4 research outputs found
Capacity Bounds for the -User Gaussian Interference Channel
The capacity region of the -user Gaussian interference channel (GIC) is a
long-standing open problem and even capacity outer bounds are little known in
general. A significant progress on degrees-of-freedom (DoF) analysis, a
first-order capacity approximation, for the -user GIC has provided new
important insights into the problem of interest in the high signal-to-noise
ratio (SNR) limit. However, such capacity approximation has been observed to
have some limitations in predicting the capacity at \emph{finite} SNR. In this
work, we develop a new upper-bounding technique that utilizes a new type of
genie signal and applies \emph{time sharing} to genie signals at receivers.
Based on this technique, we derive new upper bounds on the sum capacity of the
three-user GIC with constant, complex channel coefficients and then generalize
to the -user case to better understand sum-rate behavior at finite SNR. We
also provide closed-form expressions of our upper bounds on the capacity of the
-user symmetric GIC easily computable for \emph{any} . From the
perspectives of our results, some sum-rate behavior at finite SNR is in line
with the insights given by the known DoF results, while some others are not. In
particular, the well-known DoF achievable for almost all constant real
channel coefficients turns out to be not embodied as a substantial performance
gain over a certain range of the cross-channel coefficient in the -user
symmetric real case especially for \emph{large} . We further investigate the
impact of phase offset between the direct-channel coefficient and the
cross-channel coefficients on the sum-rate upper bound for the three-user
\emph{complex} GIC. As a consequence, we aim to provide new findings that could
not be predicted by the prior works on DoF of GICs.Comment: Presented in part at ISIT 2015, submitted to IEEE Transactions on
Information Theory on July 2015, and revised on January 201
Capacity Results for Interference Networks and Nested Cut-Set Bound
In this thesis, a full characterization of the sum-rate capacity for degraded interference networks with any number of transmitters, any number of receivers, and any possible distribution of messages among transmitters and receivers is established. It is proved that a successive decoding scheme is sum-rate optimal for these networks. Moreover, it is shown that the transmission of only a certain subset of messages is sufficient to achieve the sum-rate capacity for such networks. Algorithms are presented to determine this subset of messages explicitly. The sum-rate expression for the degraded networks is then used to derive a unified outer bound on the sum-rate capacity of arbitrary (non-degraded) interference networks. Several variations of degraded networks are identified for which the derived outer bound is sum-rate optimal. Specifically, noisy interference regimes are derived for certain classes of multi-user/multi-message large interference networks. Also, network scenarios are identified where the incorporation of both successive decoding and treating interference as noise achieves their sum-rate capacity.
Next, by taking insight from the results for degraded networks, an extension to the standard cut-set bound for general communication networks is presented which is referred to as nested cut-set bound. This bound is derived by applying a series of cuts in a nested configuration to the network first and then bounding the information rate that flows through the cuts. The key idea for bounding step is indeed to impose a degraded arrangement among the receivers corresponding to the cuts. Therefore, the bound is in fact a generalization of the outer bound for interference networks: here cooperative relaying nodes are introduced into the problem as well but the proof style for the derivation of the outer bound remains the same. The nested cut-set bound, which uniformly holds for all general communication networks of arbitrary large sizes where any subset of nodes may cooperatively communicate to any other subset of them, is indeed tighter than the cut-set bound for networks with more than one receiver. Moreover, it includes the generalized cut-set bound for deterministic networks reported by Shomorony and Avestimehr which was originally a special case of the outer bound established for the interference networks by the author (2012).
Finally, capacity bounds for the two-user interference channel with cooperative receivers via conferencing links of finite capacities are investigated. The capacity results known for this communication scenario are limited to a very few special cases of the one-sided channel. One of the major challenges in analyzing such cooperative networks is how to establish efficient capacity outer
iv
bounds for them. In this thesis, by applying new techniques, novel capacity outer bounds are presented for the interference channels with conferencing users. Using the outer bounds, several new capacity results are proved for interesting channels with unidirectional cooperation in strong and mixed interference regimes. A fact is that the conferencing link (between receivers) may be utilized to provide one receiver with information about its corresponding signal or its non-corresponding signal (interference signal). As an interesting consequence, it is demonstrated that both strategies can be helpful to achieve the capacity of the channel. Lastly, for the case of Gaussian interference channel with conferencing receivers, it is argued that our outer bound is strictly tighter than the previous one derived by Wang and Tse