Cyclic-Coded Integer-Forcing Equalization

A discrete-time intersymbol interference channel with additive Gaussian noise is considered, where only the receiver has knowledge of the channel impulse response. An approach for combining decision-feedback equalization with channel coding is proposed, where decoding precedes the removal of intersymbol interference. This is accomplished by combining the recently proposed integer-forcing equalization approach with cyclic block codes. The channel impulse response is linearly equalized to an integer-valued response. This is then utilized by leveraging the property that a cyclic code is closed under (cyclic) integer-valued convolution. Explicit bounds on the performance of the proposed scheme are also derived

Integer-Forcing MIMO Linear Receivers Based on Lattice Reduction

A new architecture called integer-forcing (IF) linear receiver has been recently proposed for multiple-input multiple-output (MIMO) fading channels, wherein an appropriate integer linear combination of the received symbols has to be computed as a part of the decoding process. In this paper, we propose a method based on Hermite-Korkine-Zolotareff (HKZ) and Minkowski lattice basis reduction algorithms to obtain the integer coefficients for the IF receiver. We show that the proposed method provides a lower bound on the ergodic rate, and achieves the full receive diversity. Suitability of complex Lenstra-Lenstra-Lovasz (LLL) lattice reduction algorithm (CLLL) to solve the problem is also investigated. Furthermore, we establish the connection between the proposed IF linear receivers and lattice reduction-aided MIMO detectors (with equivalent complexity), and point out the advantages of the former class of receivers over the latter. For the $2 \times 2$ and $4\times 4$ MIMO channels, we compare the coded-block error rate and bit error rate of the proposed approach with that of other linear receivers. Simulation results show that the proposed approach outperforms the zero-forcing (ZF) receiver, minimum mean square error (MMSE) receiver, and the lattice reduction-aided MIMO detectors.Comment: 9 figures and 11 pages. Modified the title, abstract and some parts of the paper. Major change from v1: Added new results on applicability of the CLLL reductio

Integer-Forcing Source Coding

Integer-Forcing (IF) is a new framework, based on compute-and-forward, for decoding multiple integer linear combinations from the output of a Gaussian multiple-input multiple-output channel. This work applies the IF approach to arrive at a new low-complexity scheme, IF source coding, for distributed lossy compression of correlated Gaussian sources under a minimum mean squared error distortion measure. All encoders use the same nested lattice codebook. Each encoder quantizes its observation using the fine lattice as a quantizer and reduces the result modulo the coarse lattice, which plays the role of binning. Rather than directly recovering the individual quantized signals, the decoder first recovers a full-rank set of judiciously chosen integer linear combinations of the quantized signals, and then inverts it. In general, the linear combinations have smaller average powers than the original signals. This allows to increase the density of the coarse lattice, which in turn translates to smaller compression rates. We also propose and analyze a one-shot version of IF source coding, that is simple enough to potentially lead to a new design principle for analog-to-digital converters that can exploit spatial correlations between the sampled signals.Comment: Submitted to IEEE Transactions on Information Theor

Integer-Forcing Linear Receivers

Linear receivers are often used to reduce the implementation complexity of multiple-antenna systems. In a traditional linear receiver architecture, the receive antennas are used to separate out the codewords sent by each transmit antenna, which can then be decoded individually. Although easy to implement, this approach can be highly suboptimal when the channel matrix is near singular. This paper develops a new linear receiver architecture that uses the receive antennas to create an effective channel matrix with integer-valued entries. Rather than attempting to recover transmitted codewords directly, the decoder recovers integer combinations of the codewords according to the entries of the effective channel matrix. The codewords are all generated using the same linear code which guarantees that these integer combinations are themselves codewords. Provided that the effective channel is full rank, these integer combinations can then be digitally solved for the original codewords. This paper focuses on the special case where there is no coding across transmit antennas and no channel state information at the transmitter(s), which corresponds either to a multi-user uplink scenario or to single-user V-BLAST encoding. In this setting, the proposed integer-forcing linear receiver significantly outperforms conventional linear architectures such as the zero-forcing and linear MMSE receiver. In the high SNR regime, the proposed receiver attains the optimal diversity-multiplexing tradeoff for the standard MIMO channel with no coding across transmit antennas. It is further shown that in an extended MIMO model with interference, the integer-forcing linear receiver achieves the optimal generalized degrees-of-freedom.Comment: 40 pages, 16 figures, to appear in the IEEE Transactions on Information Theor

