UC San Diego

Right from the birth of communication theory, synchronization errors have been a challenge. In the first part of this dissertation, we will consider a class of synchronization error channels and develop a rigorous information theoretic analysis. We provide analytical bounds on the capacity of channels that introduce deletions or replications. For channels that introduce deletions and replications, we develop methods to approximately estimate the achievable information rates. Following this, we consider specific applications in magnetic recording where synchronization errors play a key role. For these applications, we provide bounds and numerical estimates of the channel capacity as well as the zero-error capacity. In the second part of the dissertation, we will focus on a coding theoretic problem of analyzing a low-complexity decoding scheme for spatially coupled codes over the erasure channel. We describe the operation of windowed decoding, and analytically establish its asymptotic performance limits. For protograph-based LDPC convolutional codes, which are a variant of the spatially coupled codes, we identify characteristics of code ensembles that result in good performance with the windowed decoding algorithm over erasure channels with and without memory