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 Gaussarrive 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 issues as transmit for the whole duration of the signal; it will transmit if they were separable [1]. The collision resolution approach only until the receiver decodes the; message and instructs focuses on the random arrival of the-messages but ignores the transmitter to stop. (see Fig. 1.) Thus, if the system, is noise and trivializes the interference of the-transmitted signals; stable, with probability one, only a finite initial segment of the e.g., [2] , [3] . The multiaccess information4heoretic approach; infinite duration codeword will be transmitted 3 The decoder on the other hand, develops accurate models for the transmis treats each transmitter independently; each message is decoded sion process (noise and interference) but ignores the random regarding the other transmissions as noise; arrival of the messages, 1 e.g., [41-[7]. In addition, one can say If there are n active transmitters at a given time, the signal.. arrival of the oversimpl o that the results generated by the to-noise ratio (SNR) for-any of these active transmitters, is with some oversimplification that the results. generated by the P/((n -1)P+ N 0 W). At this point let us assume that the twoapproachesare dierent Theinformat P/((n -1)P + NoW). At this point let us assume that the two approaches are ocidiffrent character. The informationdecoder can resolve theoretic results mostfI:stat: upp p and lower bounds (which sometimes coincide) itlpierfformance of the best possible w scheme, whereas collision resolution results mostly analyze . (n -1)P+ NoW the performance-of particular algorithms., nats 3 per unit time for each transmitter. 4 Let us emphasize that Manuscript received September-30A.1994; revised Apri-l,. 1995. This work this is not a justified assmption en though the SNR see was supported by the U.S. Army Research Office, Grant DAAL03-86-K-0171. I. E. Telatar is with AT&T Bell Laboratories, Murray Hill. NJ 07974 US:' 2he radrwil noticthatwe.have assumed-thatthe transmitted signals R. G. Gallager is with the Electrical Engineering and Computer Science Department and the Laboratory of Information and Decision Systems, Mass-arc of finite duration and also of finite bandwidtl We treat this contradiction achusetts Institute of Technology. Cambridge, MA 02139 USA. as a technicality since the signals of real transmitters are-of finite duration-IEEE Log Number 9412646. and bandlimited in an approximate senst Air analysis d-la Wyner (81 would. have been more desirable.7---An information theorist will rightly point out that the randomness in the arrival process should be. taken care of by appropriate source codingt. W will use natural unitsfromlowom-lna-t = ogosie b.. -.. -However, that would introduce large delays, rendering analysis of delay in 4 Thia_ is the capacity. of a Gaussian channel with SNR Pf((-.-1)P + communication impossible. No W). --0733-8716/95$04.00 @ 1995 IEEE
The stability and delay of multi-access systems with an infinite number of transmitters and with a simplified physical layer were studied in REF .
Combining queueing theory with information theory for multiaccess
IEEE J. Sel. Areas Commun.
IEEE J. Sel. Areas Commun.
Computer Science