ISSN 0032-9460, Problems of Information Transmission, 2009, Vol. 45, No. 1, pp. 37–45.
Pleiades Publishing, Inc., 2009.
Original Russian Text
L.A. Bassalygo, 2009, published in Problemy Peredachi Informatsii, 2009, Vol. 45, No. 1, pp. 41–50.
A Model of Restricted Asynchronous Multiple Access
in the Presence of Errors
L. A. Bassalygo
Kharkevich Institute for Information Transmission Problems, RAS, Moscow
Received December 29, 2008
Abstract—The paper is based on the brief communication , where proofs of results were
omitted or drastically abridged. In the present paper, not only this gap is ﬁlled but also the
very model of restricted asynchronous multiple access from  is considered in a somewhat
more general situation.
1. MODEL DESCRIPTION AND PROBLEM STATEMENT
There are N stations, which can transmit data. The data of each station is divided into successive
blocks of length n, and each station is in advance provided with its transmission protocol, a (0, 1)
sequence of length n. We denote the protocol of the ith station by g
). If the jth
position of g
contains 0 (g
= 0), this means that the ith station is silent in this position; if it
contains 1, this means that the ith station transmits one of the binary symbols a or b.Wecallthe
N × n matrix G composed of protocols of all stations,
the protocol matrix. At each station there is a set of messages M
to be transmitted, and we assume
that the number of messages at each station is the same and equals M . Each message at the ith
station, i =1,...,N, is encoded by a binary word (in the alphabet a, b)oflengthw(g
) is the number of symbols 1 in the sequence g
; these are precisely the words that should
be transmitted at the unit positions of g
. Denote the set of codewords of the ith station by C
| = M). Access to the channel is restricted; simultaneously, at most S stations out of N have
access to the channel during time T (T ≥ n). It is assumed that there is no block synchronization
between stations (there is only symbol synchronization), so that the ﬁrst and last blocks of each
station need not entirely belong to the transmission interval [1,T]. In each block of length n each
of s stations (s ≤ S) that have gained access to the channel transmits one of its M messages
(of course, in diﬀerent blocks of the same station, diﬀerent messages can be transmitted). At the
channel output, we obtain a sequence y =(y
)oflengthT over the quaternary alphabet:
0, a, b,andx. We consider the following model of output sequence generation:
0ifattimet all s stations were silent;
a or b if at time t one station was transmitting a symbol, and this
symbol was a or b, respectively;
x if at time t two or more stations out of s were transmitting.
Supported in part by the Russian Foundation for Basic Research, project no. 06-01-00226.