Irregular LDPC Code Design using Large Girth Tanner Graphs

Abstract

Low-density parity-check (LDPC) codes are error-correcting codes that have been shown to have good performance approaching Shannon’s limit. Although initially developed in the early 1960’s, LDPC codes have experienced a remarkable comeback in recent years. As a result, numerous modern communication standards have embraced LDPC codes. To achieve high processing speed and energy efficiency, both the encoding and decoding processes must have a low level of complexity. LDPC codes can be represented graphically by Tanner graphs. Tanner graphs with a large girth are often used because of their excellent performance in terms of error correction and transmission efficiency. The primary objective of this thesis is to explore the encoding and decoding processes to answer the question why a large girth in the Tanner graph is beneficial. Moreover, this thesis presents methods to construct these large girth Tanner graphs for irregular LDPC codes.