An implementation-efficient finite alphabet decoder for polar codes relying on coarsely quantized messages and low-complexity operations is proposed. Typically, finite alphabet decoding performs concatenated compression operations on the received channel messages to aggregate compact reliability information for error correction. These compression operations or mappings can be considered as lookup tables. For polar codes, the finite alphabet decoder design boils down to constructing lookup tables for the upper and lower branches of the building blocks within the code structure. A key challenge is to realize a hardware-friendly implementation of the lookup tables. This work uses the min-sum implementation for the upper branch lookup table and, as a novelty, a computational domain implementation for the lower branch lookup table. The computational domain approach drastically reduces the number of implementation parameters. Furthermore, a restriction to uniform quantization in the lower branch allows a very hardware-friendly compression via clipping and bit-shifting. Its behavior is close to the optimal non-uniform quantization, whose implementation would require multiple high-resolution threshold comparisons. Simulation results confirm excellent performance for the developed decoder. Unlike conventional fixed-point decoders, the proposed method involves an offline design that explicitly maximizes the preserved mutual information under coarse quantization.

翻译：提出了一种基于粗量化消息与低复杂度操作的高效实现有限字母表极化码译码器。传统有限字母表译码通过对接收信道消息进行级联压缩操作，聚合用于纠错的紧凑可靠性信息，这些压缩操作或映射可视为查找表。对于极化码，有限字母表译码器设计归结为构建码结构中基本构建单元上下分支的查找表。关键挑战在于实现查找表的硬件友好型实现。本文对上分支查找表采用最小和实现，并创新性地对下分支查找表采用计算域实现方法。计算域方法大幅减少了实现参数数量。此外，下分支采用均匀量化限制，通过限幅与移位操作实现高度硬件友好的压缩，其性能接近需要多个高分辨率阈值比较的最优非均匀量化。仿真结果表明所提译码器具有卓越性能。与传统的定点译码器不同，所提方法通过离线设计显式最大化粗量化下的保留互信息。