A Decoding Algorithm for Finite-Geometry LDPC Codes

In this paper, we develop a new low-complexity algorithm to decode low-density parity-check (LDPC) codes. The developments are oriented specifically toward low cost, yet effective, decoding of (high-rate) finite-geometry LDPC codes. The decoding procedure iteratively updates the hard-decision received vector in search of a valid codeword in the vector space. Only one bit is changed in each iteration, and the bit-selection criterion combines the number of failed checks and the reliability of the received bits. Prior knowledge of the signal amplitude and noise power is not required. An optional mechanism to avoid infinite loops in the search is also proposed. Our studies show that the algorithm achieves an appealing tradeoff between performance and complexity for finite-geometry LDPC codes.