Stefano Rini

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. This paper provides a comparative overview of this channel model as it proceeds through the following contributions. First, several outer bounds are presented: (a) a new outer bound based on the idea of a broadcast channel with degraded message sets, and (b) an outer bound obtained by transforming the channel into channels with known capacity. Next, a compact Fourier-Motzkin eliminated version of the largest known inner bound derived for the discrete memoryless cognitive interference channel is presented and specialized to the Gaussian noise case, where several simplified schemes with jointly Gaussian input are evaluated in closed form and later used to prove a number of results. These include a new set of capacity results for: (a) the “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 (b) the “S-channel in strong interference” in which the primary transmitter does not interfere with the cognitive receiver and the primary receiver experiences strong interference. Next, for a general Gaussian channel the capacity is determined to within one bit/s/Hz and to within a factor two regardless of the channel parameters, thus establishing rate performance guarantees at high and low SNR, respectively. The paper concludes with numerical evaluations and comparisons of the various simplified achievable rate regions and outer bounds in parameter regimes where capacity is unknown, leading to further insight on the capacity region.

Outer bounds for the interference channel with a cognitive relay

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 the 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 the special class of deterministic interference channels for which capacity is known. The second outer bound is further tightened for the high-SNR deterministic approximation of the Gaussian channel 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.

New results on the capacity of the Gaussian cognitive interference channel

The capacity of the two-user Gaussian cognitive interference channel, a variation of the classical interference channel where one of the transmitters has knowledge of both messages, is known in several parameter regimes but remains unknown in general. In this paper, we consider the following achievable scheme: the cognitive transmitter pre-codes its message against the interference created at its intended receiver by the primary user, and the cognitive receiver only decodes its intended message, similar to the optimal scheme for “weak interference”; the primary decoder decodes both messages, similar to the optimal scheme for “very strong interference”. Although the cognitive message is pre-coded against the primary message, by decoding it, the primary receiver obtains information about its own message, thereby improving its rate. We show: (1) that this proposed scheme achieves capacity in what we term the “primary decodes cognitive” regime, i.e., a subset of the “strong interference” regime that is not included in the “very strong interference” regime for which capacity was known; (2) that this scheme is within one bit/s/Hz and a factor two of capacity for a large set of parameters, thus improving the best known constant gap result; (3) we provide insights into the trade-off between interference pre-coding at the cognitive encoder and interference decoding at the primary receiver.

The capacity region of Gaussian cognitive radio channels to within 1.81 bits

We make use of the deterministic high-SNR approximation of the Gaussian cognitive radio channel to gain insights in deriving inner and outer bounds for any SNR. We show that the derived bounds are at most 1.81 bits apart for any SNR.

Capacity to within 3 bits for a class of Gaussian Interference Channels with a Cognitive Relay

The InterFerence Channel with a Cognitive Relay (IFC-CR) consists of a classical two-user interference channel in which the two independent messages are also non-causally known at a cognitive relay node. In this work a special class of IFC-CRs in which the sources do not create interference at the non-intended destinations is analyzed. This special model results in a channel with two non-interfering point-to-point channels whose transmission is aided by an in-band cognitive relay, which is thus referred to as the Parallel Channel with a Cognitive Relay (PC-CR). We determine the capacity of the PC-CR channel to within 3 bits/s/Hz for all channel parameters. In particular, we present several new outer bounds which we achieve to within a constant gap by proper selection of Gaussian input distributions in a simple rate-splitting and superposition coding-based inner bound. The inner and outer bounds are numerically evaluated to show that the actual gap can be far less than 3 bits/s/Hz.

A new capacity result for the Z-Gaussian cognitive interference channel

This work proposes a novel outer bound for the Gaussian cognitive interference channel in strong interference at the primary receiver based on the capacity of a multi-antenna broadcast channel with degraded message set. It then shows that for the Z-channel, i.e., when the secondary receiver experiences no interference and the primary receiver experiences strong interference, the proposed outer bound not only is the tightest among known bounds but is actually achievable for sufficiently strong interference. The latter is a novel capacity result that from numerical evaluations appears to be generalizable to a larger (i.e., non-Z) class of Gaussian channels.

The capacity region of the Gaussian cognitive radio channels at high SNR

Deterministic channel models have recently proven to be powerful tools for obtaining capacity bounds for Gaussian multiuser networks that are tight in the high SNR regime. In this work we apply this technique to the Gaussian cognitive radio channel: a 2×2 interference channel in which one transmitter has non-causal knowledge of the message of the other, whose capacity region in general is unknown. We approximate the Gaussian cognitive radio channel at high SNR by an underlying binary linear deterministic channel model for which we determine the exact capacity region.

Energy Efficient Cooperative Strategies for Relay-Assisted Downlink Cellular Systems

The impact of cognitive radio techniques on the energy efficiency of a downlink cellular system in which multiple relays assist the transmission of the base station toward multiple receivers is studied. In particular, the fundamental tradeoff between the power consumption at the base station and the level of cooperation at the relay nodes is investigated. By increasing its transmit power, the base station can distribute the same message to multiple relays. In turn, the common knowledge at the relays enables cooperation, which results in a reduction in the power consumption due to interference management and coherent combining gains. This implies that the overall power efficiency can potentially be improved by an increase in the power consumption at the base station. We employ an information-theoretical analysis of the attainable power efficiency based on the chain graph representation of achievable schemes. This novel theoretical tool uses a graphical Markov model to represent coding operations and allows for the automatic derivation of achievable rate regions for general networks. This approach provides an effective tool to analyze the relationship between the energy consumption at the base station and power savings provided by relay cooperation through the use of transmission strategies such as superposition coding, interference decoding and rate-splitting. We present numerical evaluations for the scenario in which two relay nodes aid the communication between the base station and three receivers. These evaluations show that cooperative strategies at the relays provide clear advantages as compared to the non-cooperative scenario for varying channel conditions and target rates.

On capacity of the dirty paper channel with fading dirt in the strong fading regime.

The classic “writing on dirty paper” capacity result establishes that full state pre-cancellation can be attained in Gelfand-Pinsker problem with additive state and additive white Gaussian noise. This result holds under the assumption that both the transmitter and the receiver have perfect knowledge of the channel. We are interested in characterizing capacity under the more realistic assumption that only partial channel knowledge is available at the transmitter. To this end we study the “dirty paper channel with slow fading dirt”, a variation of the dirty paper channel in which the state sequence is multiplied by a slow fading value known only at the receiver. For this model we establish two approximate characterizations of capacity, one for the case in which fading takes only two values and one for the case in which fading takes M possible values but these values are greatly spaced apart. For both results, a naive strategy in which the encoder pre-codes against different fading realizations in different time slots is sufficient to approach capacity.

A general approach to random coding for multi-terminal networks

We introduce a general framework to derive achievable rate regions based on random coding for any memoryless, single-hop, multi-terminal network. We show that this general inner bound may be obtained from a graph representation that captures the statistical relationship among codewords and allows one to readily obtain the rate bounds under which the error probability vanishes as the block-length goes to infinity. The proposed graph representation naturally leads to an “automatic rate region derivator” which produces achievable rate regions combining classic random coding techniques such as coded timesharing, rate-splitting, superposition coding and binning for the general memoryless network under consideration.