Coding for insertion/deletion channels

Insertion and deletion errors represent an important category of channel impairments. Despite their importance and much work over the years, channels with such impairments are far from being fully understood as they proved to be difficult to analyze. In this dissertation, a promising coding scheme is investigated over independent and identically distributed (i.i.d.) insertion/deletion channels, i.e., interleaved concatenation of an outer low-density parity-check (LDPC) code with error-correction capabilities and an inner marker code for synchronization purposes. Marker code structures which offer the highest achievable rates are found with standard bit-level synchronization is performed. Then, to exploit the correlations in the likelihoods corresponding to different transmitted bits, a novel symbol-level synchronization algorithm that works on groups of consecutive bits is introduced. Extrinsic information transfer (EXIT) charts are also utilized to analyze the convergence behavior of the receiver, and to design LDPC codes with degree distributions matched to these channels. The next focus is on segmented deletion channels. It is first shown that such channels are information stable, and hence their channel capacity exists. Several upper and lower bounds are then introduced in an attempt to understand the channel capacity behavior. The asymptotic behavior of the channel capacity is also quantified when the average bit deletion rate is small. Further, maximum-a-posteriori (MAP) based synchronization algorithms are developed and specific LDPC codes are designed to match the channel characteristics. Finally, in addition to binary substitution errors, coding schemes and the corresponding detection algorithms are also studied for several other models with synchronization errors, including inter-symbol interference (ISI) channels, channels with multiple transmit/receive elements and multi-user communication systems.