364 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 42, NO. 2, MARCH 1996 A Rate-Splitting Approach to the Gaussian Multiple-Access Channel Bixio Rimoldi, Member, IEEE, and Riidiger Urbanke Abstract-It is shown that any point in the capacity region of a Gaussian multiple-access channel is achievable by single-user coding without requiring synchronization among users, provided that each user “splits” data and signal into two parts. Based on this result, a new multiple-access technique called rate-splitting multiple accessing (RSMA) is proposed. RSMA is a code-division multiple-access scheme for the A&-user Gaussian multiple-access channel for which the effort of finding the codes for the M users, of encoding, and of decoding is that of at most 21M- 1 independent point-to-point Gaussian channels. The effects of bursty sources, multipath fading, and inter-cell interference are discussed and directions for further research are indicated. Index Terms- Asynchronous Gaussian multiple-access chan- nel, rate-splitting multiple accessing, successive cancellation, stripping. I. INTRODUCTION T HE purpose of this paper is to shed new light on the structure of the capacity regions of Gaussian multiple- access channels and to suggest a new and promising strategy for implementing practical systems. We suppose at first that the channel is discrete-time and frame-synchronous, with power constraint P = (PI, . . . , PM), where Pi is the power constraint for user i, and noise variance g2 (see Fig. 1). Its capacity region [l]-[8] is the subset of RM containing the rate &f-tuples (RI, . . , RM) with nonnegative components satisfying v’s s {l,...,M}. (1) There are points’ in this capacity region that are known to be achievable with an implementation complexity substantially less than a general point. These are the points which, after a Manuscript received September 9, 1993; revised October 10, 1995. This work was supported by the National Science Foundation under Grants NCR- 9357689 and NCR-9304763. The material in this paper was presented in part at the International Symposium on Information Theory, Trondheim, Norway, June 27-Julyl, 1994. B. E. Rimoldi is with the Department of Electrical Engineering, Electronics Systems and Signals Research Laboratory, Washington University, St. Louis, MO 63130 USA. R. Urbanke was with the Department of Electrical Engineering, Electronics Systems and Signals Research Laboratory, Washington University, St. Louis, MO 63130 USA. He is now with AT&T Bell Laboratories, Murray Hill, NJ 07974 USA. Publisher Item Identifier S 0018-9448(96)01349-l. ‘Throughout this paper, the terms “points” and “rate tuples” are used interchangeably. xf \ Xf + 3- Y” xh 2” Fi . 1. Gaussian multi le-access channel: The received signal at time lc is Y & P = Czi Xzk + 2 , where the noise samples 2’” are i.i.d. zero-mean Gaussian random variables with variance u2, and Xs E R is the symbol transmitted by sender i. possible re-indexing, satisfy Rj 5 f log, ) j=l,...,M. (2) For these points, one can design the multiple-access code by constructing one single-user code for each user j, 1 5 j < M, assuming that user j has power constraint Pj and noise variance g2 + C. z < j Pi on his single-user channel. Unless stated otherwise, we will use the term “code” to mean an ideal random code so that the code for user i is obtained by selecting its [2”Ri] codewords by choosing each codeword independently as an i.i.d. sequence of Gaussian random variables with zero mean and variance P;. Thus the codewords of other users look like Gaussian noise to any given user. Hence, the decoder of user n/r can decode considering the codewords of user 1, . . . , M - 1 as noise. The contribution of user M can then be removed from the received word, and the procedure can be repeated until each codeword has been decoded. This idea is due to Bergmans and Cover [9] and to Wyner [6], who observed that the vertices of the capacity region satisfy (2) with equality (see the Appendix for a proof of this fact). Another account of this idea was given in [4]. The decoding procedure described above is known variously as onion peeling, stripping, successive cancellation, and superposition coding. In the communication-engineering community, the term interference cancellation has been used to describe the same decoding process, but the motivation there has been to alleviate the near/far effect in spread-spectrum multiple accessing rather than trying to achieve capacity at lower complexity. In the sequel, we will use the term single- user coding to describe the procedure of constructing and assigning a single-user code to each user combined with a OOlS-9448/96$05.00 0 1996 IEEERIMOLDI AND URBANE A RATE-SPLITTING APPROACH TO THE GAUSSIAN MULTIPLE-ACCESS CHANNEL - - TRANSMITTER VIRTUAL CHANNEL RECEIVER Fig. 2. A multiple-access system based on rate-splitting multiple accessing successive cancellation decoder at the receiver. When focusing on the actual decoding procedure, we will use the term single- user decoding. The rate tuples contained in the capacity region but not of the type described above were previously known to be attainable only by one of two methods. These “difficult” rate tuples include the important case where all users have the same power constraint and the same rate. The first method to achieve these difficult rate tuples is joint encoding/decoding of all users. This is very difficult to implement in practice (even for the synchronous case) since random codes have a decoding complexity of the order of 2nRsum, where R,,, = RI + ... + RM is the sum rate and n is the block length, and since the construction of (joint) codes in such a way as to approach the achievable rate region seems to be a formidable task. To our knowledge, the only channel model