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:硬判决译码无法保持分集阶数,导致在衰落信道中性能严重退化。相比之下,软判决译码能保持分集阶数,但计算复杂度不切实际。对于长度为$n$、维数为$k$的线性分组码$\mathscr{C}(n,k)$,软判决译码的复杂度量级为$2^k$。本文提出一种名为翻转译码器(FD)的新型硬判决译码器,该译码器能保持分集阶数。此外,所提出的翻转译码器可"通用"地适用于所有线性分组码。对于码字$\mathscr{C}(n,k)$,在最小距离为${d_{\min}}$的情况下,所提译码器的复杂度量级为$2^{({d_{\min}}-1)}$。对于低${d_{\min}}$的码字,该复杂度远低于已知的软硬判决译码算法。由于该译码器还能保持分集阶数,因此适用于物联网、超可靠低延迟通信、无线体域网及其他类似应用。本文提供了多种已知码字的仿真结果与比较,这些仿真验证并强调了所提译码器的实用性。