Network coding for the Multiple Access Relay channel using lattices (original) (raw)

Multi-user lattice coding for the multiple-access relay channel

IEEE Transactions on Wireless Communications, 2000

This paper considers the multi-antenna multiple access relay channel (MARC), in which multiple users transmit messages to a common destination with the assistance of a relay. In a variety of MARC settings, the dynamic decode and forward (DDF) protocol is very useful due to its outstanding rate performance. However, the lack of good structured codebooks so far hinders practical applications of DDF for MARC. In this work, two classes of structured MARC codes are proposed: 1) one-to-one relay-mapper aided multiuser lattice coding (O-MLC), and 2) modulo-sum relay-mapper aided multiuser lattice coding (MS-MLC). The former enjoys better rate performance, while the latter provides more flexibility to tradeoff between the complexity of the relay mapper and the rate performance. It is shown that, in order to approach the rate performance achievable by an unstructured codebook with maximum-likelihood decoding, it is crucial to use a new K-stage coset decoder for structured O-MLC, instead of the one-stage decoder proposed in previous works. However, if O-MLC is decoded with the one-stage decoder only, it can still achieve the optimal DDF diversity-multiplexing gain tradeoff in the high signal-to-noise ratio regime. As for MS-MLC, its rate performance can approach that of the O-MLC by increasing the complexity of the modulo-sum relay-mapper. Finally, for practical implementations of both O-MLC and MS-MLC, practical short length lattice codes with linear mappers are designed, which facilitate efficient lattice decoding. Simulation results show that the proposed coding schemes outperform existing schemes in terms of outage probabilities in a variety of channel settings.

Cooperative lattice coding and decoding in half-duplex channels

IEEE Journal on Selected Areas in Communications, 2007

We propose novel lattice coding/decoding schemes for half-duplex outage-limited cooperative channels. These schemes are inspired by the cooperation protocols of Azarian et al. and enjoy an excellent performance-complexity tradeoff. More specifically, for the relay channel, we first use our lattice coding framework to generalize Yang and Belfiore implementation of the non-orthogonal amplify and forward cooperation protocol. This generalization is shown to offer significant performance gains while keeping the decoding complexity manageable. We then devise a novel variant of the dynamic decode and forward protocol, along with a lattice-coded implementation, which enjoys a near-optimal diversity-multiplexing tradeoff with a low encoding/decoding complexity. Finally, for the cooperative multiple-access channel, we present a lattice-coded implementation of the non-orthogonal amplify and forward protocol and demonstrate its excellent performance-complexity tradeoff. Throughout the paper, we establish the performance gains of our proposed protocols via a comprehensive simulation study.

Wyner-Ziv lattice coding for two-way relay channel

The 2012 International Conference on Advanced Technologies for Communications, 2012

A Two-Way Relay Channel (TWRC) in which duplex transmission between two users via a relay station is considered. A physical layer network coding strategy based on compressand-forward relaying scheme for the TWRC is proposed. In the underlying coding strategy, we use nested lattices for Wyner-Ziv coding and decoding. The relay uses the weaker side information available at the receivers from the first transmission phase to broadcast a common quantized version of its received signal. We characterize the achievable rate region of the presented scheme. Then we show that lattice codes can achieve random coding rates.

Achievable Rate Regions for Two-Way Relay Channel Using Nested Lattice Coding

IEEE Transactions on Wireless Communications, 2014

This paper studies Gaussian Two-Way Relay Channel where two communication nodes exchange messages with each other via a relay. It is assumed that all nodes operate in half duplex mode without any direct link between the communication nodes. A compress-and-forward relaying strategy using nested lattice codes is first proposed. Then, the proposed scheme is improved by performing a layered coding: a common layer is decoded by both receivers and a refinement layer is recovered only by the receiver which has the best channel conditions. The achievable rates of the new scheme are characterized and are shown to be higher than those provided by the decode-andforward strategy in some regions.

Finite dimension Wyner-Ziv lattice coding for two-way relay channel

2013 IEEE 14th Workshop on Signal Processing Advances in Wireless Communications (SPAWC), 2013

Compute-and-forward on a multiaccess relay channel: Coding and symmetric-rate optimization

We consider a system in which two users communicate with a destination with the help of a halfduplex relay. Based on the compute-and-forward scheme, we develop and evaluate the performance of coding strategies that are of network coding spirit. In this framework, instead of decoding the users' information messages, the destination decodes two integer-valued linear combinations that relate the transmitted codewords. Two decoding schemes are considered. In the first one, the relay computes one of the linear combinations and then forwards it to the destination. The destination computes the other linear combination based on the direct transmissions. In the second one, accounting for the side information available at the destination through the direct links, the relay compresses what it gets using Wyner-Ziv compression and conveys it to the destination. The destination then computes the two linear combinations, locally. For both coding schemes, we discuss the design criteria, and derive the allowed symmetric-rate. Next, we address the power allocation and the selection of the integer-valued coefficients to maximize the offered symmetric-rate; an iterative coordinate descent method is proposed.

Compute-and-Forward on a Multiaccess Relay Channel: Coding and Sum-Rate Optimization

2012

Design criteria for lattice network coding

2011

The compute-and-forward (C-F) relaying strategy proposed by Nazer and Gastpar is a powerful new approach to physical-layer network coding. Nazer-Gastpars construction of C-F codes relies on asymptotically-good lattice partitions that require the dimension of lattices to tend to infinity. Yet it remains unclear how such C-F codes can be constructed and analyzed under practical constraints. Motivated by this, an algebraic approach was taken to compute-and-forward, which provides a framework to study C-F codes constructed from finite-dimensional lattice partitions. Building on the algebraic framework, this paper moves one step further; it aims to derive the design criteria for the C-F codes constructed from finite-dimensional lattice partitions (also referred to as lattice network codes). It is shown that the receiver parameters {aℓ} and α should be chosen such that the quantity Q = |α|2 + SNRΣℓ=1L ||αhℓ - αℓ||2 is minimized, and the lattice partition should be designed such that the minimum inter-coset distance is maximized. These design criteria imply that finding the optimal receiver parameters is equivalent to solving a shortest vector problem, and designing good lattice partitions can be reduced to the design of good linear codes for complex Construction A.

Structured Lattice Codes for 2\ times 2\ times 2 MIMO Interference Channel

2013

Abstract: We consider the 2\ times 2\ times 2 multiple-input multipleoutput interference channel where two source-destination pairs wish to communicate with the aid of two intermediate relays. In this paper, we propose a novel lattice strategy called Aligned Precoded Compute-and-Forward (PCoF). This scheme consists of two phases: 1) Using the CoF framework based on signal alignment we transform the Gaussian network into a deterministic finite field network.

Structured lattice codes for 2×2×2 MIMO interference channel

2013 IEEE International Symposium on Information Theory, 2013

We consider the 2 × 2 × 2 multiple-input multipleoutput interference channel where two source-destination pairs wish to communicate with the aid of two intermediate relays. In this paper, we propose a novel lattice strategy called Aligned Precoded Compute-and-Forward (PCoF). This scheme consists of two phases: 1) Using the CoF framework based on signal alignment we transform the Gaussian network into a deterministic finite field network. 2) Using linear precoding (over finite field) we eliminate the end-to-end interference in the finite field domain. Further, we exploit the algebraic structure of lattices to enhance the performance at finite SNR, such that beyond a degree of freedom result (also achievable by other means). We can also show that Aligned PCoF outperforms time-sharing in a range of reasonably moderate SNR, with increasing gain as SNR increases.

Network coding for the Multiple Access Relay channel using lattices (original) (raw)

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