ETH Series in Information
Theory and its Applications, Vol. 3
edited by Amos Lapidoth
Michèle Angela Wigger,
Cooperation on the Multiple-Access Channel.
1st edition 2008. XVIII, 224 pages, € 64,00.
We study the two-user additive white Gaussian noise (AWGN) multipleaccess channel (MAC), i.e., a scenario where two transmitters communicate with a common receiver and where the receiver observes the sum of the two transmitted signals in additive white Gaussian noise. In the classical MAC the transmitters can cooperate only through the choice of the codebooks but not based on their messages, because each transmitter is completely ignorant of the other transmitter’s message. Here, we consider two variations of the classical MAC where the transmitters have additional means to cooperate. The first variation involves that the two transmitters observe imperfect feedback from the channel outputs, and thus each transmitter can generate its signal also depending on the observed feedback outputs (which depend on both messages). The second variation involves that prior to each transmission block the two transmitters can communicate over noise-free bit-pipes of given capacities. Thus, each transmitter can generate its signal also depending on the observed pipe outputs (which depend on the other transmitter’s message). For the first variation, called the AWGN MAC with imperfect feedback, we study four different kinds of imperfect feedback: 1.) noisy feedback, where both transmitters have feedback that is corrupted by additive white Gaussian noise; 2.) noisy partial feedback, where one transmitter has noisy feedback and the other no feedback; 3.) perfect partial feedback, where one transmitter has perfect feedback and the other no feedback; and 4.) noisy feedback with receiver side-information, where both transmitters have noisy feedback and the receiver is perfectly cognizant of the feedback noises.
For all four kinds of feedback we derive new achievable rate regions. These regions exhibit that, irrespective of the Gaussian feedback-noise variances, for all four kinds of feedback the capacity region with feedback is strictly larger than without. Moreover, for certain channel parameters our new achievable region for perfect partial feedback is strictly larger than the Cover-Leung region. This answers in the negative a question posed by van der Meulen as to whether the Cover-Leung region equals the capacity region of the AWGN MAC with perfect partial feedback. Finally, our achievable region for noisy feedback converges to the perfectfeedback capacity region as both feedback-noise variances tend to 0. For the second variation, called the two-user AWGN MAC with conferencing encoders, we derive the capacity region. Our derivation introduces a new technique for proving optimality of Gaussian distributions in certain optimization problems involving mutual information expressions with a Markovity constraint. This technique is fairly general and can also be used to establish optimality of jointly Gaussian Markov distributions for the Slepian-Wolf region (for the AWGN MAC with a common message) and for the Cover-Leung region (for the AWGN MAC with perfect or perfect partial feedback).
We also consider a Costa-type extension of the AWGNMAC with conferencing encoders where the received signal suffers not only from Gaussian noise but also from Gaussian interference that is acausally known to both transmitters (but not the receiver). We show that the capacity region with interference coincides with the capacity region without interference, irrespective of whether the transmitters learn the interference sequence before or after the conference. It follows as a corollary that for the AWGN MAC with degraded message sets—which is equivalent to a special case of the AWGN MAC with conferencing encoders—the transmitters can perfectly cancel a Gaussian interference if they acausally know the interference. Our Costa-type achievability results generalize to settings with arbitrary (not necessarily Gaussian) ergodic noise. Additionally, we generalize Cohen and Lapidoth’s achievability result for single-user channels with additive white Gaussian interference and independent (not necessarily Gaussian) ergodic noise to channels with dependent interference and noise.
Keywords: additive white Gaussian noise, bit-pipes, capacity region, channel capacity, conferencing encoders, cooperation, Costa, feedback, interference, Markov conditions, multiple-access channel, noisy feedback, partial feedback, writing on dirty paper.
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