In this paper we show a polar coding scheme for the deletion channel with a probability of error that decays roughly like $2^{-\sqrt{\Lambda}}$, where $\Lambda$ is the length of the codeword. That is, the same decay rate as that of seminal polar codes for memoryless channels. This is stronger than prior art in which the square root is replaced by a cube root. Our coding scheme is similar yet distinct from prior art. The main differences are: 1) Guard-bands are placed in almost all polarization levels; 2) Trellis decoding is applied to the whole received word, and not to segments of it. As before, the scheme is capacity-achieving. The price we pay for this improvement is a higher decoding complexity, which is nonetheless still polynomial, $O(\Lambda^4)$.

翻译：本文展示了删信道的一种极化编码方案，其错误概率衰减速率约为$2^{-\sqrt{\Lambda}}$，其中$\Lambda$为码字长度。该衰减速率与无记忆信道中经典极化码的衰减速率一致，优于此前将平方根替换为立方根的研究成果。本编码方案与现有技术相似但存在差异，主要区别在于：1）在几乎所有极化层级中插入保护带；2）对完整接收词而非其分段进行网格译码。如同先前方案，本方案仍能达到信道容量。为获得这一改进，我们付出的代价是译码复杂度提升至$O(\Lambda^4)$，但仍属于多项式复杂度。