In this paper, we consider a Gaussian multiple access channel with multiple independent additive white Gaussian interferences. Each interference is known to exactly one transmitter non-causally. The capacity region is characterized to within a constant gap regardless of channel parameters. These results are based on a layered modulo-lattice scheme which realizes distributed interference cancellation.
State-dependent networks with partial state knowledge available at different nodes have been studied in various scenarios. Kotagiri al @cite_7 study the state-dependent two-user MAC with state non-causally known to a transmitter, and for the Gaussian case they characterize the capacity asymptotically at infinite interference ( @math ) as the informed transmitter's power grows to infinity. Somekh-Baruch al @cite_1 study the problem with the same set-up as @cite_7 while the informed transmitter knows the other's message, and they characterize the capacity region completely. Zaidi al @cite_15 study another case of degraded message set. The achievability part of @cite_7 , @cite_1 , and @cite_15 are based on random binning. Philosof al @cite_19 , on the other hand, characterize the capacity region of the doubly-dirty MAC to within a constant gap at infinite interference (i.e., @math , @math ), by lattice strategies @cite_14 . They also show that strategies based on Gaussian random binning is unboundedly worse than lattice-based strategies. Zaidi al @cite_11 @cite_13 and Akhbari al @cite_12 study a state-dependent relay channel where the state is only known either at the source or the relay.
@cite_14 @cite_7 @cite_1 @cite_19 @cite_15 @cite_13 @cite_12 @cite_11
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In Costa's dirty-paper channel, Gaussian random binning is able to eliminate the effect of interference which is known at the transmitter, and thus achieve capacity. We examine a generalization of the dirty-paper problem to a multiple access channel (MAC) setup, where structured (lattice-based) binning seems to be necessary to achieve capacity. In the dirty-MAC, two additive interference signals are present, one known to each transmitter but none to the receiver. The achievable rates using Costa's Gaussian binning vanish if both interference signals are strong. In contrast, it is shown that lattice-strategies (“lattice precoding”) can achieve positive rates, independent of the interference power. Furthermore, in some cases-which depend on the noise variance and power constraints-high-dimensional lattice strategies are in fact optimal. In particular, they are optimal in the limit of high SNR-where the capacity region of the dirty MAC with strong interference approaches that of a clean MAC whose power is governed by the minimum of the users' powers rather than their sum. The rate gap at high SNR between lattice-strategies and optimum (rather than Gaussian) random binning is conjectured to be 1 2 log2(πe 6) ≈ 0.254 bit. Thus, the doubly dirty MAC is another instance of a network setting, like the Korner-Marton problem, where (linear) structured coding is potentially better than random binning. A generalization of the Gaussian dirty-paper problem to a multiple access setup is considered. There are two additive interference signals, one known to each transmitter but none to the receiver. The rates achievable using Costa's strategies (i.e. by a random binning scheme induced by Costa's auxiliary random variables) vanish in the limit when the interference signals are strong. In contrast, it is shown that lattice strategies ("lattice precoding") can achieve positive rates independent of the interferences, and in fact in some cases - which depend on the noise variance and power constraints - they are optimal. In particular, lattice strategies are optimal in the limit of high SNR. It is also shown that the gap between the achievable rate region and the capacity region is at most 0.167 bit. Thus, the dirty MAC is another instance of a network setup, like the Korner-Marton modulo-two sum problem, where linear coding is potentially better than random binning. Lattice transmission schemes and conditions for optimality for the asymmetric case, where there is only one interference which is known to one of the users (who serves as a "helper" to the other user), and for the "common interference" case are also derived. In the former case the gap between the helper achievable rate and its capacity is at most 0.085 bit. We consider the generalized dirty-paper channel Y=X+S+N,E X sup 2 spl les P sub X , where N is not necessarily Gaussian, and the interference S is known causally or noncausally to the transmitter. We derive worst case capacity formulas and strategies for "strong" or arbitrarily varying interference. In the causal side information (SI) case, we develop a capacity formula based on minimum noise entropy strategies. We then show that strategies associated with entropy-constrained quantizers provide lower and upper bounds on the capacity. At high signal-to-noise ratio (SNR) conditions, i.e., if N is weak relative to the power constraint P sub X , these bounds coincide, the optimum strategies take the form of scalar lattice quantizers, and the capacity loss due to not having S at the receiver is shown to be exactly the "shaping gain" 1 2log(2 spl pi e 12) spl ap 0.254 bit. We extend the schemes to obtain achievable rates at any SNR and to noncausal SI, by incorporating minimum mean-squared error (MMSE) scaling, and by using k-dimensional lattices. For Gaussian N, the capacity loss of this scheme is upper-bounded by 1 2log2 spl pi eG( spl Lambda ), where G( spl Lambda ) is the normalized second moment of the lattice. With a proper choice of lattice, the loss goes to zero as the dimension k goes to infinity, in agreement with the results of Costa. These results provide an information-theoretic framework for the study of common communication problems such as precoding for intersymbol interference (ISI) channels and broadcast channels. We consider a state-dependent three-terminal full-duplex relay channel with the channel states noncausally available at only the source, that is, neither at the relay nor at the destination. This model has application to cooperation over certain wireless channels with asymmetric cognition capabilities and cognitive interference relay channels. We establish lower bounds on the channel capacity for both discrete memoryless (DM) and Gaussian cases. For the DM case, the coding scheme for the lower bound uses techniques of rate-splitting at the source, decode-and-forward (DF) relaying, and a Gel'fand-Pinsker-like binning scheme. In this coding scheme, the relay decodes only partially the information sent by the source. Due to the rate-splitting, this lower bound is better than the one obtained by assuming that the relay decodes all the information from the source, that is, full-DF. For the Gaussian case, we consider channel models in which each of the relay node and the destination node experiences on its link an additive Gaussian outside interference. We first focus on the case in which the links to the relay and to the destination are corrupted by the same interference; and then we focus on the case of independent interferences. We also discuss a model with correlated interferences. For each of the first two models, we establish a lower bound on the channel capacity. The coding schemes for the lower bounds use techniques of dirty paper coding or carbon copying onto dirty paper, interference reduction at the source and decode-and-forward relaying. The results reveal that, by opposition to carbon copying onto dirty paper and its root Costa's initial dirty paper coding (DPC), it may be beneficial in our setup that the informed source uses a part of its power to partially cancel the effect of the interference so that the uninformed relay benefits from this cancellation, and so the source benefits in turn.