Binary convolutional coding (BCC) has been a cornerstone of the IEEE 802.11 wireless LAN standard since its inception, and it remains relevant today across the full generational arc from the legacy 802.11a/g through Wi-Fi 6 (802.11ax) and into the forthcoming Wi-Fi 8 (802.11bn). Although low-density parity-check (LDPC) codes now dominate high-throughput applications, BCC is mandatory for backward compatibility and continues to serve as the default forward-error-correction scheme in bandwidth-constrained and cost-sensitive deployments: 20 MHz-only devices, Internet-of-Things nodes, and other implementations where LDPC's decoder complexity is prohibitive. Critically, BCC at rate 1/2 is the coding scheme used throughout the packet preamble in every IEEE 802.11-compliant frame, making it indispensable regardless of which data-field code is selected. Furthermore, the new Enhanced Long Range (ELR) packet format introduced in the 802.11bn/UHR amendment mandates rate-1/2 BCC for the data portion of the frame, reinforcing the continued importance of this code in next-generation deployments. The performance of BCC under Viterbi decoding is governed by the distance spectrum of the convolutional code. This note explains how to compute that spectrum exactly for the IEEE 802.11 mother code (rate 1/2, K=7, generators octal 133 / octal 171) and its three standard punctured derivatives (rates 2/3, 3/4, 5/6) obtained via rate-compatible puncturing. Union-bound BEP and FER curves are derived for AWGN with BPSK/QPSK and Gray-coded M-QAM modulation and validated against Monte Carlo simulation. Python, Julia, and C++ implementations are openly available at https://github.com/geekymode/bcc_spectrum.

翻译：二进制卷积编码自诞生以来一直是 IEEE 802.11 无线局域网标准的基石，并且至今仍具有重要价值，其应用贯穿从传统的 802.11a/g 到 Wi-Fi 6，直至即将到来的 Wi-Fi 8 的完整代际演进。尽管低密度奇偶校验码如今主导着高吞吐量应用，但二进制卷积编码对于向后兼容性是强制要求的，并且继续作为带宽受限和成本敏感部署场景中的默认前向纠错方案，例如仅支持 20 MHz 带宽的设备、物联网节点以及其他因 LDPC 解码器复杂度过高而无法应用的场景。至关重要的是，码率为 1/2 的二进制卷积编码是每个符合 IEEE 802.11 标准的帧中整个数据包前导码所使用的编码方案，这使得无论选择何种数据域编码，它都不可或缺。此外，802.11bn/UHR 修订案中引入的新型增强型远距离数据包格式，强制要求帧的数据部分使用码率为 1/2 的二进制卷积编码，这进一步强化了该编码在下一代部署中的持续重要性。二进制卷积编码在维特比解码下的性能由卷积码的距离谱决定。本说明解释了如何精确计算 IEEE 802.11 母码及其三个通过速率兼容打孔获得的标准打孔衍生码的距离谱。该母码参数为：码率 1/2，约束长度 K=7，生成器八进制表示为 133 和 171；其衍生码码率分别为 2/3、3/4 和 5/6。推导了在 AWGN 信道下，采用 BPSK/QPSK 和格雷编码 M-QAM 调制的误比特率和误帧率联合界曲线，并通过蒙特卡洛仿真进行了验证。Python、Julia 和 C++ 实现代码已在 https://github.com/geekymode/bcc_spectrum 开源提供。