Ghaya Rekaya-Ben Othman

Augmented Lattice Reduction for MIMO Decoding

Lattice reduction algorithms, such as the Lenstra-Lenstra-Lovasz (LLL) algorithm, have been proposed as preprocessing tools in order to enhance the performance of suboptimal receivers in multiple-input multiple-output (MIMO) communications. A different approach, introduced by Kim and Park, allows to combine right preprocessing and detection in a single step by performing lattice reduction on an v{augmented channel matrix}. In this paper we propose an improvement of the augmented matrix approach which guarantees a better performance. We prove that our method attains the maximum receive diversity order of the channel. Simulation results evidence that it significantly outperforms LLL reduction followed by successive interference cancellation (SIC) while requiring a moderate increase in complexity. A theoretical bound on the complexity is also derived.

Construction of New Delay-Tolerant Space-Time Codes

Perfect space-time codes (STC) are optimal codes in their original construction for multiple-input multiple-output (MIMO) systems. Based on cyclic division algebras (CDA), they are full-rate, full-diversity codes, have non-vanishing determinants (NVD) and hence achieve diversity-multiplexing tradeoff (DMT). In addition, these codes have led to optimal distributed space-time codes when applied in cooperative networks under the assumption of perfect synchronization between relays. However, they lose their diversity when delays are introduced and thus are not delay-tolerant. In this paper, using the cyclic division algebras of perfect codes, we construct new codes that maintain the same properties as perfect codes in the synchronous case. Moreover, these codes preserve their full-diversity in asynchronous transmission.

Polarization-time coding for PDL mitigation in long-haul PolMux OFDM systems

In this paper, we present a numerical, theoretical and experimental study on the mitigation of Polarization Dependent Loss (PDL) with Polarization-Time (PT) codes in long-haul coherent optical fiber transmissions using Orthogonal Frequency Division Multiplexing (OFDM). First, we review the scheme of a polarization-multiplexed (PolMux) optical transmission and the 2 × 2 MIMO model of the optical channel with PDL. Second, we introduce the Space-Time (ST) codes originally designed for wireless Rayleigh fading channels, and evaluate their performance, as PT codes, in mitigating PDL through numerical simulations. The obtained behaviors and coding gains are different from those observed on the wireless channel. In particular, the Silver code performs better than the Golden code and the coding gains offered by PT codes and forward-error-correction (FEC) codes aggregate. We investigate the numerical results through a theoretical analysis based on the computation of an upper bound of the error probability of the optical channel with PDL. The derived upper bound yields a design criterion for optimal PDL-mitigating codes. Furthermore, a transmission experiment of PDL-mitigation in a 1,000 km optical fiber link with inline PDL validates the numerical and theoretical findings. The results are shown in terms of Q-factor distributions. The mean Q-factor is improved with PT coding and the variance is also narrowed.

Space-Time Codes for Optical Fiber Communication with Polarization Multiplexing

Polarization effects may induce severe performances degradation in polarization multiplexed optical fiber transmis- sions. Those systems can be seen as 2×2 multi-antennas systems as the emitted polarizations can be considered as 2 input signals and the received polarizations as 2 output signals. Therefore, Space-Time code can be used to take benefit of this configuration and enhance the transmission performances but they have to be combined with optical OFDM to suppress the fiber dispersion and allow their decoding. In wireless 2×2 multi-antennas systems, the Golden and the Silver code are respectively the two best Space- Time codes so, we propose to use those two codes on polarization multiplexed systems. The performances of the Space-Time codes on the optical fiber channel are different than on the wireless channel. Simulations show than the Silver code outperforms the Golden code. Nevertheless, we also show that Space-Time coding can dramatically mitigate the polarization dependent loss (PDL) impairments.

Golden Space–Time Block-Coded Modulation

In this paper, block-coded modulation is used to design a 2 times 2 multiple-input multiple-output (MIMO) space-time code for slow fading channels. The golden code is chosen as the inner code; the scheme is based on a set partitioning of the golden code using two-sided ideals whose norm is a power of two. In this case, a lower bound for the minimum determinant is given by the minimum Hamming distance. The description of the ring structure of the quotients suggests further optimization in order to improve the overall distribution of determinants. Simulation results show that the proposed schemes achieve a significant gain over the un-coded golden code.

Bounded Delay-Tolerant Space Time Block Codes for Asynchronous Cooperative Networks

When distributed cooperative nodes are communicating with a destination, the received signal can be asynchronous due to the propagation or processing delays. This can destroy the space time block code properties designed initially for synchronous case. In this paper, a new construction method of bounded delay tolerant codes is presented. These new codes preserve the full diversity with optimal rates if the relative delays are in a designed delay tolerance interval. The general design method is based on the concatenation and permutation of optimal synchronous space time block codes and works for an arbitrary number of transmitting and receiving antennas. Examples of bounded delay tolerant codes based on the Alamouti code, the Golden code and Threaded Algebraic Space-Time (TAST) codes are given. Theoretical proofs are used to show that the new codes respect the design criteria. Simulation results manifest better error rate performance of the new codes compared to other known delay tolerant codes.

Space-Time Coding Schemes for MDL-Impaired Mode-Multiplexed Fiber Transmission Systems

Spatial division multiplexing (SDM) holds out the prospects of increasing the capacities of optical fiber transmission links, especially with the recent achievements in the design of few-mode fibers and few-mode optical amplifiers. However, these systems are impaired by the capacity-limiting mode dependent loss (MDL) arising from imperfections in the optical fiber and inline components. Optical solutions were suggested to reduce, yet not completely remove, the accumulated MDL in the link through the use of strong coupling fibers and mode scramblers. Inspired by our previous study on mitigating polarization dependent loss (PDL), we present space-time (ST) coding schemes to mitigate MDL in mode-multiplexed optical transmission systems. We show, for the first time, that the combination of redundancy-free ST coding solutions with inline mode scrambling and optimal maximum-likelihood (ML) detection can completely absorb the SNR penalties induced by the MDL. The performance was assessed through simulations of three- and six-mode multiplexed systems where MDL levels up to 10 dB were observed. However, given the increased computational complexity of the suggested ML-decoded ST schemes, we present two reduced-complexity ST solutions offering a near-optimal performance. The first one consists in using a sub-optimal decoder and the second is a multiblock ST coding approach that can be scaled up for larger SDM systems.

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.

New soft stack decoder for MIMO channel

In this paper, we investigate the use of soft output decoders for signals transmitted on linear channels when applied to multiple input multiple output (MIMO) systems. A new soft output MIMO decoder is proposed. Its an extension of the hard stack decoder. A straightforward idea was to exploit internal nodes still stored in the stack at the end of hard decoding process to calculate LLR. We show that the potential gain of such method is rather large then classical soft decoders.

A New Incomplete Decode-and-Forward Protocol

In this work, we explore the introduction of distributed space-time codes in decode-and-forward (DF) protocols. We propose a new Incomplete DF protocol, based on a partial decoding at the relays. This strategy allows the new protocol to bring both full diversity and full symbol rate. Outage probabilities and simulation results show that the Incomplete DF protocol has better performance than any existing DF protocol and than NAF protocols using the same space-time codes.