State of the cognitive interference channel: a new unified inner bound

The capacity region of the interference channel in which one transmitter non-causally knows the message of the other, termed the cognitive interference channel, has remained open since its inception in 2005. A number of subtly differing achievable rate regions and outer bounds have been derived, some of which are tight under specific conditions. In this work we present a new unified inner bound for the discrete memoryless cognitive interference channel. We show explicitly how it encompasses all known discrete memoryless achievable rate regions as special cases. The presented achievable region was recently used in deriving the capacity region of the general deterministic cognitive interference channel, and thus also the linear high-SNR deterministic approximation of the Gaussian cognitive interference channel. The high-SNR deterministic approximation was then used to obtain the capacity of the Gaussian cognitive interference channel to within 1.87 bits.Comment: Presented at the 2010 International Zurich Seminar on Communications - an 2nd updated version

On the Capacity Region of the Two-User Interference Channel

One of the key open problems in network information theory is to obtain the capacity region for the two-user Interference Channel (IC). In this paper, new results are derived for this channel. As a first result, a noisy interference regime is given for the general IC where the sum-rate capacity is achieved by treating interference as noise at the receivers. To obtain this result, a single-letter outer bound in terms of some auxiliary random variables is first established for the sum-rate capacity of the general IC and then those conditions under which this outer bound is reduced to the achievable sum-rate given by the simple treating interference as noise strategy are specified. The main benefit of this approach is that it is applicable for any two-user IC (potentially non-Gaussian). For the special case of Gaussian channel, our result is reduced to the noisy interference regime that was previously obtained. Next, some results are given on the Han-Kobayashi (HK) achievable rate region. The evaluation of this rate region is in general difficult. In this paper, a simple characterization of the HK rate region is derived for some special cases, specifically, for a novel very weak interference regime. As a remarkable characteristic, it is shown that for this very weak interference regime, the achievable sum-rate due to the HK region is identical to the one given by the simple treating interference as noise strategy.Comment: 12 pages. In this paper a noisy interference regime is identified for any two-user interference channel (potentially non-Gaussian). For conference publicatio

Achievable and Crystallized Rate Regions of the Interference Channel with Interference as Noise

The interference channel achievable rate region is presented when the interference is treated as noise. The formulation starts with the 2-user channel, and then extends the results to the n-user case. The rate region is found to be the convex hull of the union of n power control rate regions, where each power control rate region is upperbounded by a (n-1)-dimensional hyper-surface characterized by having one of the transmitters transmitting at full power. The convex hull operation lends itself to a time-sharing operation depending on the convexity behavior of those hyper-surfaces. In order to know when to use time-sharing rather than power control, the paper studies the hyper-surfaces convexity behavior in details for the 2-user channel with specific results pertaining to the symmetric channel. It is observed that most of the achievable rate region can be covered by using simple On/Off binary power control in conjunction with time-sharing. The binary power control creates several corner points in the n-dimensional space. The crystallized rate region, named after its resulting crystal shape, is hence presented as the time-sharing convex hull imposed onto those corner points; thereby offering a viable new perspective of looking at the achievable rate region of the interference channel.Comment: 28 pages, 12 figures, to appear in IEEE Transactions of Wireless Communicatio

Lattice Codes for Many-to-One Interference Channels With and Without Cognitive Messages

A new achievable rate region is given for the Gaussian cognitive many-to-one interference channel. The proposed novel coding scheme is based on the compute-and-forward approach with lattice codes. Using the idea of decoding sums of codewords, our scheme improves considerably upon the conventional coding schemes which treat interference as noise or decode messages simultaneously. Our strategy also extends directly to the usual many-to-one interference channels without cognitive messages. Comparing to the usual compute-and-forward scheme where a fixed lattice is used for the code construction, the novel scheme employs scaled lattices and also encompasses key ingredients of the existing schemes for the cognitive interference channel. With this new component, our scheme achieves a larger rate region in general. For some symmetric channel settings, new constant gap or capacity results are established, which are independent of the number of users in the system.Comment: To appear in IEEE Transactions on Information Theor