Communication over channels with synchronization errors

Digital communication systems suffer from imperfect timing information, so receivers need to figure out the best instants at which to sample the received (or read-back) signal. Conventional timing recovery methods function well at reasonably high signal-to-noise ratios. At low signal-to-noise ratios, however, conventional timing recovery methods become unstable, and produce large residual timing errors. Such timing errors lead to substantial performance degradation, and prevent us from fully utilizing the powerful channel codes designed for additive channel distortions.; In this thesis we study several problems related to reliable communications through channels with synchronization (or timing) errors. We first study timing recovery in the classical (i.e., non-iterative) setting, where the synchronization is performed in real-time by a timing recovery loop. We propose two optimality criteria for designing timing recovery loops: (1) based on joint timing error and input sequence detection, and (2) based on timing error detection. We show that both criteria lead to recursive algorithms using state propagation rules. The resulting loop structures are the similar conventional first order phase-locked loops. Simulation results show that the proposed loops reduce the occurrence of cycle-slips in the residual timing errors.; The second problem we consider is optimal (soft-output) channel detector design when there exist large residual timing errors and intersymbol interference. We derive a finite-state homogeneous trellis representation of the discrete random walk timing error process. Based on the trellis, we formulate a forward-backward symbol detection algorithm using the maximum a posteriori probability principle. Using this proposed soft-output detection algorithm, we propose an iterative method that performs timing recovery in cooperation with error-correcting codes. This iterative timing recovery method utilizes the idea of conventional turbo equalization. It is achieved by exchanging extrinsic information between the proposed soft-output detector and an iteratively decodable codes in an iterative manner. Simulation results show that this iterative timing recovery method greatly reduces the bit-error rate, and has the ability to detect cycle-slips.; Finally, we study the achievable transmission rates of channels corrupted by timing errors and finite intersymbol interference. We show that, when the channel input is a finite order Markov process, the channel output process is a hidden Markov process, whose embedded Markov chain has a finite number of states. We further show that this hidden Markov process is ergodic and asymptotically stationary. We then prove that the channels are information stable, as long as the input is a Markov process of finite order. The proof is extended from the proof by Dobrushin for memoryless channels with independent timing errors. Thereby, we show that the Markov-input channel capacity is achievable. We also propose simulation-based methods to numerically bound the asymptotic mutual information rate.