Analysis and Design of Finite-Length LDPC Codes

We consider the performance analysis and code construction of finite-length low-density parity-check (LDPC) codes. First, by convergence analysis based on the extrinsic information evolution, we analyze the performance of both regular and irregular finite-length LDPC codes under iterative decoding. Next, by focusing on a special class of LDPC codes, namely, systematic irregular repeat-accumulate (IRA) codes, we propose a design procedure to construct finite-length LDPC codes. In addition to giving rise to a simple encoding structure, the special structure of IRA codes can be exploited to introduce unequal protection with cycle control for different types of nodes in the factor-graph code representation. We propose a modified bit-filling algorithm that leads to the construction of a set of finite-length IRA codes with low error floors.