Abstract Broadband single-carrier modulated signals experience severe multipath distortion when propagating through the physical medium. Correcting the distortion with channel equalization is the foremost task of the detector. Prior information about the transmitted signals in the form of channel decoder feedback can significantly enhance equalization accuracy. An algorithm that iteratively performs channel decoding and equalization with prior information is generally denoted a turbo equalizer. This thesis focuses on turbo equalization with prior information using the principle of interference cancellation followed by minimum mean squared error (MMSE) filtering. Receiver algorithms, receiver convergence, and coding and modulation in the context of MMSE turbo equalization are studied. Computationally efficient versions of the receiver algorithm through approximate time-average filtering, matched filtering, square-root time-variant filtering and frequency-domain filtering are studied. The frequency-domain turbo equalizer (FDTE) is found to exhibit both superior convergence and low computational complexity among the compared equalizer algorithms. Multi-dimensional extrinsic information transfer (EXIT) charts are introduced for the purpose of tracking the convergence of the turbo equalization of layered MIMO transmissions. Generic properties of the equalizer EXIT functions defining the equalizer convergence are analyzed. The principles for detector ordering, maximum sum-rate code design and maximum rate symmetric design are derived from the properties of the multidimensional EXIT functions. Semi-analytical EXIT charts are developed for the convergence analysis of the FDTE. The effects of channel parameters and the channel code are analyzed with semi-analytical methods. A new approach for the design of irregular low-density parity-check (LDPC) codes using a convergence outage principle is proposed. A performance gain is demonstrated in a single-input multiple output (SIMO) channel over non-optimized regular LDPC codes and irregular LDPC codes optimized for the AWGN channel. The outage convergence based design, which takes advantage of the semi-analytical convergence analysis method, is also extended to layered MIMO transmissions. Quadrature amplitude modulation using multilevel bit-interleaved coded modulation (MLBICM) is studied as an alternative to regular bit-interleaved coded modulation (BICM) for highly bandwidth-efficient transmission in MMSE turbo equalized systems. A linear bit-to-symbol mapping is introduced that enables the use of a computationally efficient MMSE turbo equalizer at the receiver. The proposed coded modulation is compared with BICM in channel measurement data based simulations and found to exhibit superior robustness against changes in spatial channel parameters. An automatic repeat request (ARQ) configuration using one ARQ controller for each equally performing group of code levels is proposed. The configuration takes advantage of the unequal error protection (UEP) property of the coded modulation. The semi-analytical convergence analysis is extended to the multilevel modulated case and applied in a channel measurement based convergence evaluation. The construction of the MLBICM is found to have an inherently better convergence behavior than BICM. Finally, the outage convergence based channel code design is extended to the layered MIMO multilevel signalling case.

We consider a two-way relay channel in which two transmitters want to exchange information through a central relay. The relay observes a superposition of the trans- mitted signals from which a function of the transmitted messages is computed for broadcast. We consider the design of codebooks which permit the recovery of a function at the relay and derive information-theoretic bounds on the rates for reliable decoding at the relay. In the spirit of compute-and-forward, we present a multilevel coding scheme that permits reliable computation (or, decoding) of a class of functions at the relay. The function to be decoded is chosen at the relay depending on the channel realization. We define such a class of reliably computable functions for the proposed coding scheme and derive rates that are universally achievable over a set of channel gains when this class of functions is used at the relay. We develop our framework with general modulation formats in mind, but numerical results are presented for the case where each node transmits using 4-ary and 8-ary modulation schemes. Numerical results demonstrate that the flexibility afforded by our proposed scheme permits substantially higher rates than those achievable by always using a fixed function or considering only linear functions over higher order fields. Our numerical results indicate that it is favorable to allow the relay to attempt both compute-and-forward and decode-and-forward decoding. Indeed, either method considered separately is suboptimal for computation over general channels. However, we obtain a converse result when the transmitters are restricted to using identical binary linear codebooks generated uniformly at random. We show that it is impossible for this code ensemble to achieve any rate higher than the maximum of the rates achieved using compute-and-forward and decode-and-forward decoding. Finally, we turn our attention to the design of low density parity check (LDPC) ensembles which can practically achieve these information rates with joint-compute- and-forward message passing decoding. To this end, we construct a class of two-way erasure multiple access channels for which we can exactly characterize the performance of joint-compute-and-forward message passing decoding. We derive the processing rules and a density evolution like analysis for several classes of LDPC ensembles. Utilizing the universally optimal performance of spatially coupled LDPC ensembles with message passing decoding, we show that a single encoder and de- coder with puncturing can achieve the optimal rate region for a range of channel parameters.

<p>In this thesis, a practical superposition coding scheme based on multilevel low-density parity-check (LDPC) codes is proposed for discrete memoryless broadcast channels. The simulation results show that the performance of the proposed scheme approaches the information-theoretic limits. We also propose a method for optimizing the degree distribution of multilevel LDPC codes based on the analysis of EXIT functions.</p> / Master of Applied Science (MASc)