A symbol-reliability based message-passing decoding algorithm for nonbinary LDPC codes over finite fields

Based on the idea of plurality voting, we develop a low-complexity symbol-reliability based message-passing decoding algorithm for nonbinary low-density parity-check (LDPC) codes over finite fields. A key feature of the algorithm is that the message passed in the Tanner graph is the field element with the highest reliability. This leads to a very simple check node update. The algorithm requires only finite and integer operations. Moreover, the estimation of the signal-to-noise ratio (SNR) is not needed. Compared to the Fast Fourier Transform based q-ary sum-product algorithm (FFT-QSPA), the proposed decoding algorithm provides an excellent trade-off between performance and complexity for the nonbinary LDPC codes constructed based on finite geometries, finite fields and cyclotomic cosets.