Inner and Outer Bounds for the Gaussian Cognitive Interference Channel and New Capacity Results

The capacity of the Gaussian cognitive interference channel, a variation of the classical two-user interference channel where one of the transmitters (referred to as cognitive) has knowledge of both messages, is known in several parameter regimes but remains unknown in general. In this paper we provide a comparative overview of this channel model as we proceed through our contributions: we present a new outer bound based on the idea of a broadcast channel with degraded message sets, and another series of outer bounds obtained by transforming the cognitive channel into channels with known capacity. We specialize the largest known inner bound derived for the discrete memoryless channel to the Gaussian noise channel and present several simplified schemes evaluated for Gaussian inputs in closed form which we use to prove a number of results. These include a new set of capacity results for the a) "primary decodes cognitive" regime, a subset of the "strong interference" regime that is not included in the "very strong interference" regime for which capacity was known, and for the b) "S-channel" in which the primary transmitter does not interfere with the cognitive receiver. Next, for a general Gaussian cognitive interference channel, we determine the capacity to within one bit/s/Hz and to within a factor two regardless of channel parameters, thus establishing rate performance guarantees at high and low SNR, respectively. We also show how different simplified transmission schemes achieve a constant gap between inner and outer bound for specific channels. Finally, we numerically evaluate and compare the various simplified achievable rate regions and outer bounds in parameter regimes where capacity is unknown, leading to further insight on the capacity region of the Gaussian cognitive interference channel.Comment: submitted to IEEE transaction of Information Theor

Some Properties Of Memoryless Multiterminal Interference Channels

This paper examines some properties of memoryless multiterminal interference channels. A general formula for the capacity of such channels is presented. However this formula does not easily lend itself to computation. Motivated by the fact that for a single user memoryless channel (l/N)Sup[ I(X;Y) ] is independent of N (where X and Y are N-vectors and the suprema is taken over all probability distributions on X), we are investigating the possibility that the general capacity formula has an analogous simplification. A specific example of a Gaussian interference channel with two independent users is considered. It is shown that certain probability distributions for N=2 achieve points on the boundary of the capacity region. We hope that some form of this result will generalize to other multiterminal communication channels, and possibly give some insight into the nature of the channel capacity in terms of a single-letter description. Presently, the capacity region of such channels is, in general, unknown

Capacity Analysis for Gaussian and Discrete Memoryless Interference Networks

Interference is an important issue for wireless communication systems where multiple uncoordinated users try to access to a common medium. The problem is even more crucial for next-generation cellular networks where frequency reuse becomes ever more intense, leading to more closely placed co-channel cells. This thesis describes our attempt to understand the impact of interference on communication performance as well as optimal ways to handle interference. From the theoretical point of view, we examine how interference affects the fundamental performance limits, and provide insights on how interference should be treated for various channel models under different operating conditions. From the practical design point of view, we provide solutions to improve the system performance under unknown interference using multiple independent receptions of the same information. For the simple two-user Gaussian interference channel, we establish that the simple Frequency Division Multiplexing (FDM) technique suffices to provide the optimal sum- rate within the largest computable subregion of the general achievable rate region for a certain interference range. For the two-user discrete memoryless interference channels, we characterize different interference regimes as well as the corresponding capacity results. They include one- sided weak interference and mixed interference conditions. The sum-rate capacities are derived in both cases. The conditions, capacity expressions, as well as the capacity achieving schemes are analogous to those of the Gaussian channel model. The study also leads to new outer bounds that can be used to resolve the capacities of several new discrete memoryless interference channels. A three-user interference up-link transmission model is introduced. By examining how interference affects the behavior of the performance limits, we capture the differences and similarities between the traditional two-user channel model and the channel model with more than two users. If the interference is very strong, the capacity region is just a simple extension of the two-user case. For the strong interference case, a line segment on the boundary of the capacity region is attained. When there are links with weak interference, the performance limits behave very differently from that of the two-user case: there is no single case that is found of which treating interference as noise is optimal. In particular, for a subclass of Gaussian channels with mixed interference, a boundary point of the capacity region is determined. For the Gaussian channel with weak interference, sum capacities are obtained under various channel coefficients and power constraint conditions. The optimalities in all the cases are obtained by decoding part of the interference. Finally, we investigate a topic that has practical ramifications in real communication systems. We consider in particular a diversity reception system where independently copies of low density parity check (LDPC) coded signals are received. Relying only on non-coherent reception in a highly dynamic environment with unknown interference, soft-decision combining is achieved whose performance is shown to improve significantly over existing approaches that rely on hard decision combining

Capacity of interference networks : achievable regions and outer bounds

textIn an interference network, multiple transmitters communicate with multiple receivers using the same communication channel. The capacity region of an interference network is defined as the set of data rates that can be simultaneously achieved by the users of the network. One of the most important example of an interference network is the wireless network, where the communication channel is the wireless channel. Wireless interference networks are known to be interference limited rather than noise limited since the interference power level at the receivers (caused by other user's transmissions) is much higher than the noise power level. Most wireless communication systems deployed today employ transmission strategies where the interfering signals are treated in the same manner as thermal noise. Such strategies are known to be suboptimal (in terms of achieving higher data rates), because the interfering signals generated by other transmitters have a structure to them that is very different from that of random thermal noise. Hence, there is a need to design transmission strategies that exploit this structure of the interfering signals to achieve higher data rates. However, determining optimal strategies for mitigating interference has been a long standing open problem. In fact, even for the simplest interference network with just two users, the capacity region is unknown. In this dissertation, we will investigate the capacity region of several models of interference channels. We will derive limits on achievable data rates and design effective transmission strategies that come close to achieving the limits. We will investigate two kinds of networks - "small" (usually characterized by two transmitters and two receivers) and "large" where the number of users is large.Electrical and Computer Engineerin

A Theory of Network Equivalence, Parts I and II

A family of equivalence tools for bounding network capacities is introduced. Part I treats networks of point-to-point channels. The main result is roughly as follows. Given a network of noisy, independent, memoryless point-to-point channels, a collection of communication demands can be met on the given network if and only if it can be met on another network where each noisy channel is replaced by a noiseless bit pipe with throughput equal to the noisy channel capacity. This result was known previously for the case of a single-source multicast demand. The result given here treats general demands -- including, for example, multiple unicast demands -- and applies even when the achievable rate region for the corresponding demands is unknown in the noiseless network. In part II, definitions of upper and lower bounding channel models for general channels are introduced. By these definitions, a collection of communication demands can be met on a network of independent channels if it can be met on a network where each channel is replaced by its lower bounding model andonly if it can be met on a network where each channel is replaced by its upper bounding model. This work derives general conditions under which a network of noiseless bit pipes is an upper or lower bounding model for a multiterminal channel. Example upper and lower bounding models for broadcast, multiple access, and interference channels are given. It is then shown that bounding the difference between the upper and lower bounding models for a given channel yields bounds on the accuracy of network capacity bounds derived using those models. By bounding the capacity of a network of independent noisy channels by the network coding capacity of a network of noiseless bit pipes, this approach represents one step towards the goal of building computational tools for bounding network capacities.Comment: 91 pages, 18 figures. Submitted to the IEEE Transactions on Information Theory on April 14, 2010. Draft