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局部可译码（crLDC）（Blocki等，《信息论汇刊》'21），并给出两种新的构造。第一种构造是汉明crLDC，其概念上比先前构造更为简洁，利用了数字签名方案和适当选择的汉明码。第二种构造是我们的汉明crLDC的扩展，用于处理插入-删除（InsDel）错误，从而得到一种InsDel crLDC。此扩展关键依赖于Block等人（FSTTCS '20）的噪声二分搜索技术来处理InsDel错误。两种crLDC构造均采用二进制码字字母表，分别能抵抗恒定比例的汉明错误和InsDel错误，在适当参数选择下具有多对数局部性和编码长度——与消息长度呈线性关系，与安全参数呈多项式关系。这些参数在多对数局部性机制下优于先前构造。