We revisit computationally relaxed locally decodable codes (crLDCs) (Blocki et al., Trans. Inf. Theory '21) and give two new constructions. Our first construction is a Hamming crLDC that is conceptually simpler than prior constructions, leveraging digital signature schemes and an appropriately chosen Hamming code. Our second construction is an extension of our Hamming crLDC to handle insertion-deletion (InsDel) errors, yielding an InsDel crLDC. This extension crucially relies on the noisy binary search techniques of Block et al. (FSTTCS '20) to handle InsDel errors. Both crLDC constructions have binary codeword alphabets, are resilient to a constant fraction of Hamming and InsDel errors, respectively, and under suitable parameter choices have poly-logarithmic locality and encoding length linear in the message length and polynomial in the security parameter. These parameters compare favorably to prior constructions in the poly-logarithmic locality regime.

翻译：我们重新审视了计算松弛局部可译码（crLDC）（Blocki 等人，《信息论汇刊》，'21），并给出了两种新构造。第一种构造是汉明型 crLDC，其概念上比先前的构造更简洁，利用了数字签名方案和适当选择的汉明码。第二种构造是汉明型 crLDC 的扩展，以处理插入-删除（InsDel）错误，从而得到一种 InsDel 型 crLDC。此扩展关键依赖于 Block 等人（FSTTCS '20）的带噪二分搜索技术来处理 InsDel 错误。两种 crLDC 构造均采用二进制码字字母表，分别能抵御恒定比例的汉明错误和 InsDel 错误，并且在适当的参数选择下，具有亚对数级的局部性和与消息长度成线性、与安全参数成多项式关系的编码长度。在亚对数局部性范围内，这些参数优于先前的构造。