Hard-decision decoding does not preserve the diversity order. This results in severe performance degradation in fading channels. In contrast, soft-decision decoding preserves the diversity order at an impractical computational complexity. For a linear block code $\mathscr{C}(n,k)$ of length $n$ and dimension $k$, the complexity of soft-decision decoding is of the order of $2^k$. This paper proposes a novel hard-decision decoder named Flip decoder (FD), which preserves the diversity order. Further, the proposed Flip decoder is `universally' applicable to all linear block codes. For a code $\mathscr{C}(n,k)$, with a minimum distance ${d_{\min}}$, the proposed decoder has a complexity of the order of $2^{({d_{\min}}-1)}$. For low ${d_{\min}}$ codes, this complexity is meager compared to known soft and hard decision decoding algorithms. As it also preserves diversity, it is suitable for IoT, URLLC, WBAN, and other similar applications. Simulation results and comparisons are provided for various known codes. These simulations corroborate and emphasize the practicality of the proposed decoder.
翻译：保持多样性的线性分组码通用硬判决译码器
翻译后的摘要：
硬判决译码未能保持多样性，导致在衰落信道中性能严重下降。与之相反，软判决译码虽然保持了多样性，但计算复杂度不可接受。对于长度为 $n$，维度为 $k$ 的线性分组码 $\mathscr{C}(n,k)$，软判决译码的复杂度为 $2^k$。本文提出了一种新颖的硬判决译码器 Flip 译码器 (FD)，它能够保持多样性，并且适用于所有线性分组码。对于最小距离为 ${d_{\min}}$ 的码 $\mathscr{C}(n,k)$，所提出的译码器的复杂度为 $2^{({d_{\min}}-1)}$。对于低 ${d_{\min}}$ 码而言，该复杂度相比已知的软硬判决译码算法非常低。由于它也保持了多样性，因此适用于物联网、超可靠低延迟通信、人体区域网络和其他类似的应用领域。本文提供了多种已知码的模拟结果和比较。这些模拟结果证实并强调了所提出的译码器的实用性。
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