Lattice Strategies for the Dirty Multiple Access Channel

In this paper, a class of relay networks is considered. We assume that, at a node, outgoing channels to its neighbors are orthogonal, while incoming signals from neighbors can interfere with each other. We are interested in the multicast capacity of these networks. As a subclass, we first focus on Gaussian relay networks with interference and find an achievable rate using a lattice coding scheme. It is shown that there is a constant gap between our achievable rate and the information theoretic cut-set bound. This is similar to the recent result by Avestimehr, Diggavi, and Tse, who showed such an approximate characterization of the capacity of general Gaussian relay networks. However, our achievability uses a structured code instead of a random one. Using the same idea used in the Gaussian case, we also consider linear finite-field symmetric networks with interference and characterize the capacity using a linear coding scheme. Index TermsWireless networks, multicast capacity, lattice codes, structured codes, multiple-access networks, relay networks I. INTRODUCTION Characterizing the capacity of general relay networks has been of great interest for many years. In this paper, we confine our interest to the capacity of single source multicast relay networks, which is still an open problem. For instance, the capacity of single relay channels is still unknown except for some special cases [1]. However, if we confine the class of networks further, there are several cases in which the capacity is characterized.Recently, in [2], the multicast capacity of wireline networks was characterized. The capacity is given by the max-flow min-cut bound, and the key ingredient to achieve the bound is a new coding technique called network coding. Starting from this seminal work, many efforts have been made to incorporate wireless effects in the network model, such as broadcast, interference, and noise. In [3], the broadcast nature was incorporated into the network model by requiring each relay node to send the same signal on all outgoing channels, and the unicast capacity was determined. However, the model assumed that the network is deterministic (noiseless) and has no interference in reception at each node. In [4], the work was extended to multicast capacity. In [5], the interference nature was also incorporated, and an achievable multicast rate was computed. This achievable rate has a cut-set-like representation and meets the information theoretic cut-set bound [27] in some special cases. To incorporate the noise, erasure networks with broadcast or interference only were considered in [7], [8]. However, the network models in [7], [8] assumed that the side information on the location of all erasures in the network is provided to destination nodes. Noisy networks without side information at destination nodes were considered in [12] and [13] for finite-field additive noise and erasure cases, respectively.

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“…Similar forms of achievable rate were observed in [10], [15], [16], [25] for some equal power Gaussian networks.…”

Section: Gaussian Relay Network With Interferencesupporting

confidence: 80%

Nested Lattice Codes for Gaussian Relay Networks With Interference

Nam

Chung

Lee

2011

IEEE Trans. Inform. Theory

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“…The direct part (14) follows from Lemmas III.10 and III.11 ahead. Before stating these lemmas, we define a region through rate constraints similar to those defining but with two additional constraints, so Nevertheless, as we shall see, this set is rich enough in the sense that its convex hull contains , i.e., the set of all rate pairs that are achievable in the absence of interference (see Theorem III.2).…”

Section: On the Proof Of Theorem Iii3mentioning

confidence: 91%

“…Unlike our scenario, in these scenarios, the capacity region depends on whether the transmitters learn the interference before or after the conferencing. Multiaccess setups without conferencing where both transmitters know only parts of the interference were also studied in [9], [10], [14]- [16], [19]- [21], and [27].…”

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confidence: 99%

Dirty-Paper Coding for the Gaussian Multiaccess Channel With Conferencing

Bross

Lapidoth

Wigger

2012

IEEE Trans. Inform. Theory

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Abstract-We derive the capacity region of the two-user dirtypaper Gaussian multiaccess channel (MAC) with conferencing encoders. In this MAC, prior to each transmission block, the transmitters can hold a conference in which they can communicate with each other over error-free bit pipes of given capacities. The received signal suffers not only from additive Gaussian noise but also from additive interference, which is known noncausally to the transmitters but not to the receiver. The additive interference is modeled as Gaussian or uniform over a sphere. We show that the interference can be perfectly mitigated, i.e., that the capacity region without interference can also be achieved in its presence. This holds irrespective of whether the transmitters learn the interference before or after the conference. It follows as a corollary that also for the MAC with degraded message sets, the interference can be perfectly mitigated if it is known noncausally to the transmitters. To derive our results, we generalize Costa's single-user writing-on-dirty-paper achievability result to channels with dependent interference and not-necessarily Gaussian noise.

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“…Comparing this capacity with the sum -capacity of the MAC, i.e., with 1 2 log(1 + M · SNR), we observe that we suffer from two losses 8 (see also [10], [6], [8]). First, we lose a factor of M in power.…”

Section: ) Symmetric Casementioning

confidence: 99%

“…There has been considerable progress in recent years in deriving structured coding schemes and capacity results for single-user channels as well as networks with AWGN noise, e.g., [2], [7], [10], [4], [6], [1]. A key ingredient in these results is the use of linear/lattice codes that are particularly well suited for additive noise channels.…”

Section: Introductionmentioning

confidence: 99%

A modulo-lattice transformation for multiple-access channels

Erez

Zamir

2008

2008 IEEE 25th Convention of Electrical and Electronics Engineers in Israel

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Abstract-A simple lemma is derived that allows to transform a general single-user (non-Gaussian, non-additive) continuousalphabet channel as well as a general multiple-access channel into a modulo-additive noise channel. While in general the transformation is information lossy, it allows to leverage linear coding techniques and capacity results derived for networks comprised of additive Gaussian nodes to more general networks.

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Lattice Strategies for the Dirty Multiple Access Channel

Cited by 77 publications

References 28 publications

Nested Lattice Codes for Gaussian Relay Networks With Interference

Nested Lattice Codes for Gaussian Relay Networks With Interference

Dirty-Paper Coding for the Gaussian Multiaccess Channel With Conferencing

A modulo-lattice transformation for multiple-access channels

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