ISSN 0032-9460, Problems of Information Transmission, 2013, Vol. 49, No. 2, pp. 111–126.
Pleiades Publishing, Inc., 2013.
Original Russian Text
E.V. Pustovalov, A.M. Turlikov, 2013, published in Problemy Peredachi Informatsii, 2013, Vol. 49, No. 2, pp. 17–33.
Random Multiple Access in a Vector
E. V. Pustovalov and A. M. Turlikov
St. Petersburg State University of Aerospace Instrumentation
Received October 12, 2012; in ﬁnal form, March 1, 2013
Abstract—We consider a random multiple access (RMA) procedure in a vector disjunctive
channel. We show that exploiting properties of the channel allows one to reduce collision
resolution time and thus increase the maximal stable throughput (MST) of RMA algorithms
in this channel. We propose an algorithm, belonging to the class of splitting algorithms, which
achieves the MST of 0.603.
Random multiple access (RMA) algorithms are an eﬃcient way for providing users’ access to
a common channel in communication systems with low intensity traﬃc. They ensure low packet
delay even in the case of a large number of users. The mean packet delay in RMA algorithms grows
with the input ﬂow rate, and an RMA algorithm cannot provide ﬁnite delay if the overall traﬃc
intensity exceeds a certain threshold, referred to as the maximal stable throughput (MST) of the
algorithm. The MST value depends on a particular RMA algorithm.
At the end of 1970s, an RMA model was introduced in , which will be referred to as classical
hereafter. The classical RMA model assumes that if several packets are transmitted simultaneously,
the corresponding signals will be corrupted due to interference, and none of the packets can be
received correctly. This event is called a collision. To resolve a collision, all colliding packets
should be retransmitted according to the rules of the RMA algorithm in use. For the classical
RMA algorithm, an MST upper bound of 0.567 is proved , and the best known algorithm is
a splitting algorithm with MST of 0.4877  (though algorithms with higher MST are shown to
Recently, a novel RMA model with so-called successive interference cancellation was introduced.
The model assumes that when a collision occurs, a signal received from the channel can be stored
in the receiver memory, and after one of the users retransmits its data, the successfully received
packet can be “subtracted” from the stored signal so that to recover the remaining packet. Thus,
we can reduce the total number of retransmissions and thus increase the MST. This procedure was
called SIC (Successive Interference Cancellation). The best known algorithm constructed in the
SIC framework is SICTA (Successive Interference Cancellation Tree Algorithm), belonging to the
class of tree (stack-based) algorithms, which achieves the MST of 0.693 .
However, SICTA performs well in an ideal adder channel only. It is assumed that when a
collision of any multiplicity occurs, by successive subtraction of successively received packets it is
ﬁnally possible to recover the remaining packet. If errors in interference cancellation occur, so that
remaining packets become impossible to recover, then SICTA will resolve the collision inﬁnitely long.
Another drawback of SICTA is that it may also fail if there are restrictions on the memory used to