Abstract
Since polar codes are capacity-achieving codes, there have been various research works devoted to devising efficient implementation methods as well as improving error-correction performance. Since quantization is a critical implementation issue, in this paper, a nonuniform quantization method is proposed for the successive cancellation (SC) decoder of polar codes, which finds quantization boundary values based on the analysis of various quantization levels over the additive white Gaussian noise channel. Since low computational complexity, high reliability, and efficient memory management are required in the next-generation communication and memory systems, 2-4 bit precision levels are mainly considered in the proposed nonuniform quantization method. Depending on the presence of erasure, quantization levels are divided into three types, and the message alphabets and update rules are derived for each type. Also, a construction method of polar codes suitable for the proposed nonuniform-quantized SC decoder is proposed, which simultaneously determines the information set and the quantization boundary values based on the density evolution analysis and an upper bound of the block error probability. To determine quantization boundary values, a multivariate objective function is defined and an iterative coarse-to-fine search algorithm to minimize this objective function is proposed. In addition, a scaling method of quantizer output values is proposed when the number of quantization levels of quantizer is smaller than the number of quantization levels of decoder. Finally, simulation results confirm that the proposed nonuniform-quantized SC decoder shows better error-correction performance, lower decoding complexity, and higher memory efficiency compared to the best known uniform-quantized SC decoder.
Highlights
It is well known that polar codes achieve the capacity of any symmetric binary-input discrete memoryless channel (B-DMC) with an explicit construction [1]
Since upper bound (UB) and block error probabilities of [26] are almost the same according to signal-to-noise ratio (SNR), in this paper, the error correcting performance of the proposed method is compared to the UB of block error probability (BEP) of optimal uniform-quantized successive cancellation (SC) decoding [26]
In this paper, an effective nonuniform quantization method (NQM) and nonuniform-quantized SC (NQSC) decoding algorithm for polar codes are proposed over additive white Gaussian noise (AWGN) channels
Summary
It is well known that polar codes achieve the capacity of any symmetric binary-input discrete memoryless channel (B-DMC) with an explicit construction [1]. NQMs are proposed for the cases where the number of quantization levels of quantizer is equal to or smaller than the number of quantization levels of decoder Note that if the latter is applied to the memory systems, the number of threshold-voltage sensing operations can be reduced without noticeable error-correction performance degradation. The proposed NQSC decoding algorithm has lower decoding complexity and higher memory efficiency compared to the optimal uniform-quantized SC decoder in [26] by the following reasons: (i) the proposed decoding algorithm does not perform quantization for each node operation, (ii) the messages updated by the proposed decoding algorithm are not fixed-point numbers but integers, and (iii) the number of QB values to be stored is small.
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