Iterative majority logic decoding of a class of Euclidean Geometry codes

Hard decision decoding of low density parity check (LDPC) codes has potential applications in practical settings like data storage. For this purpose, it is important for the code to have an assured minimum distance and, hence, guaranteed error correction capability. In this paper, we show that with very high probability the guaranteed error correction capability of Euclidean geometry (EG) codes using threshold-optimized, iterative majority logic (ML) decoding is much greater than the usual single iteration ML decoding, making these codes much more attractive for hard decision decoding. For instance, the (262143, 242461, t≥256) EG code (a (512, 512)-regular LDPC code) can correct t=580 bit errors with probability better than 1-1×10^-58.