Distributed Structure: Joint Expurgation for the Multiple-Access Channel

In this work we show how an improved lower bound to the error exponent of the memoryless multiple-access (MAC) channel is attained via the use of linear codes, thus demonstrating that structure can be beneficial even in cases where there is no capacity gain. We show that if the MAC channel is modulo-additive, then any error probability, and hence any error exponent, achievable by a linear code for the corresponding single-user channel, is also achievable for the MAC channel. Specifically, for an alphabet of prime cardinality, where linear codes achieve the best known exponents in the single-user setting and the optimal exponent above the critical rate, this performance carries over to the MAC setting. At least at low rates, where expurgation is needed, our approach strictly improves performance over previous results, where expurgation was used at most for one of the users. Even when the MAC channel is not additive, it may be transformed into such a channel. While the transformation is lossy, we show that the distributed structure gain in some "nearly additive" cases outweighs the loss, and thus the error exponent can improve upon the best known error exponent for these cases as well. Finally we apply a similar approach to the Gaussian MAC channel. We obtain an improvement over the best known achievable exponent, given by Gallager, for certain rate pairs, using lattice codes which satisfy a nesting condition.Comment: Submitted to the IEEE Trans. Info. Theor

Algebraic Approach to Physical-Layer Network Coding

The problem of designing physical-layer network coding (PNC) schemes via nested lattices is considered. Building on the compute-and-forward (C&F) relaying strategy of Nazer and Gastpar, who demonstrated its asymptotic gain using information-theoretic tools, an algebraic approach is taken to show its potential in practical, non-asymptotic, settings. A general framework is developed for studying nested-lattice-based PNC schemes---called lattice network coding (LNC) schemes for short---by making a direct connection between C&F and module theory. In particular, a generic LNC scheme is presented that makes no assumptions on the underlying nested lattice code. C&F is re-interpreted in this framework, and several generalized constructions of LNC schemes are given. The generic LNC scheme naturally leads to a linear network coding channel over modules, based on which non-coherent network coding can be achieved. Next, performance/complexity tradeoffs of LNC schemes are studied, with a particular focus on hypercube-shaped LNC schemes. The error probability of this class of LNC schemes is largely determined by the minimum inter-coset distances of the underlying nested lattice code. Several illustrative hypercube-shaped LNC schemes are designed based on Construction A and D, showing that nominal coding gains of 3 to 7.5 dB can be obtained with reasonable decoding complexity. Finally, the possibility of decoding multiple linear combinations is considered and related to the shortest independent vectors problem. A notion of dominant solutions is developed together with a suitable lattice-reduction-based algorithm.Comment: Submitted to IEEE Transactions on Information Theory, July 21, 2011. Revised version submitted Sept. 17, 2012. Final version submitted July 3, 201

Reticulados em problemas de comunicação

Orientadores: Sueli Irene Rodrigues Costa, Vinay Anant VaishampayanTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação CientíficaResumo: O estudo de códigos no contexto de reticulados e outras constelações discretas para aplicações em comunicações é um tópico de interesse na área de teoria da informação. Certas construções de reticulados, como é o caso das Construções A e D, e de outras constelações que não são reticulados, como a Construção C, são utilizadas na decodificação multi-estágio e para quantização vetorial eficiente. Isso motiva a primeira contribuição deste trabalho, que consiste em investigar características da Construção C e propor uma nova construção baseada em códigos lineares, que chamamos de Construção $C^\star,$ analisando suas propriedades (condições para ser reticulado, uniformidade geométrica e distância mínima) e relação com a Construção C. Problemas na área de comunicações envolvendo reticulados podem ser computacionalmente difíceis à medida que a dimensão aumenta, como é o caso de, dado um vetor no espaço real $n-$dimensional, determinar o ponto do reticulado mais próximo a este. A segunda contribuição deste trabalho é a análise desse problema restrito a um sistema distribuído, ou seja, onde o vetor a ser decodificado possui cada uma de suas coordenadas disponíveis em um nó distinto desse sistema. Nessa investigação, encontramos uma solução aproximada para duas e três dimensões considerando a partição de Babai e também estudamos o custo de comunicação envolvidoAbstract: The study of codes in the context of lattices and other discrete constellations for applications in communications is a topic of interest in the area of information theory. Some lattice constructions, such as the known Constructions A and D, and other special nonlattice constellations, as Construction C, are used in multi-stage decoding and efficient vector quantization. This motivates the first contribution of this work, which is to investigate characteristics of Construction C and to propose a new construction based on linear codes that we called Construction $C^\star,$ analyzing its properties (latticeness, geometric uniformity and minimum distance) and relations with Construction C. Communication problems related to lattices can be computationally hard when the dimension increases, as it is the case of, given a real vector in the $n-$dimensional space, determine the closest lattice point to it. The second contribution of this work is the analysis of this problem restricted to a distributed system, i.e., where the vector to be decoded has each coordinate available in a separated node in this system. In this investigation, we find the approximate solution for two and three dimensions considering the Babai partition and study the communication cost involvedDoutoradoMatematica AplicadaDoutora em Matemática Aplicada140797/2017-3CNPQCAPE

