Turbo design for LDPC codes with large girth

LDPC codes, with performance extremely close to the theoretical limit, are gaining increased attention of the communication systems designers. LDPC codes with good girth properties are of particular interest. In this paper, we design large girth regular LDPC codes in a turbo-like manner. Specifically, we describe codes that are two sub-trees interconnected by an interleaver. Careful design of the interleaver block eliminates short cycles in its factor graph. We present designs for turbo-like LDPC codes with column weight j ≥ 3 and girth at least 8 and with column weight j = 2 and girth at least 16. These proposed codes support a wide range of code rates and code block length, suitable for most practical applications.