Análise de desempenho de receptores baseados em reticulados para MIMO e fastICA em sistemas MIMO cego massivos

Orientador: Gustavo FraidenraichTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: Estatísticas da taxa-soma dos decodificadores Integer Forcing (IF) e outros decodificadores baseados em reticulados para sistemas de Múltipla Entrada e Múltipla Saída (MIMO) são analisadas. Duas aproximações para a taxa-soma de decodificadores lineares são derivadas. A primeira aproximação é baseada no algoritimo Gauss-Lagrange para sistemas com duas antenas no transmissor e receptor (arranjo 2x2) e canais descorrelacionados. A segunda aproximação considera um sistema com um arranjo nxn de antenas, para o caso correlacionado e descorrelacionado e é baseado no segundo teorema de Minkowiski O desempenho de decodificadores IF e Compute and Forward Transform (CFT) são analisados na presença de erro de estimação de canal. Uma aproximação para a taxa-soma média na presença de erros de estimação de canal e canais com realização fixa é derivada. Uma aproximação para a taxa-soma ergódica dos decodificadores IF na presença de canais correlacionados e descorrelacionados também é derivada. Decodificadores lineares IF atraíram atenção significativa devido ao seu potencial de atingir melhor desempenho do que outros decodificadores lineares, especialmente quando as matrizes de canal são aproximadamente singulares. No entanto, uma análise mais profunda de seu desempenho na presença de canais não determinísticos é necessária para que se possa quantificar sua vantagem em relação a decodificadores lineares clássicos e para que se possa corretamente projetar sistemas baseados nestes decodificadoresAbstract: The statistics of the sum-rate of Integer Forcing (IF) and other lattice-based Multiple Input Multiple Output (MIMO) systems are analyzed. Two approximations to the achievable sum-rate of the IF linear receiver and their respective analytical probability density functions (PDF) are derived. The first approximation is based on the Gauss-Lagrange algorithm for systems with two antennas at the transmitter and receiver (2x2 arrays) and uncorrelated channels. The second approximation considers an nxn array for both correlated and uncorrelated channels and its derivation is based on Minkowiski's second theorem. The performance of IF and Compute and Forward Transform (CFT) receivers is also analyzed under the presence of channel estimation errors. An approximation to their average sum-rate in the presence of these errors for fixed channel realizations is derived. An approximation to the Ergodic IF sum-rate for correlated and uncorrelated channels is also derived. IF linear receiver has attracted significant attention recently due to their potential to perform better than other linear receivers, especially in the presence of channel matrices that are close to singular. However, a more in-depth analysis of its performance in the presence of non-deterministic channels is necessary in order to quantify its advantage over classical linear receivers and to correctly design systems that rely on these decoders. Another contribution of this work involves blind decoding in Massive MIMO systems. We propose a variation to the fast Independent Component Analysis (fastICA) which takes into consideration the shape of the constellations to obtain better performanceDoutoradoTelecomunicações e TelemáticaDoutor em Engenharia ElétricaCAPE

Compute-and-Forward Relay Networks with Asynchronous, Mobile, and Delay-Sensitive Users

