throughput of the vector disjunctive channel.
This paper deals with the error exponent of the regular graph-based binary low-density parity-check (LDPC) codes under the maximum likelihood (ML) decoding algorithm in the binary symmetric channel (BSC). Unlike other papers where error exponents are considered for the case when the length of LDPC codes tends to infinity (asymptotic analysis) we considered the finite length case (finite length analysis). In this paper we describe the method of deriving the lower bound on the error exponent for regular graph- based LDPC code with finite length under ML decoding and analyze the dependency of the error exponent on various LDPC code parameters. The numerical results, obtained for the considered lower bound, are represented and analyzed at the end of the paper.
The paper is concerned with the problem of calculating the stationary probabilities for a simplified model of the control of the access to the resources of a wireless wideband network with various thresholds for turning off and turning on the access to the resources of the network, depending on the class of service. Three variants of mutual position of hystereses are studied and, for each type of the arrangement of the hystereses, algorithms for calculating the stationary probabilities of the distribution of the amount of employed network resource are presented.