On Uniform Quantization for Successive Cancellation Decoder of Polar Codes

Polar codes have a regular-recursive structure, which can efficiently be mapped to hardware for practical applications. A good quantization scheme plays a great important role in hardware implementation. In this paper, three uniform quantizers are designed for successive cancellation (SC) decoding of polar codes based on either optimizing the equivalent channel capacity, cutoff rate or mean-squared error (MSE). Moreover, exploiting the cutoff rate maximizing criterion, a modified Gaussian approximation (GA) method is proposed to construct polar codes and estimate frame error rate (FER) performance under the quantized decoding algorithms. Simulation results have shown that a 6-bit uniform quantized SC decoder can achieve a near floating point performance and the upperbound of FER can be estimated precisely using the modified GA method under quantized decoding algorithms.