A message-passing decoding algorithm for q-ary LDPC codes with low-complexity

This paper presents a novel low-complexity iterative reliability-based decoding algorithm for LDPC codes over q-ary finite fields. This proposed algorithm has low complexity and hence provides an effective trade-off between error performance and decoding complexity compared to q-ary sum product algorithm. This decoding algorithm is devised based on simple orthogonal concept of one-step majority-logic decoding for q-ary linear block codes. It requires only integer and finite field operations and converges very fast in decoding. It is particularly effective for decoding LDPC codes constructed based on finite geometries and finite fields.