Focusing on the analysis and system design for single-user communication with noiseless feedback, this dissertation consists of two parts. The first part explores the analysis of feedback systems using incremental redundancy (IR) with noiseless transmitter confirmation (NTC). For IR-NTC systems based on finite-length codewords and decoding attempts only at certain specified decoding times, this dissertation studies the asymptotic expansion achieved by random coding, provides rate-compatible sphere-packing (RCSP) performance approximations, and presents simulation results of tail-biting convolutional codes. The RCSP approximations show great agreement with the convolutional code simulations. Both the approximations and the simulations yield expected throughputs significantly higher than random codes at short latencies.

Motivated by the analyses and optimizations in the first part, the second part of this dissertation proposes a new class of rate-compatible low-density parity-check codes, called Protograph-Based Raptor-Like (PBRL) codes. Similar to Raptor codes, PBRL codes can efficiently produce incremental redundancy, providing extensive rate compatibility. The construction and optimization of PBRL codes suitable for both long-blocklength and short-blocklength applications are discussed. Finally, this dissertation provides examples of constructing PBRL codes with different blocklengths. Extensive simulation results of the PBRL code examples and three other standardized channel codes (3GPP-LTE, CCSDS and DVB-S2) are presented and compared.