On error correction capability of bit-flipping algorithm for LDPC codes

The error correction capability of bit-flipping decoding algorithm for low density parity-check (LDPC) codes is studied by introducing variable node adjacency (VNA) graphs which are derived from Tanner graphs of LDPC codes. For codes with column weight λ and girth g = 8, it can be shown that error patterns of weight less than or equal to λ - 1 can be corrected. This result implies that the bit-flipping algorithm could decode up to the random error-correcting capability over binary symmetric channel for girth 8 codes whose random error-correcting capability is equal to λ - 1.