Abstract:
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.
