Combining Queueing Theory with Information Theory for Multiaccess

We develop and analyze a multiaccess communi-In this paper we present an analysis of a system with just cation model over the additive Gaussian noise channel. The enough complexity to exhibit both aspects of a multiaccess framework is information-theoretic; nonetheless it also incorpo-problem. In the analysis we use tools borrowed from both rates some queuteing-theoretic aspects of the problem. queueing theory and information theory. As a result, we are able to indicate the trade-offs between queueing-theoretic I. INTRODUCTION quantities and information-theoretic quantities, such as the A MULTIACCESS communication system consists of a trade-off between delay and error probability. set of transmitters sending information to a single receiver. Each transmitter is fed by an information source II. TE MODEL AND A PRELIMINARY ANALYSIS generating a sequence of messages; the successive messages arrive for transmission at random times. We will assume Our multiaccess environment consists of an additive Gauss-arrive for transmission at random times. We will assume oise channel with noise density No/2 and two-sided that the information sources that feed the transmitters are 'an n bandwidth 2W. All the transmitters have equal power P. independent processes and that the messages generated by a T h e messages are generated in accordance equal Poisson given information source form an independent sequence. The The messages are generate and we wil accordance with message is signal received at the receiver is a stochastic function of the roc a signals sent by the transmitters. We will further assume that transmitted by a different transmitter. In effect, there are an the feedback from the receiver is limited; in particular, the infinite number of transmitters, each handling one message. This assumption simplifies the model so that we do not have possibility of any transmitter observing the received signal is This assumption simplifies the model so that we do not have ruled out. to consider message queues at individual transmitters. Each From the description above, one sees that there are two message consists of a sequence of bits of (possibly) variable issues of interest: (1) the random arrival of the messages to the length. As soon as the message arrives, the transmitter encodes transmitters, and (2) the noise and interference that affect the it into a time signal of infinite duration (henceforth codeword) transmission of these messages. The main bodies of research i and starts transmitting it. However, the transmitter will-not multiaccess communications seem to treat these two …