Optimal Output Quantization of Binary Input AWGN Channel for Belief-Propagation Decoding of LDPC Codes

Optimal quantizers for channel output are especially necessary for very high speed and memory-cell sensing applications where high-precision analog-to-digital converters are not available. This paper investigates a method to find optimal output quantizers for a binary input (BI) additive white Gaussian noise (AWGN) channel when regular low-density parity-check (LDPC) codes are used with belief-propagation (BP) decoding. The optimal quantizers are found by uni-parametric and multi-parametric optimization methods based on the discretized density evolution (DE). The capacity of various LDPC code ensembles are also provided with the BI-AWGN channel outputs quantized using these optimal quantizers. It is demonstrated that only 3 bits of quantization precision performs almost within 0.1 dB of the infinite precision channel output. The effect of the code rate and the degree distribution of LDPC codes on the optimal quantization boundaries is analyzed.