Abstract-The cognitive interference channel is a two-user interference channel in which one transmitter is non-causally provided with the message of the other transmitter. This channel model has been extensively studied in the past years and capacity results have been proved for certain classes of channels. This paper presents new inner and outer bounds for the capacity region of the cognitive interference channel, as well as new capacity results. Previously proposed outer bounds are expressed in terms of auxiliary random variables for which no cardinality constraint of their alphabet is known. Consequently, it is not possible to evaluate such outer bounds explicitly for a given channel. The outer bound derived in this work is based on an idea originally devised by Sato for channels without receiver cooperation and results in an outer bound that does not contain auxiliary random variables, thus allowing it to be more easily evaluated. The inner bound presented in this work-which includes rate splitting, superposition coding, a broadcast channel-like binning scheme and Gel'fand Pinsker coding-is the largest known to date and is explicitly shown to include all previously proposed achievable rate regions. The novel inner and outer bounds are shown to coincide in certain cases. In particular, capacity is proved for a class of channels in the so-called "better cognitive decoding" regime, which includes the regimes in which capacity was known. Finally, the capacity region of the semi-deterministic cognitive interference channel, in which the signal at the cognitive receiver is an arbitrary deterministic function of the channel inputs, is established.Index Terms-Achievable region, better cognitive decoding regime, capacity, cognitive channel, cognitive interference channel, inner bound, interference channel with degraded message sets, outer bound, semi-deterministic channel.

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. degraded message sets [6], or the cognitive interference channel [7]. This channel consists of a two-user interference channel, where one transmitter-receiver pair is referred to as the primary user and the other as the cognitive. The primary transmitter has knowledge of one of the two independent messages to be sent, while the cognitive transmitter has full, non-causal knowledge of both messages, thus idealizing the cognitive user's ability to detect transmissions taking place in the network. Since the cognitive transmitter can "broadcast" information to both receivers, the capacity of the cognitive interference channel contains features of both the interference and the broadcast channel.Although the assumption of full, non-causal knowledge of the primary user's message at the cognitive transmitter might not be practical, the simplicity of the resulting model leads to closed form results and provides powerful insights on the role of unilateral cooperation among the users. The more practical scenario of causal unilateral cooperation may be studied in the framework of interference channels with generalized feedback of [8] (and references therein), but is outside the scope of this work. A. Past workCapacity results. The co...

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In this paper, we first present an outer bound for a general interference channel with a cognitive relay, i.e., a relay that has non-causal knowledge of both independent messages transmitted in the interference channel. This outer bound reduces to the capacity region of the deterministic broadcast channel and of the deterministic cognitive interference channel through nulling of certain channel inputs. It does not, however, reduce to that of certain deterministic interference channels for which capacity is known. As such, we subsequently tighten the bound for channels whose outputs satisfy an "invertibility" condition. This second outer bound now reduces to the capacity of this special class of deterministic interference channels. The second outer bound is further tightened for the high SNR deterministic approximation of the Gaussian interference channel with a cognitive relay by exploiting the special structure of the interference. We provide an example that suggests that this third bound is tight in at least some parameter regimes for the high SNR deterministic approximation of the Gaussian channel. Another example shows that the third bound is capacity in the special case where there are no direct links between the non-cognitive transmitters.Index Terms-cognitive channel, interference channel, broadcast channel, relay channel, deterministic channel, high SNR deterministic approximation.

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