Relaying Strategies for Cooperative Systems

In this thesis, we investigate several relaying strategies for cooperative networks with the aim of finding techniques to improve the performance of such networks. The objective here is to increase the spectral efficiency while achieving full diversity. Therefore, we focus on two-way relaying and relay assignment since they are both efficient ways in improving the spectral efficiency of cooperative networks. Specifically,we propose efficient relay strategies to cope with the asymmetric data rates in two-way relay channels and address practical issues in relay assignment. In the first part of the thesis, we consider two decode-and-forward (DF) relaying schemes for two-way relaying channels where the two sources may have different rate requirements. One scheme combines hierarchical zero padding and network coding (HZPNC) at the relay. The novelty of this scheme lies in the way the two signals (that have different lengths) are network-coded at the relay. The other scheme is referred to as opportunistic user selection (OUS) where the user with a better end-to-end channel quality is given priority for transmission. We analyze both schemes where we derive closed form expressions for the end-to-end(E2E) bit error rate (BER). Since the two schemes offer a trade-off between performance and throughput, we analyze and compare both schemes in terms of channel access probability and average throughput. We show that HZPNC offers better throughput and fairness for both users, whereas OUS offers better performance. We also compare the performance of HZPNC with existing schemes including the original zero padding, nesting constellation modulation and superposition modulation. We demonstrate through examples the superiority of the proposed HZPNC scheme in terms of performance and/or reduced complexity. In the second part of the thesis, we consider a hybrid relaying scheme for two-way relay channels. As per the proposed scheme, if the E2E signal-to-noise ratio (SNR) of both users is above a specified threshold, both sources transmit over orthogonal channels and the relay node uses hierarchical modulation and network coding to relay the combined signals to both sources in the third time slot. Otherwise, the user with the better E2E SNR transmits, while the other user remains silent. The advantage of the proposed scheme is that it compromises between throughput and reliability. That is, when both users transmit, the throughput improves. Whereas when the better user transmits, multiuser diversity is achieved. Assuming asymmetric channels, we derive exact closed-form expressions for the E2E BER, access probability and throughput for this scheme and compare its performance to that of existing schemes. We also investigate the asymptotic performance of the proposed scheme at high SNRs where we derive the achievable diversity order of both users. We show through analytically and simulation results that the proposed scheme improves 1) the overall system throughput, 2) fairness between the two users, and 3) the transmission reliability. This all comes while achieving diversity two for both users, which is the maximal diversity. In the third part of the thesis, we study relay assignment with limited feedback. In networks with many multiple source-destination pairs, it is normally diffcult for destinations to acquire the channel state information (CSI) of the entire network without feedback. To this end, we design a practical limited feedback strategy in conjunction with two relay assignment schemes, i.e., fullset selection and subset selection, which are based on maximizing the minimum E2E SNR among all pairs. In this strategy, each destination acquires its SNR,quantizes it, and feeds it back to the relays. The relays then construct the E2E SNR table and select the relay assignment permutation from all possible relay assignment permutations or only a subset of these permutations. We analyze the performance of these schemes over independent Rayleigh fading channels in terms of the worst E2E SNR. We derive closed-form expressions for the E2E BER and investigate the asymptotic performance at high SNR. We show that relay assignment with quantized CSI can achieve the same first-order diversity as that of the full CSI case, but there is a second-order diversity loss. We also demonstrate that increasing the quantization levels yields performance that is close to that of having full knowledge of the CSI

