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. List decoding of the inner code 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. 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. 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：删除线性函数(ELF)是一种线性外码，用于消除内码的低重量码字。ELF既可设计为最大化被删除码的最小距离，也可最小化其码字错误率(CER)。从无噪声全零码字出发对内码进行列表译码，是识别能最大化被删除码最小距离的ELF的有效方法。针对卷积内码，本文给出了级联码CER的距离谱联合(DSU)上界。在短码字长度下，ELF可将优良内码转化为卓越级联码。对于恒定消息大小$K=64$比特或恒定码字块长度$N=152$比特，在CER $10^{-6}$处，ELF可将单独内码超过1 dB的DSU与随机编码联合(RCU)界之间的差距缩小至级联码的0.23 dB。DSU界还可表征能降低ELF速率开销的删余技术，同时保持DSU-RCU差距。DSU-RCU差距的缩小仅以平均复杂度的最小化增长为代价。由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，且平均列表大小随信噪比增加而收敛至1。因此，其平均复杂度与内码网格上的维特比译码相当。对于发生频率低于内码误帧率的罕见大幅噪声事件，通过列表深度搜索可获取ML码字。