Article

Lattice Strategies for the Dirty Multiple Access Channel

EE - Systems Department, Tel Aviv University, Tel Aviv, Israel. Email:
05/2009; DOI: 10.1109/ISIT.2007.4557256
Source: arXiv

ABSTRACT 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.

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    • "Now we propose an achievable rate region using lattice based coding for the Gaussian degraded " Z " channel with additive interference non-causally available at both of the encoders under the high-SNR and strong interference regime utilizing the standard notation of [13], [14], and [15]. Our method is based on lattice transmission scheme, jointly decoding at the first decoder and successive decoding at the second decoder. "
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    ABSTRACT: In this paper we study the Z channel with side information non-causally available at the encoders. We use the notion of Han-Kobayashi rate splitting along with Gelfand-Pinsker random binning scheme and Chong-Motani-Garg-El Gamal (CMGE) jointly decoding to find the achievable rate region. We will see that our achievable rate region gives the achievable rate of the multiple access channel with side information and also degraded broadcast channel with side information. We will also derive an inner bound and an outer bound on the capacity region of the state-dependent degraded discrete memoryless Z channel. We will also see that using Costa dirty paper coding, we can remove the negative effect of the interference from the direction of one transmitter-receiver pair. Also, by assuming the high signal to noise ratio and strong interference regime, and using the lattice strategies, we derive an achievable rate region for the Gaussian degraded Z channel with additive interference non-causally available at both of the encoders. Our method is based on lattice transmission scheme, jointly decoding at the first decoder and successive decoding at the second decoder. Using such coding scheme we remove the effect of the interference completely.
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    • "Philosof-Zamir [8], [9], extended Jafar's work and provided achievable rate regions for the discrete memoryless MAC with correlated side information known non-causally at the encoders using a random binning technique. They also considered the Gaussian doubly dirty MAC in the high-SNR strong interference regime [8] [9] [10] [11] [12] [13].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. "
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    ABSTRACT: In this paper, we establish achievable rate regions for the multiple access channel (MAC) with side information partially known (estimated or sensed version) at the transmitters. Actually, we extend the lattice strategies used by Philosof-Zamir for the MAC with full side information at the transmitters to the partially known case. We show that the sensed or estimated side information reduces the rate regions, the same as that occurs for Costa Gaussian channel.
    Information Theory Proceedings (ISIT), 2012 IEEE International Symposium on; 05/2012
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    • "More recently, we showed that structured codes offer large gains for reliable computation over multiple-access channels [19]. Philosof et al. demonstrated that structured codes enable distributed dirty paper coding for Gaussian multiple-access channels in [20]. The celebrated paper of Ahlswede et al. on network coding showed that for wired networks, relays must send out functions of received data, rather than just routing it [21]. "
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    ABSTRACT: Interference is usually viewed as an obstacle to communication in wireless networks. This paper proposes a new strategy, compute-and-forward, that exploits interference to obtain significantly higher rates between users in a network. The key idea is that relays should decode linear functions of transmitted messages according to their observed channel coefficients rather than ignoring the interference as noise. After decoding these linear equations, the relays simply send them towards the destinations, which given enough equations, can recover their desired messages. The underlying codes are based on nested lattices whose algebraic structure ensures that integer combinations of codewords can be decoded reliably. Encoders map messages from a finite field to a lattice and decoders recover equations of lattice points which are then mapped back to equations over the finite field. This scheme is applicable even if the transmitters lack channel state information.
    IEEE Transactions on Information Theory 11/2011; 57(10-57):6463 - 6486. DOI:10.1109/TIT.2011.2165816 · 2.65 Impact Factor
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