Asma Mejri

Practical Physical Layer Network Coding in Multi-Sources Relay Channels via the Compute-and-Forward

Recent years have witnessed the development of the Compute-and-Forward (CF) as a successful solution to perform noiseless linear Physical Layer Network Coding (PLNC). Research outcomes shed considerable light on the promising gain of this strategy from information-theoretic perspective. What misses is to design practical PLNC schemes based on the Compute-and-Forward and to evaluate their end-to-end performance in real communication scenarios. In this work we try to fill the gap between theory and practice: we investigate end-to-end communication over a Multi-Sources Relay Channel where the CF is used at intermediate nodes. We figure out practical constraints that deserve special attention in real end-to-end communication design and propose reliable solutions that enable to meet the promised potential of the CF. In order to confirm our theoretical analysis, we evaluate performance of the proposed schemes at the destination in terms of both average achievable rate and error rates under practical low complexity nested lattice encoding.

Lattice decoding for the Compute-and-Forward protocol

In this work we focus exclusively on the Compute-and-Forward (C&F) protocol as a channel coding-based approach for Physical Layer Network Coding. The Core principle of this relaying strategy is based on using Nested Lattice Codes. The source nodes in a relay network encode their messages into lattice codewords and transmit them to the relay. The latter receives a noisy mixing of these codewords and decodes an integer linear combination of them for sequential transmission. To the best of our knowledge, all existent works related to the Compute-and-Forward protocol study only its theoretical limits and no experimental analysis has been proposed so far. Our contribution through this work concerns a plethora of practical aspects, related to lattice decoding for the C&F, that need to be solved to achieve the promising potential of this strategy. We propose practical decoding approaches and investigate the achieved diversity order and identify the relevant parameters that may influence it. We provide simulation results to compare the performance of the different proposed decoding approaches and to link theoretical results with practical aspects.

MAP decoder for physical-layer network coding using lattice sphere decoding

We focus in this work on optimal maximum a posteriori (MAP) decoding for lattice-based physical-layer network coding operating in Gaussian multiple access relay channels. We consider a general lattice design that makes our results hold for any lattice coding schemes of any dimensions including the Compute-and-Forward framework. By examining the MAP decoding rule, we first derive an analytical bound on the codeword error probability taking into consideration decoding errors at the relay. Besides, we derive a novel MAP decoding metric using which we develop a novel, practical and easy-to-implement MAP decoding algorithm based on lattice sphere decoding. We further provide numerical results that demonstrate the effectiveness of our algorithm and show its outperformance over existing suboptimal decoders.

Bidirectional relaying via network coding: Design algorithm and performance evaluation

Research works shed considerable light on the merit of the Physical Layer Network Coding in the Two-Way Relay Channel using lattice codes. This potential is proved under a capacity achieving perspective. However, it is not completely understood if this promised gain is attainable in practical settings. We try in this work to answer to this issue by investigating two network coding strategies: the Compute-and-Forward and the Analog Network Coding. We analyze end-to-end communication using these methods and evaluate their performance in terms of error rate and exchange rate using a low-complexity lattice encoding scheme.

Reduced-complexity ML decodable STBCs: Revisited design criteria

In this work, we revisit the structure of weight matrices for Linear Dispersion STBCs to admit ML decoding with low-complexity. We first propose novel sufficient design criteria for linear STBCs considering an arbitrary number of antennas and an arbitrary coding rate. Then we apply the derived criteria to three families of codes, multi-group decodable, fast decodable, and fast-group decodable codes. We provide analytical proofs showing that the ML-decoding complexity of such codes depends only on the weight matrices and their ordering and not on the channel gains or the number of antennas and explaining why the so far used Hurwitz-Radon theory-based approaches do not exactly determine the complexity of all classes of STBCs under ML decoding.

Practical Implementation of Integer Forcing Linear Receivers in MIMO Channels

Integer Forcing (IF) architecture has been recently proposed to design linear receivers in MIMO systems. Research works show the promise of this architecture from a capacity achieving perspective. However, it is not totally understood how to select IF coefficient matrix and if the promised theoretical gain of the resulting receivers is attainable in practical settings. We try in this work to fill the gap between theory and practice: we propose algorithms to select optimal IF receiver parameters that lead to the maximization of the total achievable rate. We propose an implementation of an IF-based MIMO system considering a practical scenario where lattice codes are used. Experimental studies are carried out to evaluate the error rate performance of the proposed algorithms and compare them to traditional linear receivers. Our proposed implementation shows that the theoretical potential of the IF receivers is achievable even with finite-length lattice codes.

On the diversity of the Naive Lattice Decoder

“Naive Lattice Decoding” (NLD) and its low-complexity approximations such as lattice reduction-aided linear decoders represent an alternative to Maximum Likelihood lattice decoders for MIMO systems. Their diversity order has been investigated in recent works. These showed that the NLD achieves only the receive diversity and that MMSE-GDFE left preprocessing followed by NLD or its approximations achieves the maximum diversity. All the theoretical results have so far focused on the diversity order but this is not the only relevant parameter to achieve good performance and the coding gain also needs to be considered. In addition, up to now there has not been any numerical analysis of the actual performance of these techniques for the coded systems for moderate SNR. In this paper, we consider MIMO systems using high-dimensional perfect space-time codes. We show that by adding MMSE-GDFE preprocessing, the NLD has a loss of only 1.5 dB with respect to optimal decoding in the case of the Perfect Code 4×4. However, even with MMSE-GDFE preprocessing, the performance of lattice-reduction aided linear receivers is still very poor for high-dimensional lattices.

Reduced-Complexity Stack Decoder for MIMO Systems

In this work, we propose a novel sequential decoder for MIMO systems termed the Zigzag Stack decoder. The algorithm combines the search strategy of the Stack decoder with the Schnorr-Euchner zigzagging method. We show that the Zigzag Stack provides ML performance with a reduced complexity compared to the original Stack decoder and a complexity reduction of 40% in average over the commonly used sphere decoder.

Reduced-complexity lattice spherical decoding

Lattice sequential decoders based on a spherical search region, such as the Sphere Decoder and the SB-Stack decoder, implement a tree-search strategy to find the ML solution while visiting only the lattice points that belong to a sphere of a predefined radius. Their computational complexity depends then critically on the choice of the initial sphere radius. We propose in this work novel initial sphere radius selection methods for spherical-region based sequential lattice decoders and show through simulations the complexity reduction allowed by such methods when the Sphere Decoder is used while maintaining ML performance.

Early termination techniques for MIMO lattice sequential decoders

In practical communication systems and realistic radio applications, there are throughput and latency restraints that have to be fulfilled together with a fixed hardware decoding complexity constraint that should be satisfied. Because of these requirements, in some bad channel realizations, a guaranteed throughput needs to be enforced with a premature end of the decoding process at the expense of a bit error rate performance penalty. In such scenarios, the decoding algorithm should stop and return a premature estimation of the original data such that the authorized decoding complexity and convergence time are respected. This problem is known as early termination decoding. In this work we propose efficient termination techniques for best-first tree-search sequential decoders applicable to a plurality of linear communication systems including MIMO channels addressed in this paper.