Lattice Strategies for the Dirty Multiple Access Channel

EE - Systems Department, Tel Aviv University, Tel Aviv, Israel. Email:
IEEE Trans. Inf. Theory 05/2009; 57. DOI: 10.1109/ISIT.2007.4557256
Source: arXiv


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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Available from: Ashish Khisti, Nov 24, 2014
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    • "The aforementioned papers accomplished this using block-Markov schemes that encode messages of the current block as well as some information about the state and messages from previous block. When the state information is known noncausally, the work [17] considered the dirty-paper special case (additive interference composed of two components each known noncausally to one and only one encoder in Gaussian noise). For this case, a straightforward extension of Gelfand-Pinsker coding turns out to be highly suboptimal. "
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    ABSTRACT: The capacity regions of semideterministic multiuser channels, such as the semideterministic relay channel and the multiple access channel with partially cribbing encoders, have been characterized using the idea of partial-decode-forward. However, the requirement to explicitly decode part of the message at intermediate nodes can be restrictive in some settings; for example, when nodes have different side information regarding the state of the channel. In this paper, we generalize this scheme to $\textit{cooperative-bin-forward}$ by building on the observation that explicit recovering of part of the message is not needed to induce cooperation. Instead, encoders can bin their received signals and cooperatively forward the bin index to the decoder. The main advantage of this new scheme is illustrated by considering state-dependent extensions of the aforementioned semideterministic setups. While partial-decode-forward is not applicable in these new setups, cooperative-bin-forward continues to achieve capacity.
    Full-text · Article · Aug 2015 · IEEE Transactions on Information Theory
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    • "For notational convenience, we define . Further, this lattice based technique has been used to study the capacity of Gaussian relay networks [12],[13] and the multiple access channel [14]. "
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    ABSTRACT: In this paper, we study the achievable region for a Gaussian broadcast channel in the presence of an additional interference at the receivers. We consider that a noisy version of this interference is known to the transmitter and the receivers. A nested lattice code coupled with a dirty paper code is used to compute the achievable region. A two phase causal encoding technique is also proposed in which the interference signal is estimated at the end of the first phase and then the desired signal is transmitted in the second phase. Numerical results show that causal knowledge of the interference can significantly improve the achievable rate region over a scheme that does not use interference cancellation. Results are also shown when the transmitter operates in both half-duplex and full-duplex modes.
    Full-text · Article · Apr 2014 · Journal of Communications
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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.
    Full-text · Article · Jan 2013
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