We aim to exploit cognition to maximize network performance What is the side information at a cognitive node? What is the best encoding scheme given this side information? A model for cognition in IT: Perfect side information at the cognitive pair Very optimistic Cognitive and non-cognitive pair communication modeled as: Converse The Capacity Region of the Cognitive Z-interference Channel with a Noiseless Non-cognitive Link Nan Liu, Ivana Marić, Andrea Goldsmith and Shlomo Shamai (Shitz) In the considered scenario, interference can be minimized by exploiting the structure of interference and cognition at the nodes The corresponding encoding scheme requires 1)Superposition coding 2) Gel’fand-Pinsker coding This is in contrast to the Gaussian case For the GP problem, the optimum interference has superposition structure We considered single-user cognitive models that capture delay in related work [Marić, Liu and Goldsmith 2008] Channel Model ? In some scenarios, interference can be minimized by exploiting the structure of interference and cognition at the nodes. Cognition should be used by the encoder to precode against part of the interference caused to its receiver. Capacity of networks with cognitive users are unknown. Consequently, optimal ways how to operate such networks are not understood, nor it is clear how cognitive nodes should exploit the obtained information. IT channel models suitable for networks with cognitive users still need to be proposed. Capacity of Z-interference channel is still unknown. Encoding scheme was proposed that exploits cognition and is optimal in certain scenarios IMPACT NEXT-PHASE GOALS ACHIEVEMENT DESCRIPTION Introduction In multiuser networks: A key issue is how to handle and exploit interference created by simultaneous transmissions Not well understood: Capacity of the interference channel an open problem Capacity of the Z-interference channel an open problem Cognitive radio networks: Multiuser networks in which some users cognitive, i.e., can sense the environment and hence obtain side information about transmissions in neighborhood How to exploit cognition in optimal ways? STATUS QUO NEW INSIGHTS MAIN ACHIEVEMENT: 1) The capacity region of the discrete cognitive Z- interference channel with a noiseless non-cognitive link 2) An inner and outer bound for the cognitive Z-interference channel 3) Solution to the generalized Gel’fand- Pinsker (GP) problem in which a transmitter-receiver pair communicates in the presence of interference non causally known to the encoder. Our solution determines the optimum structure of interference. HOW IT WORKS: Non-cognitive encoder uses superposition coding to enable partial decoding of interference. The cognitive encoder precodes against the rest of interference using GP encoding. ASSUMPTIONS AND LIMITATIONS: The considered channel model: 1) Optimal scheme for some channels 2) Superposition coding and Gel’fand-Pinsker coding may be required in order to minimize interference, in some channels. This is in contrast to the Gaussian channel. 3) For the GP problem, the optimal interference has a superposition structure Evaluate a numerical example Apply proposed encoding scheme to larger networks and to different cognitive node models Motivation Previous Work Connection to the Gel’fand-Pinsker Problem Summary and Future Work An achievable rate region and an outer bound for the cognitive ZIC were derived The capacity result for the ZIC with a noiseless non-cognitive link was obtained The Generalized Gel’fand-Pinsker problem was solved Future work: Evaluate a numerical example Apply proposed encoding scheme to larger networks and to different cognitive node models Theorem: Achievable rate pairs (R 1,R 2 ) belong to a union of rate regions given by where the union is over all probability distributions p( v,u,x 2 )p( x 1 | u,x 2 ) Encoder 1 is cognitive in the sense that it knows the message of other user Summary Achievability Achievability Implications dest1 dest2 cognitive encoder non-cognitive encoder W2W2 W1W1 W 1 W 2 W2W2 dest1 dest2 source 1 source 2 W2W2 W1W1 W1W1 W2W2 Theorem: Achievable rate pairs (R 1,R 2 ) are given by a union of rate regions given by where the union is over all probability distributions p( v,u,x 2 )p( x 1 | u,x 2 ) Encoding scheme: Encoder 2: - rate-splits its message into two messages - encodes using superposition coding with an inner codebook v n and an outer codebook x 2 n Encoder 1: - for each v n it performs binning, i.e., Gel’fand-Pinsker encoding in order to precode against interference x 2 n given v n Encoding: Decoding: Two messages: Rates: In general, the achievable rates and the converse result do no meet Markovity U→(V,X 2 )→Y 2 implies: I(U;X 2 | V) ≥ I(U;Y 2 | V) For Y 2 =X 2 the two regions are the same. This leads to the following: Capacity Result Theorem: For the cognitive ZIC with a noiseless non- cognitive link i.e., p(y 2 |x 2 ) is a deterministic one-to-one function, the capacity region is given by the union of rate regions: where the union is over all probability distributions p( v,u,x 2 )p( x 1 | u,x 2 ) Alphabet for encoder t : Communication in the presence of interference (state) non-causally known to the encoder In the cognitive ZIC, when X 2 =Y 2, X 2 can be viewed as a state i.i.d. distributed on a set of size of 2 nR2 We can design not only the codebook of the cognitive encoder, but also the structure of the state When reduces to the GP rate achieved in the channel with an iid state and uniformly distributed on X [Marić, Yates, Kramer], [Devroye, Mitran, Tarokh] 2006 [Wu, Vishwanath, Arapostathis], [Jovičić, Viswanath], [Sridharan, Vishwanath] 2007 [Marić, Goldsmith, Shamai, Kramer], [Jiang, Xin], [Cao, Chen] 2008 Capacity results known in special cases of ‘strong’ and ‘weak’ interference Thus, for the given rate R2 of the interferer, the optimal interference has the superposition structure