Improved reversible LDPC codes

We provide a thorough analysis for a class of iteratively encodable low-density parity-check codes. The iterative encoding technique is based upon the graphical representation of the code and allows the decoder circuit to also be used for encoding, thus saving circuit area. The analysis identifies a weakness in the structure of the code, which arises due to a repetitive pattern in its factor graph. We show that the graph supports pseudo-codewords of low pseudo-weight, and relate this to the empirical observation of some near-codewords. We then propose a new recursive technique for constructing iteratively encodable codes which have improved expansion. The new codes offer a large amount of flexibility in the choice of code length and rate, and performance that compares well to both randomly generated and extended Euclidean-geometry codes