Dirty-Paper Coding for the Gaussian Multiaccess Channel With Conferencing

Abstract

Abstract-We derive the capacity region of the two-user dirtypaper Gaussian multiaccess channel (MAC) with conferencing encoders. In this MAC, prior to each transmission block, the transmitters can hold a conference in which they can communicate with each other over error-free bit pipes of given capacities. The received signal suffers not only from additive Gaussian noise but also from additive interference, which is known noncausally to the transmitters but not to the receiver. The additive interference is modeled as Gaussian or uniform over a sphere. We show that the interference can be perfectly mitigated, i.e., that the capacity region without interference can also be achieved in its presence. This holds irrespective of whether the transmitters learn the interference before or after the conference. It follows as a corollary that also for the MAC with degraded message sets, the interference can be perfectly mitigated if it is known noncausally to the transmitters. To derive our results, we generalize Costa's single-user writing-on-dirty-paper achievability result to channels with dependent interference and not-necessarily Gaussian noise.

Conferencing in Wyner's asymmetric interference network: Effect of number of rounds

“…The same applies also to the two-user memoryless Gaussian MAC [4]; the three-user Gaussian or discrete memoryless MAC where the transmitters cooperate over "public links" that are observed by all transmitters [9]; and for the compound discrete memoryless MAC [19]. For the three-user memoryless Gaussian MAC with "private" conferencing links where each transmitter can send cooperation information only to its left-neighbour, two conferencing rounds-during which the transmitters share and relay parts of their messages-are sum-rate optimal at high signal-to-noise ratio (SNR) [8].…”

“…Adapting Corollary IV.2 in [4] similarly as in Remark IV.4 of [4], and in view of footnote 10, we obtain the following: If Tx k sends its source message M k to Rx k using dirty-paper coding over spheres [4, Section V] of power P and designed for a channel with normalised noise variance N = 1 + α 2 k P P +1 and interference sequence S n k , and if the rate of the source message…”

“…3 This again ensures that each Rx-conferencing link is used at a rate of at most 1 2 log(1 + P ). 4 Transmitters 1, . .…”

“…It then encodes its source message M k using dirty-paper coding over spheres [6], [4,Section V] 9 of power P and designed for the channel in (102) with additive state sequence S…”

“…In fact, since the state-sequence S n k is not uniform over a sphere, the dirty-paper encoding over spheres needs to be extended as described in the proof of Remark III-5 in [4]. The analysis of this extended dirty-paper coding over spheres only requires that the normalised lengths of the noise and the state sequences are approximately constant and the noise and state sequences are approximately orthogonal [4]. Given event Q k−1 , our setup satisfies these conditions:…”