Spatially Coupled Sparse Regression Codes for Single- and Multi-user Communications

Sparse regression codes (SPARCs) are a class of channel codes for efficient communication over the single-user additive white Gaussian noise (AWGN) channel at rates approaching the channel capacity. In a standard SPARC, codewords are sparse linear combinations of columns of an i.i.d. Gaussian design matrix, and the user message is encoded in the indices of those columns. Techniques such as power allocation and spatial coupling have been proposed to improve the performance of low-complexity iterative decoding algorithms such as approximate message passing (AMP). In this thesis we investigate spatially coupled SPARCs, where the design matrix has a block- wise band-diagonal structure, and modulated SPARCs, which generalise standard SPARCs by introducing modulation to the encoding of user messages. We introduce a base matrix framework which provides a unified way to construct power allocated and spatially coupled design matrices, and propose AMP decoders for modulated SPARCs constructed using base matrices. We prove that phase shift keying modulated and spatially coupled SPARCs with AMP decoding asymptotically achieve the capacity of the (complex) AWGN channel. We also show via numerical simulations that they can achieve lower error rates than standard coded modulation schemes at finite code lengths. A sliding window AMP decoder is proposed for spatially coupled SPARCs that significantly reduces the decoding latency and complexity. We then investigate coding schemes based on random linear models and AMP decoding for the multi-user Gaussian multiple access channel in the asymptotic regime where the number of users grows linearly with the code length. For a fixed target error rate and message size per user (in bits), we obtain the exact trade-off between energy-per-bit and the user density achievable in the large system limit. We show that a coding scheme based on spatially coupled Gaussian matrices and AMP decoding achieves near-optimal trade-off for a large range of user densities. To the best of our knowledge, this is the first efficient coding scheme to do so in this multiple access regime. Moreover, the spatially coupled coding scheme has a practical interpretation: it can be viewed as block-wise time-division with overlap.Funded by a Doctoral Training Partnership Award from the Engineering and Physical Sciences Research Council

State-of-the-art in Power Line Communications: from the Applications to the Medium

In recent decades, power line communication has attracted considerable attention from the research community and industry, as well as from regulatory and standardization bodies. In this article we provide an overview of both narrowband and broadband systems, covering potential applications, regulatory and standardization efforts and recent research advancements in channel characterization, physical layer performance, medium access and higher layer specifications and evaluations. We also identify areas of current and further study that will enable the continued success of power line communication technology.Comment: 19 pages, 12 figures. Accepted for publication, IEEE Journal on Selected Areas in Communications. Special Issue on Power Line Communications and its Integration with the Networking Ecosystem. 201

Successive Integer-Forcing and its Sum-Rate Optimality

Integer-forcing receivers generalize traditional linear receivers for the multiple-input multiple-output channel by decoding integer-linear combinations of the transmitted streams, rather then the streams themselves. Previous works have shown that the additional degree of freedom in choosing the integer coefficients enables this receiver to approach the performance of maximum-likelihood decoding in various scenarios. Nonetheless, even for the optimal choice of integer coefficients, the additive noise at the equalizer's output is still correlated. In this work we study a variant of integer-forcing, termed successive integer-forcing, that exploits these noise correlations to improve performance. This scheme is the integer-forcing counterpart of successive interference cancellation for traditional linear receivers. Similarly to the latter, we show that successive integer-forcing is capacity achieving when it is possible to optimize the rate allocation to the different streams. In comparison to standard successive interference cancellation receivers, the successive integer-forcing receiver offers more possibilities for capacity achieving rate tuples, and in particular, ones that are more balanced.Comment: A shorter version was submitted to the 51st Allerton Conferenc

Spatially-Coupled LDPC Codes for Decode-and-Forward Relaying of Two Correlated Sources over the BEC

We present a decode-and-forward transmission scheme based on spatially-coupled low-density parity-check (SC-LDPC) codes for a network consisting of two (possibly correlated) sources, one relay, and one destination. The links between the nodes are modeled as binary erasure channels. Joint source-channel coding with joint channel decoding is used to exploit the correlation. The relay performs network coding. We derive analytical bounds on the achievable rates for the binary erasure time-division multiple-access relay channel with correlated sources. We then design bilayer SC-LDPC codes and analyze their asymptotic performance for this scenario. We prove analytically that the proposed coding scheme achieves the theoretical limit for symmetric channel conditions and uncorrelated sources. Using density evolution, we furthermore demonstrate that our scheme approaches the theoretical limit also for non-symmetric channel conditions and when the sources are correlated, and we observe the threshold saturation effect that is typical for spatially-coupled systems. Finally, we give simulation results for large block lengths, which validate the DE analysis.Comment: IEEE Transactions on Communications, to appea