ISSN 0032-9460, Problems of Information Transmission, 2012, Vol. 48, No. 3, pp. 243–249.
Pleiades Publishing, Inc., 2012.
Original Russian Text
D.S. Osipov, A.A. Frolov, V.V. Zyablov, 2012, published in Problemy Peredachi Informatsii, 2012, Vol. 48, No. 3, pp. 52–59.
Multiple Access System for a Vector
Kharkevich Institute for Information Transmission Problems,
Russian Academy of Sciences, Moscow
firstname.lastname@example.org email@example.com firstname.lastname@example.org
Received January 17, 2012; in ﬁnal form, May 28, 2012
Abstract—We address the problem of constructing a multiple access system for a disjunctive
vector channel, similar to a multiuser channel without intensity information as described in .
To solve the problem, a signal-code construction based on nonbinary codes is proposed. For
the resulting multiple access system, a lower bound on the relative group rate is derived. The
bound coincides asymptotically with an upper bound.
We consider a multiple-user channel of the following type. Assume that the channel consists
of q, q>2, independent nonoverlapping subchannels. Furthermore, it is assumed that multiple
users can simultaneously transmit information over the channel (we denote the number of users
by S, S ≥ 2), and besides at each time a user chooses one of the subchannels for transmission. The
output of the channel is a list of all subchannels at which the transmission was performed. Note
that information about the number of users transmitting in a particular subchannel is not available
at the output of the channel. In addition, the channel is assumed to be noiseless; in other words,
the only obstacle to correct reception of information transmitted by a user is activity of other users
also transmitting information over the channel. The channel model was introduced in . In [2–5],
asymptotic bounds on the capacity of the channel were derived.
Note that the channel model allows for a broader interpretation. Channel inputs (subchannels)
can be viewed as binary vectors of length q. The value of each element of the vector associated with
a certain user depends on whether the user transmits in the subchannel. In this case, the channel
output can be viewed as elementwise disjunction of vectors at the input. Thus, the channel is in
fact a disjunctive vector channel.
Our goals are suggesting a signal-code construction with the use of a channel model described
above and investigating the performance of the multiple access system built on the basis of the
construction. A signal-code construction based on nonbinary codes is introduced. A lower bound
on the relative group rate is derived. The bound coincides asymptotically with an upper bound.
2. DESCRIPTION OF THE SIGNAL-CODE CONSTRUCTION
Consider the above-described model of a vector channel in which S users are transmitting vectors.
Assume that all the users use the same alphabet: symbols of GF (q).
Transmission. Each user encodes information to be transmitted with the help of a q-ary
(n, k, d)codeC (all users use the same code). Consider the process of sending a message by the ith