Quantized decoders that maximize mutual information for polar codes

In this paper, we innovatively associate the mutual information with the frame error rate (FER) performance and propose novel quantized decoders for polar codes. Based on the optimal quantizer of binary-input discrete memoryless channels (B-DMCs), the proposed decoders quantize the virtual subchannels of polar codes to maximize mutual information (MMI) between source bits and quantized symbols. The nested structure of polar codes ensures that the MMI quantization can be implemented stage by stage. Simulation results show that the proposed MMI decoders with 4 quantization bits outperform the existing nonuniform quantized decoders that minimize mean-squared error (MMSE) with 4 quantization bits, and yield even better performance than uniform MMI quantized decoders with 5 quantization bits. Furthermore, the proposed 5-bit quantized MMI decoders approach the floating-point decoders with negligible performance loss.