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When rate of interferer’s codebook small Does not place burden for destination to decode interference When rate of interferer’s codebook large Treating it as i.i.d. sequence and use Gel’fand-Pinsker Superposition Codebook Encoding Against an Interferer’s Codebook Ivana Maric, Nan Liu and Andrea Goldsmith Studied cognitive radio from novel and realistic perspectives Primary user is not willing to perform joint codebook design Primary user uses a randomly generated codebook codebook structure i.i.d. or superposition Cognition is achieved through delay and noise Provided capacity definitions for random interferer’s codebook Proposed achievability schemes under various scenarios Showed that taking into account interference comes from a codebook helps Proved that structured interferer’s codebook is helpful In the more realistic scenario: cognition through delay and noise In the case of i.i.d. sequence, delayed cognition=no cognition Delayed cognition is still useful when state is a codeword Capacity Definitions Structure of the interferer’s codeword transmitted by a node in vicinity can be exploited for higher rates at the cognitive node. Delay has a different impact depending on whether the interference is i.i.d. or a codeword of an interferer. Capacity of networks with cognitive users are unknown and, consequently, so are the optimal ways in which to operate these networks Majority of current information- theoretic models for cognitive capabilities of the nodes are somewhat idealistic By exploiting the structure of the interference created by the nodes in its vicinity, cognitive nodes can achieve higher rates END-OF-PHASE GOAL COMMUNITY CHALLENGE ACHIEVEMENT DESCRIPTION Encoding Against an Interferer’s Codebook Introduction STATUS QUO NEW INSIGHTS MAIN RESULTS: Demonstrated that exploiting the structure of interference can bring higher gains for cognitive communications. Evaluated these gains for a specific channel. Derived two outer bounds on the performance. Analyzed cases with and without delay in side information knowledge. Showed that impact of delay differs depending whether the interference is i.i.d. or has a structure. HOW IT WORKS: Without delay, the encoder uses Gel’fand- Pinsker precoding; or, if interferer’s rate is small, it forwards the interfering message enabling the receiver to decode it. With delay, it attempts to decode the interferer’s message and then use cognitive encoding strategies. ASSUMPTIONS AND LIMITATIONS: The noncausal knowledge assumption is in general too optimistic. Single letter rate characterizations are difficult to obtain due to the structure of interference. Evaluate the outer bound Generalize observations to networks with cognitive and noncognitive users Prize level: Capacity results for networks with cognitive and noncognitive users Motivation System Model Gel’fand-Pinsker with Codebook Example Future Work I.I.D. Sequence with Delay Interferer Codeword with Delay and Noise Conclusions Evaluate the obtained upper bounds Use the obtained insights to design networks with cognitive and noncognitive users Interference degradation depends on realization of codebook Definition 1 Communication rate same for any realization Probability of error different for different realizations Rate can be supported by some realizations : supremum over all rate supported by majority Definition 2 Allow communication rate to differ for each realization There is a capacity associated with each realization : the capacity that can be supported by majority Taking into account that the state is a codebook helps Forwarding interference can outperform GP precoding uniformly takes a row of a randomly generated codebook Codebook of i.i.d. structure Codebook of superposition structure More realistically: encoder knows through noisy channel Encoding at time depend on and Theorem 1 : Lemma 1: Achievable rate Noncognitive stage Gel’fand-Pinsker with codebook stage Encoder splits its message into two parts and First symbols, sends as if does not know channel state Encoder is able to decode state sequence after symbols For the remaining symbols, send using Lemma 1 Cognitive radios have ability to obtain (through sensing) and exploit (through advanced processing) information about communications in their vicinity Due to advanced technology, the cognitive encoder can use sophisticated encoding schemes to improve the network performance Due to their capabilities, cognitive radios can coexist with noncognitive users and thus improve spectral usage of the spectrum Capacity of cognitive radio networks are in general unknown In information theoretic approach, cognitive capabilities are modeled as a side information at the cognitive encoder about the transmissions in its vicinity Cognitive encoding strategies will depend on the amount of side information available Decoding the other user’s message introduces delay in the availability of side information at the cognitive encoder We first analyze the case when X i =f i (W, S 1, …, S i-1 ) We have the following: Lemma 3: The capacity is Lemma 2 implies that the rate equals the rate without side information at the encoder i.i.d. side information obtained with delay does not help x is a deterministic function of (v, u, x s ) is given by the interferer Lemma 2: Achievable rate for joint distribution that factors as Rates of Lemma 1 are then a special case: when V=0 (no decoding) or X s =0 (full decoding) When the interferer uses a superposition coding, the cognitive user can improve its rate It decodes the codebook (the cloud) of the lower rate R 1s and uses Gel’fand-Pinsker encoding against the higher rate codebook. The following rate is achievable: Capacity of the channel with random states noncausally known at the encoder is obtained by Gel’fand-Pinsker precoding against interference scheme For a network with one cognitive and one noncognitive pair, we have previously developed cognitive encoding strategies that bring gains, under the assumption of noncausal message knowledge at the cognitive encoder Such knowledge can be obtained through decoding, or through cooperation with noncognitive encoder This work focuses on communication of the cognitive radio pair while treating the noncognitive transmitter as an interferer We assume that we don’t have the freedom to design the interferer’s codebook Codebook is already chosen to be i.i.d. or is a superposition codebook Our goal is to exploit the structure of the interference (codebook of the interferer) for rate gains and to consider the impact of delay in learning interferer’s message at the cognitive encoder Summary