| Low-density parity-check (LDPC) codes are a family of codes proven to have good asymptotic ensemble properties. There are many open theoretical and practical issues related to LDPC codes such as how to construct finite length LDPC codes with guaranteed properties, how to realize rate compatibility with these codes, and how to apply LDPC codes to source coding. This contribution first explains the relationship between cycles, stopping sets and codewords from perspectives of both linear algebra and graph theory. A method based on extrinsic message degree (EMD) is proposed to construct irregular LDPC codes that have good cycle properties. As a result, these codes achieve near capacity capability and low error floors. The performance of different construction schemes are compared and the roles of cycles and stopping sets in affecting capacity and error-floors are analyzed. Next, a rate-compatible scheme based on LDPC codes is proposed. It is based on two techniques: parity puncturing and information nulling. Simulations show that this scheme achieves close-to-capacity performance over a wide range of code rates. Finally, a density evolution analysis is developed for compression of correlated sources using irregular LDPC codes. The standard density evolution algorithm is modified to incorporate the Hidden Markov Model (HMM) defining the correlation model between sources. The proposed algorithm achieves a compression rate close to the theoretical Slepian-Wolf limit. |
