Low Complexity Progressive Edge-Growth Algorithm Based on Chinese Remainder Theorem

Progressive edge-growth (PEG) algorithm construction builds the Tanner graph for an LDPC code by establishing edges between the symbol nodes and the check nodes in an edge-by-edge manner and maximizing the local girth in a greedy fashion. This approach is simple but the computational complexity of the PEG algorithm scale as O(nm), where n is the number of symbol nodes and m is the number of check nodes. We deal with this problem by first construct a base LDPC code of length n
₁
with the PEG algorithm and then extend this LDPC code into an LDPC code of length n, where n ≥ n
₁
, via the the chinese remainder theorem (CRT). This method increase the code length of an LDPC code generated with the PEG algorithm, without decreasing its girth. Due to the code length reducing in the PEG construction step, the computational complexity of the whole code construction process is reduced. Furthermore, the proposed algorithm have a potential advantage by storing a small parity-check matrix of a base code and extending it “on-the-fly” in hardware.