Burst Correction Coding From Low-Density Parity-Check Codes

BURST CORRECTION CODING FROM LOW-DENSITY PARITY-CHECK CODES Wai Han Fong, PhD George Mason University, 2015 Dissertation Director: Dr. Shih-Chun Chang Dissertation Co-Director: Dr. Shu Lin This thesis explores techniques and theoretical bounds on efficiently encodable low-density parity-check (LDPC) codes for correcting single and multiple bursts of erasures and/or errors. The approach is to construct good burst correction codes via superposition techniques from smaller constituent codes, such as product codes and/or use existing codes with newer decodings, such as randomly generated LDPC codes with simple recursive erasure decoding. Another goal is to design codes that perform well in a random error environment as well a bursty environment for some channels that change from one state to the other, i.e. a satellite optical link that suffers from fades due to atmospheric scintillation. Novel decoding approaches are explored, i.e. iterative decoding of constituent codes and/or decoding over the entire code. The motivation for this work is the use of multiple burst correction coding for the following types of applications: 1) optical laser communications where atmospheric turbulence create burst errors; 2) wireless communications where fading is created by multipath, or interference from random impulses and jamming; and 3) packet networks where traffic congestion can create erasure bursts from packet losses. Chapter 1: Introduction This thesis is focused on finding new solutions to the classical problem of burst erasure and burst error control for bursty channels. Bursty channels are the result of correlated errors/erasures patterns. Traditional solutions to the this problem involve implementing Reed-Solomon codes. Specifically, this work is focused on exploiting low-density paritycheck (LDPC) codes to solve this problem. Recently, there have been work in this field, [1–3]. We will explore and extend LDPC codes; and apply these codes to multi-dimensional structures, such as product codes and others, as well as use randomly generated LDPC codes in novel approaches.