Embedded Rank Distance Codes for ISI channels

Designs for transmit alphabet constrained space-time codes naturally lead to questions about the design of rank distance codes. Recently, diversity embedded multi-level space-time codes for flat fading channels have been designed from sets of binary matrices with rank distance guarantees over the binary field by mapping them onto QAM and PSK constellations. In this paper we demonstrate that diversity embedded space-time codes for fading Inter-Symbol Interference (ISI) channels can be designed with provable rank distance guarantees. As a corollary we obtain an asymptotic characterization of the fixed transmit alphabet rate-diversity trade-off for multiple antenna fading ISI channels. The key idea is to construct and analyze properties of binary matrices with a particular structure induced by ISI channels.Comment: Submitted to IEEE Transactions on Information Theor

Coding for Relay Networks with Parallel Gaussian Channels

A wireless relay network consists of multiple source nodes, multiple destination nodes, and possibly many relay nodes in between to facilitate its transmission. It is clear that the performance of such networks highly depends on information for- warding strategies adopted at the relay nodes. This dissertation studies a particular information forwarding strategy called compute-and-forward. Compute-and-forward is a novel paradigm that tries to incorporate the idea of network coding within the physical layer and hence is often referred to as physical layer network coding. The main idea is to exploit the superposition nature of the wireless medium to directly compute or decode functions of transmitted signals at intermediate relays in a net- work. Thus, the coding performed at the physical layer serves the purpose of error correction as well as permits recovery of functions of transmitted signals. For the bidirectional relaying problem with Gaussian channels, it has been shown by Wilson et al. and Nam et al. that the compute-and-forward paradigm is asymptotically optimal and achieves the capacity region to within 1 bit; however, similar results beyond the memoryless case are still lacking. This is mainly because channels with memory would destroy the lattice structure that is most crucial for the compute-and-forward paradigm. Hence, how to extend compute-and-forward to such channels has been a challenging issue. This motivates this study of the extension of compute-and-forward to channels with memory, such as inter-symbol interference. The bidirectional relaying problem with parallel Gaussian channels is also studied, which is a relevant model for the Gaussian bidirectional channel with inter-symbol interference and that with multiple-input multiple-output channels. Motivated by the recent success of linear finite-field deterministic model, we first investigate the corresponding deterministic parallel bidirectional relay channel and fully characterize its capacity region. Two compute-and-forward schemes are then proposed for the Gaussian model and the capacity region is approximately characterized to within a constant gap. The design of coding schemes for the compute-and-forward paradigm with low decoding complexity is then considered. Based on the separation-based framework proposed previously by Tunali et al., this study proposes a family of constellations that are suitable for the compute-and-forward paradigm. Moreover, by using Chinese remainder theorem, it is shown that the proposed constellations are isomorphic to product fields and therefore can be put into a multilevel coding framework. This study then proposes multilevel coding for the proposed constellations and uses multistage decoding to further reduce decoding complexity

Distributed Reception in the Presence of Gaussian Interference

abstract: An analysis is presented of a network of distributed receivers encumbered by strong in-band interference. The structure of information present across such receivers and how they might collaborate to recover a signal of interest is studied. Unstructured (random coding) and structured (lattice coding) strategies are studied towards this purpose for a certain adaptable system model. Asymptotic performances of these strategies and algorithms to compute them are developed. A jointly-compressed lattice code with proper configuration performs best of all strategies investigated.Dissertation/ThesisDoctoral Dissertation Electrical Engineering 201