Principles And Code-Design Of LDPC Codes

Low-density parity-check codes come to be one of the best coding technologies because of their low-complicity iterative decoding algorithm and capacity approaching performance, and they attract more and more researchers' eyes in recent years. In this dissertation, the basic principles of the coding and decoding of LDPC codes are studied systematically, and some code-design problems such as the design of degree distribution sequences, the design of girths and the design of efficient encode-able LDPC codes are analyzed in detail. Based on all these efforts, some positive results are obtained and summarized as follow:1. The coding and decoding ideas of low-density parity-check codes on graphs are systematically summarized, and the density evolution theory is introduced. The two leading factors on the performance of LDPC codes, i.e. the degree distribution sequences and the girths of these codes, are analyzed in detail;2. The principles of Erasure codes used under Binary Erasure Channels are summarized and Erasure codes which belong to standard classes of RS codes are introduced with emphasis on cascaded low-density erasure codes with linear time encoding and erasure recover algorithms.Thresholds of regular degree distributions are analyzed. It is shown that low-density erasure codes based on (d,2d) -regular sequences of degree distribution are not close to optimal (d 3) .Two pares of irregular degree distribution sequences are introduced and a pare of improved right regular sequences of low-density erasure codes are presented, It is testified that the new sequences are asymptotically quasi-optimal. In the meantime, simulations of cascaded low-density erasure codes based on a few types of special sequences of degree distribution available are given, together with performance analyses on these codes.3. The available design methods of LDPC codes with large girth are introduced and a new construction of regular LDPC codes with large girth is brought along with its realization algorithm, and the performances of the LDPC codes generated by this method are analyzed and simulated under AWGN channels. Improved Progressive Edge-Growth algorithm is presented by which the LDPC codes generated can satisfy the given degree distribution strictly.4. The efficient encoding problem of LDPC codes is discussed in detail, and the reasons that Tornado codes and repeat accumulate codes are linear encode-able and the relationships between them and efficient encode-able LDPC codes are presented. Two constructions of linear encode-able LDPC codes are brought up and their performances under AWGN channels are simulated.