Low–Complexity, Fast–Convergence Decoding in AWGN Channels: A Joint LLR Correction and Decoding Approach

Thanks to the product rule of Gaussian distributions, the memory of channel coding schemes, such as low–density parity–check (LDPC) codes used in this paper, is reflected in the mean of a single Gaussian distribution, obtained through the product of re–scaled Gaussian observations in additive white Gaussian noise (AWGN) channels. Consequently, employing a novel bit log–liklihood ratio (LLR) updating algorithm, in conjunction with an appropriate scheduling procedure, increases the convergence speed of the decoder considerably. Bit LLR values close to zero are accumulated with those obtained in the current iteration of the receiver. Simulation results demonstrate a substantial improvement (close to 50%) in the convergence speed of the proposed algorithm compared to traditional ones. This approach can also be applied to conventional sequence and symbol detection strategies in the presence of memory. Although this approach only affects convergence in AWGN channels, it could play a vital role in scenarios involving nonlinear parameters, such as phase noise and multipath channels.