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S

ETH Series in Information Theory and its Applications,
Vol. 3
edited by Amos Lapidoth
Michèle Angela
Wigger,
Cooperation on the MultipleAccess
Channel.
1^{st} edition 2008. XVIII, 224 pages, € 64,00.
ISBN 3866282311
Abstract
We study the twouser 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 noisefree bitpipes 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
sideinformation, 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 feedbacknoise 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 CoverLeung region. This answers in the negative a
question posed by van der Meulen as to whether the CoverLeung 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 feedbacknoise variances tend to 0. For the second variation,
called the twouser 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 SlepianWolf region (for the AWGN MAC with a common
message) and for the CoverLeung region (for the AWGN MAC with perfect or
perfect partial feedback).
We also consider a Costatype 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 Costatype
achievability results generalize to settings with arbitrary (not necessarily
Gaussian) ergodic noise. Additionally, we generalize Cohen and Lapidoth’s
achievability result for singleuser 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, bitpipes, capacity region, channel capacity,
conferencing encoders, cooperation, Costa, feedback, interference, Markov
conditions, multipleaccess channel, noisy feedback, partial feedback, writing
on dirty paper.
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and its Applications" im HartungGorre
Verlag
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