Reliability-output Decoding and Low-latency Variable-length Coding Schemes for Communication with Feedback
Feedback links are ubiquitous in modern communication systems. This dissertation is focused on the short-blocklength performance of coded communication systems with feedback and is organized in three main parts. The first section presents a novel reliability-output decoding algorithm for tail-biting convolutional codes, based on Raghavan and Baum's Reliability-Output Viterbi Algorithm (ROVA) for terminated convolutional codes. Whereas terminated convolutional codes suffer from a rate penalty at short blocklengths, tail-biting convolutional codes do not suffer from rate loss, making them throughput-efficient and suitable for used in reliability-based retransmission schemes with short blocklengths.
The second portion of the dissertation analyzes the performance of deterministic variable-length feedback coding schemes, focusing on blocklengths less than 300 symbols. In both the decision-feedback and information-feedback settings, we demonstrate that tail-biting convolutional codes can deliver rates surpassing the random-coding lower bound at blocklengths less than 100 symbols. The decision-feedback scheme uses the tail-biting ROVA to determine when to stop transmission, which requires only a single bit of feedback (ACK/NACK) after each decoding attempt. In contrast, the information-feedback scheme employs two-phase incremental redundancy and uses feedback of the received symbols to confirm or reject the decoder's tentative estimate. Finally, we discuss implications of these schemes when used in practical systems, namely the performance when decoding is limited to packets instead of individual symbols.
Finally, using the information-theoretic framework of the second section, the third part of this dissertation investigates the energy efficiency of variable-length feedback codes compared to that of fixed-length block codes without feedback. While the latency reduction obtained with feedback can decrease transmitter power consumption, attempting decoding after every received symbol significantly increases receiver power consumption. Care must be taken to choose decoding intervals that balance the competing interests of transmitter and receiver power.