2 research outputs found
Trade-off between Communication and Cooperation in the Interference Channel
We consider the problem of coding over the multi-user Interference Channel
(IC). It is well-known that aligning the interfering signals results in
improved achievable rates in certain setups involving more than two users. We
argue that in the general interference problem, senders face a tradeoff between
communicating their message to their corresponding decoder or cooperating with
other users by aligning their signals. Traditionally, interference alignment is
carried out using structured codes such as linear codes and group codes. We
show through an example that the usual structured coding schemes used for
interference neutralization lack the necessary flexibility to optimize this
tradeoff. Based on this intuition, we propose a new class of codes for this
problem. We use the example to show that the application of these codes gives
strict improvements in terms of achievable rates. Finally, we derive a new
achievable region for the three user IC which strictly improves upon the
previously known inner bounds for this problem
How to Compute Modulo Prime-Power Sums ?
A new class of structured codes called Quasi Group Codes (QGC) is introduced.
A QGC is a subset of a group code. In contrast with group codes, QGCs are not
closed under group addition. The parameters of the QGC can be chosen such that
the size of is equal to any number between
and . We analyze the performance of a
specific class of QGCs. This class of QGCs is constructed by assigning
single-letter distributions to the indices of the codewords in a group code.
Then, the QGC is defined as the set of codewords whose index is in the typical
set corresponding to these single-letter distributions. The asymptotic
performance limits of this class of QGCs is characterized using single-letter
information quantities. Corresponding covering and packing bounds are derived.
It is shown that the point-to-point channel capacity and optimal
rate-distortion function are achievable using QGCs. Coding strategies based on
QGCs are introduced for three fundamental multi-terminal problems: the
K\"orner-Marton problem for modulo prime-power sums, computation over the
multiple access channel (MAC), and MAC with distributed states. For each
problem a single-letter achievable rate-region is derived. It is shown, through
examples, that the coding strategies improve upon the previous strategies based
on unstructured codes, linear codes and group codes.Comment: 52 pages, Submitted to IEEE Transaction on Information Theor