An expurgating linear function (ELF) is a linear outer code that disallows the low-weight codewords of the inner code. ELFs can be designed either to maximize the minimum distance or to minimize the codeword error rate (CER) of the expurgated code. A list-decoding sieve of the inner code starting from the noiseless all-zeros codeword is an efficient way to identify ELFs that maximize the minimum distance of the expurgated code. For convolutional inner codes, this paper provides distance spectrum union (DSU) upper bounds on the CER of the concatenated code. For short codeword lengths, ELFs transform a good inner code into a great concatenated code. For a constant message size of $K=64$ bits or constant codeword blocklength of $N=152$ bits, an ELF can reduce the gap at CER $10^{-6}$ between the DSU and the random-coding union (RCU) bounds from over 1 dB for the inner code alone to 0.23 dB for the concatenated code. The DSU bounds can also characterize puncturing that mitigates the rate overhead of the ELF while maintaining the DSU-to-RCU gap. The reduction in DSU-to-RCU gap comes with a minimal increase in average complexity at desired CER operating points. List Viterbi decoding guided by the ELF approaches maximum likelihood (ML) decoding of the concatenated code, and average list size converges to 1 as SNR increases. Thus, average complexity is similar to Viterbi decoding on the trellis of the inner code at high SNR. For rare large-magnitude noise events, which occur less often than the FER of the inner code, a deep search in the list finds the ML codeword.

翻译：删余线性函数（ELF）是一种线性外码，通过禁止内码的低权重码字实现删余功能。ELF既可设计为最大化删余码的最小距离，也可最小化其码字错误率（CER）。从无噪声全零码字出发的内码列表译码筛选是识别最大化删余码最小距离的ELF的高效方法。针对卷积内码，本文给出了级联码CER的距离谱联合（DSU）上界。在短码长场景下，ELF可将优质内码转化为卓越级联码。对于固定消息长度K=64比特或固定码字分组长度N=152比特，在CER为10^{-6}时，ELF可将DSU界与随机编码联合（RCU）界之间的间距从内码单独使用的超过1 dB压缩至级联码的0.23 dB。DSU界还可表征在保持DSU-RCU间距的同时缓解ELF速率开销的凿孔方案。DSU-RCU间距的缩减仅以目标CER工作点处平均复杂度的极小增长为代价。基于ELF引导的列表维特比译码可逼近级联码的最大似然（ML）译码，且平均列表长度随信噪比增加收敛至1。因此在高信噪比条件下，其平均复杂度接近于内码网格上的维特比译码。对于发生频率低于内码误帧率的罕见大幅噪声事件，列表中的深度搜索可找到ML码字。