Ldpc Codes Of Girth Increase

Achieving reliable communication approaching Shannon's capacity limit ate?ective power cost is the ultimate object of modern channel coding technique.It is possible to come close to the object, since the discovery and the developmentof low-density parity-check (LDPC) codes. Combining the existing theory andpractical results, constructions of LDPC codes with excellent performance andlow encoding complexity have been research focus. In this dissertation, the girthof LDPC codes are investigated. The main fruits are summarized as follows:1. We introduce the basic compositions of digital communication system ,the development of channel encoding technique , the model of additivegaussian white noise channel and current research situation of quasi-cyclicLDPC (QC-LDPC) codes.2. We introduce the strcture of the LDPC codes, the Tanner graph represen-tation and the girth of LDPC codes.3. We summarize some important theorems and properties about the girth ofLDPC codes, and prsent the former results by tables, in which the minimalorder of circulant permutation matrices to acheive given girth are given.4. We develop a greedy search algorithm which greatly improve the former re-sults of minimum matrix extension order. We get some codes by using thisalgorithm. Simulation results present for these codes. Using BPSK modu-lating in additive gaussian white noise channel, the characteristic curve ofdecipher hastens and borders on Shannon's limit more and more, and willnot appear error ?oor.5. We propose the concept and definition of balanced-cycles, provide a uniform form of balanced-cycles, point out the way to find balanced-cycles in theparity-check matrix.