An analytically tractable model for Gaussian multiuser channels with fading is studied, and the capacity region of this model is found to be a good approximation of the capacity region of the original Gaussian network. This work extends the existing body of work on deterministic models for Gaussian multiuser channels to include the physical phenomenon of fading. In particular, it generalizes these results to a unicast, multiple node network setting with fading. / text

Sparse regression codes (SPARCs) are a recently introduced coding scheme for the additive white Gaussian noise channel, for which polynomial time decoding algorithms have been proposed which provably achieve the Shannon channel capacity. One such algorithm is the approximate message passing (AMP) decoder. However, directly implementing these decoders does not yield good empirical performance at practical block lengths. This thesis develops techniques for improving both the error rate performance, and the time and memory complexity, of the AMP decoder. It focuses on practical and efficient implementations for both single- and multi-user scenarios. A key design parameter for SPARCs is the power allocation, which is a vector of coefficients which determines how codewords are constructed. In this thesis, novel power allocation schemes are proposed which result in several orders of magnitude improvement to error rate compared to previous designs. Further improvements to error rate come from investigating the role of other SPARC construction parameters, and from performing an online estimation of a key AMP parameter instead of using a pre-computed value. Another significant improvement to error rates comes from a novel three-stage decoder which combines SPARCs with an outer code based on low-density parity-check codes. This construction protects only vulnerable sections of the SPARC codeword with the outer code, minimising the impact to the code rate. The combination provides a sharp waterfall in bit error rates and very low overall codeword error rates. Two changes to the basic SPARC structure are proposed to reduce computational and memory complexity. First, the design matrix is replaced with an efficient in-place transform based on Hadamard matrices, which dramatically reduces the overall decoder time and memory complexity with no impact on error rate. Second, an alternative SPARC design is developed, called Modulated SPARCs. These are shown to also achieve the Shannon channel capacity, while obtaining similar empirical error rates to the original SPARC, and permitting a further reduction in time and memory complexity. Finally, SPARCs are implemented for the broadcast and multiple access channels, and for the multiple description and Wyner-Ziv source coding models. Designs for appropriate power allocations and decoding strategies are proposed and are found to give good empirical results, demonstrating that SPARCs are also well suited to these multi-user settings.

The low-voltage power distribution network is considered today as a serious candidate to provide residential customers with a high-speed access to communication services such as Internet. Outdoor Power-Line Communications (PLC) systems represent an alternative to the other classical 'last-mile solutions' such as ADSL, cable modems, or wireless access systems. We developed an accurate powerline channel simulation tool based on the Multiconductor Transmission Line theory. This tool is able to predict the end-to-end channel responses on the basis of the multiconductor cable structure and the network topology. Then the issue of optimal resource allocation in a multiuser environment was addressed in the light of the Multiuser Information Theory. Simultaneously active users are in competition for the limited resources that are the power (constrained by electro-magnetic compatibility restrictions) and the bandwidth (in the range of 1 to 10 MHz for outdoor PLC). The concept of multiuser balanced capacity was introduced to characterize the optimal resource allocation providing the maximum data rates with fairness constraints among the subscribers. The optimal PLC system was shown to require the shaping of the signal spectrum in the transmitters, and successive decoding in the receiver. A generic multiple access scheme based on Filter Banks (FB) was proposed, which offers the required spectral shaping with limited degrees of freedom. Classical multiple-access techniques (TDMA, CDMA, OFDMA) can be obtained by selecting the appropriate FB. The Minimum-Mean-Square-Error Decision-Feedback Joint Detector was shown to approach the performance of the optimal successive decoding receiver. Finally, the robustness of the proposed system against channel estimation and timing synchronization errors was addressed. The problem of multiuser timing synchronization was introduced, and practical multiuser timing error detectors were proposed.

Since direct-sequence code-division multiple-access (DS-CDMA) is an interference-limited random multiple-access scheme, the reduction of co-channel interference with either interference suppression or interference cancellation multiuser receivers and/or power control to prevent detrimental near-far situations is vital for improved performance. Up to date, some contributions investigated randomly-spread asymptotically - large number of users and large bandwidth - large CDMA systems with multiuser receivers and power control via random matrix theoretic and free probability theoretic tools especially over Gaussian and single-path fading channels. As complement within this thesis, we analyze also within the generalized random spreading framework but at finite system sizes and without power control the capacity achievable with linear multichannel multiuser receivers / i.e. RAKE, zero-forcing decorrelator, linear minimum mean-squared error (LMMSE) multiuser receivers, within a single-cell setting over generalized time-varying GWSSUS - Rayleigh/Ricean - fading channels via random matrix theoretic tools. Assuming maximal-ratio combining (MRC) of resolved frequency - multipath - diversity channels due to wideband transmission, the signal-to-interference ratios (SIRs) with multichannel multiuser receivers that set the basis for further derivations are statistically characterized. The information-theoretic ergodic and outage sum-rates spectral efficiencies are then derived and analyzed.