We consider a wireless network consisting of multiple source nodes, a set of relays and a destination node. Suppose the sources transmit their messages simultaneously to the relays and the destination aims to decode all the messages. At the physical layer, a conventional approach would be for the relay to decode the individual message one at a time while treating rest of the messages as interference. Compute-and-forward is a novel strategy which attempts to turn the situation around by treating the interference as a constructive phenomenon. In compute-and-forward, each relay attempts to directly compute a combination of the transmitted messages and then forwards it to the destination. Upon receiving the combinations of messages from the relays, the destination can recover all the messages by solving the received equations. When identical lattice codes are employed at the sources, error correction to integer combination of messages is a viable option by exploiting the algebraic structure of lattice codes. Therefore, compute-and-forward with lattice codes enables the relay to manage interference and perform error correction concurrently. It is shown that compute-and-forward exhibits substantial improvement in the achievable rate compared with other state-of-the-art schemes for medium to high signal-to-noise ratio regime. Despite several results that show the excellent performance of compute-and-forward, there are still important challenges to overcome before we can utilize compute-and- forward in practice. Some important challenges include the assumptions of \perfect timing synchronization "and \quasi-static fading", since these assumptions rarely hold in realistic wireless channels. So far, there are no conclusive answers to whether compute-and-forward can still provide substantial gains even when these assumptions are removed. When lattice codewords are misaligned and mixed up, decoding integer combination of messages is not straightforward since the linearity of lattice codes is generally not invariant to time shift. When channel exhibits time selectivity, it brings challenges to compute-and-forward since the linearity of lattice codes does not suit the time varying nature of the channel. Another challenge comes from the emerging technologies for future 5G communication, e.g., autonomous driving and virtual reality, where low-latency communication with high reliability is necessary. In this regard, powerful short channel codes with reasonable encoding/decoding complexity are indispensable. Although there are fruitful results on designing short channel codes for point-to-point communication, studies on short code design specifically for compute-and-forward are rarely found. The objective of this dissertation is threefold. First, we study compute-and-forward with timing-asynchronous users. Second, we consider the problem of compute-and- forward over block-fading channels. Finally, the problem of compute-and-forward for low-latency communication is studied. Throughout the dissertation, the research methods and proposed remedies will center around the design of lattice codes in order to facilitate the use of compute-and-forward in the presence of these challenges

Capacity-Achieving Coding Mechanisms: Spatial Coupling and Group Symmetries

The broad theme of this work is in constructing optimal transmission mechanisms for a wide variety of communication systems. In particular, this dissertation provides a proof of threshold saturation for spatially-coupled codes, low-complexity capacity-achieving coding schemes for side-information problems, a proof that Reed-Muller and primitive narrow-sense BCH codes achieve capacity on erasure channels, and a mathematical framework to design delay sensitive communication systems. Spatially-coupled codes are a class of codes on graphs that are shown to achieve capacity universally over binary symmetric memoryless channels (BMS) under belief-propagation decoder. The underlying phenomenon behind spatial coupling, known as “threshold saturation via spatial coupling”, turns out to be general and this technique has been applied to a wide variety of systems. In this work, a proof of the threshold saturation phenomenon is provided for irregular low-density parity-check (LDPC) and low-density generator-matrix (LDGM) ensembles on BMS channels. This proof is far simpler than published alternative proofs and it remains as the only technique to handle irregular and LDGM codes. Also, low-complexity capacity-achieving codes are constructed for three coding problems via spatial coupling: 1) rate distortion with side-information, 2) channel coding with side-information, and 3) write-once memory system. All these schemes are based on spatially coupling compound LDGM/LDPC ensembles. Reed-Muller and Bose-Chaudhuri-Hocquengham (BCH) are well-known algebraic codes introduced more than 50 years ago. While these codes are studied extensively in the literature it wasn’t known whether these codes achieve capacity. This work introduces a technique to show that Reed-Muller and primitive narrow-sense BCH codes achieve capacity on erasure channels under maximum a posteriori (MAP) decoding. Instead of relying on the weight enumerators or other precise details of these codes, this technique requires that these codes have highly symmetric permutation groups. In fact, any sequence of linear codes with increasing blocklengths whose rates converge to a number between 0 and 1, and whose permutation groups are doubly transitive achieve capacity on erasure channels under bit-MAP decoding. This pro-vides a rare example in information theory where symmetry alone is sufficient to achieve capacity. While the channel capacity provides a useful benchmark for practical design, communication systems of the day also demand small latency and other link layer metrics. Such delay sensitive communication systems are studied in this work, where a mathematical framework is developed to provide insights into the optimal design of these systems