ISSN 0032-9460, Problems of Information Transmission, 2014, Vol. 50, No. 2, pp. 133–143.
Pleiades Publishing, Inc., 2014.
Original Russian Text
A.A. Frolov, V.V. Zyablov, 2014, published in Problemy Peredachi Informatsii, 2014, Vol. 50, No. 2, pp. 20–30.
On the Capacity of a Multiple-Access
Vector Adder Channel
A. A. Frolov and V. V. Zyablov
Kharkevich Institute for Information Transmission Problems,
Russian Academy of Sciences, Moscow, Russia
Received September 25, 2013; in ﬁnal form, February 27, 2014
Abstract—We investigate the capacity of the Q-frequency S-user vector adder channel (chan-
nel with intensity information) introduced by Chang and Wolf. Both coordinated and unco-
ordinated types of transmission are considered. Asymptotic (under the conditions Q →∞,
S = γQ,0<γ<∞) upper and lower bounds on the relative (per subchannel) capacity are
derived. The lower bound for the coordinated case is shown to increase with γ.Atthesame
time, the relative capacity for the uncoordinated case is upper bounded by a constant.
In  two multi-user channel models were introduced: the A-channel (or channel without in-
tensity information) and B-channel (or channel with intensity information). The capacity of the
A-channel was investigated in [1,2] for the case of coordinated transmission and in [3–7] for the case
of uncoordinated transmission (the terminology is borrowed from [8, 9]).
Note that the A-channel
is in fact a vector disjunctive channel (OR channel) [10, 11].
In this paper we investigate the capacity of the B-channel. The B-channel is a noiseless multi-
user vector adder channel. Denote the number of active users by S, S ≥ 2. Ataﬁxedtimeinstantτ ,
channel inputs are binary vectors x
, i =1, 2,...,S,oflengthQ (the number of frequencies or
subchannels) and of weight 1, and the channel output at time τ is given by the elementwise sum
of vectors at the input
Note that the elements are added as real numbers.
The capacity of the B-channel for the coordinated case was investigated in  when Q is ﬁxed
and S →∞. In this paper we are interested in the following asymptotics: Q →∞, S = γQ
(0 <γ<∞). If we pass to the limit as Q →∞, then the result of  corresponds to the case γ →∞.
We also investigate the asymptotic capacity of the B-channel for uncoordinated transmission, i.e.,
the type of transmission where a user transmits information independently of other users. This
fact allows us to consider other users as noise (single-user detection). Uncoordinated transmission
is preferable for high-rate applications, where joint decoding is not possible for complexity reasons.
Our contribution is as follows. Asymptotic (under the conditions Q →∞, S = γQ,0<γ<∞)
upper and lower bounds on the relative (per subchannel) capacity are derived. The lower bound
Supported in part by the Russian Foundation for Basic Research, project no. 13-01-12458-oﬁ-m2.
In the literature, the terms “synchronous” and “asynchronous” are also used.