Low Complexity Soft Decoder for Nordstrom-Robinson Code With Application to the Chinese DTTB Standard

Nordstrom-Robinson (NR) code followed by 4 quadrature-amplitude modulation (4QAM) mapping is one of the working modes in the Chinese digital television terrestrial broadcasting (DTTB) standard, where the outer code is a low-density parity-check (LDPC) code. Since LDPC decoders usually accept soft rather than hard inputs for better error performance, soft NR decoders are highly recommended. In this paper, several novel low-complexity soft NR decoders are proposed with excellent error performance. Simulation results show that the proposed algorithm based on the maximum, second and third maximum (MST) cross correlation values achieves very low complexity at the cost of performance loss only about 0.1 dB at bit error rate (BER) of $10^{-6}$ , under both additive white Gaussian noise (AWGN) and independent Rayleigh fading channels, compared to the ideal maximum a posteriori (MAP) decoder.