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：我们重新审视计算松弛的局部可译码（crLDCs）（Blocki 等人，《信息论汇刊》'21），并给出两种新构造。第一种构造是汉明型 crLDC，其概念上比先前构造更简洁，利用了数字签名方案以及适当选取的汉明码。第二种构造是对我们的汉明型 crLDC 的扩展，以处理插入-删除（InsDel）错误，从而得到一种 InsDel crLDC。该扩展关键依赖于 Block 等人（FSTTCS '20）的噪声二分搜索技术来处理 InsDel 错误。两种 crLDC 构造均采用二元码字字母表，分别能容忍恒定比例的汉明错误和 InsDel 错误，且在适当参数选择下，具有多对数级别的对数量度，编码长度与消息长度呈线性关系，并与安全参数呈多项式关系。这些参数在多对数对数量度范围内优于先前构造。