| The main goal for the communication engineer is to design the encoder and decoder so that the system can transmit data reliably at the highest possible transmission rate. To achieve this goal, channel coding, which is the focus of this thesis, strategically adds redundancy to the transmitted data, and coding theory has provided specific transmission schemes that approach the capacity for point-to-point links.;Historically, most of the aforementioned schemes are designed for the case of memoryless channels. For channels with memory, however, few results exist on capacity-achieving codes. This is the first direction explored in this thesis, i.e. finding capacity-achieving scheme for channels with memory. In particular, capacity-achieving codes are constructed for channels with memory when the receiver employs maximum likelihood decoding. The codes are derived from the corresponding capacity-achieving codes for memoryless channels by using block-wise Markov quantization. The constructed quantized codes induce Markov distribution on the channel input sequence and are shown to achieve the corresponding information rate.;It has been well known that feedback can improve the error performance and/or simplify the transmission scheme, and may increase the capacity. There have been several remarkable results on designing transmission schemes with feedback, but again, most of these results are for the case of memoryless channels. The second direction in this thesis, therefore, is to design simple transmission schemes for channels with memory in the presence of feedback. As the starting point of the investigation, a single-letter capacity expression is derived for the channel in consideration. Based on this capacity expression and corresponding capacity-achieving distribution, a feedback transmission scheme which achieves the capacity of channels with memory and feedback is proposed. For the case of channels with no inter-symbol interference (ISI) it is shown that the proposed transmission scheme is a straightforward generalization of the one proposed for memoryless channels. For the case where ISI is present a substantially different scheme is proposed and shown to achieve the channel capacity. |
