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

Multiaccess Channels with State Known to Some Encoders and Independent Messages

We consider a state-dependent multiaccess channel (MAC) with state non-causally known to some encoders. We derive an inner bound for the capacity region in the general discrete memoryless case and specialize to a binary noiseless case. In the case of maximum entropy channel state, we obtain the capacity region for binary noiseless MAC with one informed encoder by deriving a non-trivial outer bound for this case. For a Gaussian state-dependent MAC with one encoder being informed of the channel state, we present an inner bound by applying a slightly generalized dirty paper coding (GDPC) at the informed encoder that allows for partial state cancellation, and a trivial outer bound by providing channel state to the decoder also. The uninformed encoders benefit from the state cancellation in terms of achievable rates, however, appears that GDPC cannot completely eliminate the effect of the channel state on the achievable rate region, in contrast to the case of all encoders being informed. In the case of infinite state variance, we analyze how the uninformed encoder benefits from the informed encoder's actions using the inner bound and also provide a non-trivial outer bound for this case which is better than the trivial outer bound.Comment: Accepted to EURASIP Journal on Wireless Communication and Networking, Feb. 200

On the Capacity of a Class of MIMO Cognitive Radios

Cognitive radios have been studied recently as a means to utilize spectrum in a more efficient manner. This paper focuses on the fundamental limits of operation of a MIMO cognitive radio network with a single licensed user and a single cognitive user. The channel setting is equivalent to an interference channel with degraded message sets (with the cognitive user having access to the licensed user's message). An achievable region and an outer bound is derived for such a network setting. It is shown that under certain conditions, the achievable region is optimal for a portion of the capacity region that includes sum capacity.Comment: 13 pages, 8 figures, Accepted for publication in Journal of Selected Topics in Signal Processing (JSTSP) - Special Issue on Dynamic Spectrum Acces