用于电阻式交叉开关上模拟计算的多纠错码
Multiple-Error-Correcting Codes for Analog Computing on Resistive Crossbars
AI总结：
本文研究电阻式交叉开关模拟计算中的多错误定位问题，提出基于球形码和稀疏析取矩阵的多纠错码构造，并给出高效译码方法及行最大汉明重量的改进界。
摘要：
本文研究了实数域上的纠错码，用于在电阻式交叉开关上进行实向量-矩阵乘法的近似计算时定位离群计算错误。此前的工作集中于定位单个离群错误，本文提出了几类能够处理多个错误的码。首先证明了已知构造中的一种——基于球形码的构造——实际上能够处理多个离群错误。然后提出了第二类码，其具有稀疏且析取的$\zeroone$奇偶校验矩阵；这类矩阵在其他应用中也有使用，特别是在组合群测试中。此外，证明了通过这种构造获得的某一类码具有高效可译码性。作为对稀疏析取矩阵研究的一部分，本文还给出了此类矩阵中行最大汉明重量的改进下界和上界。
英文摘要：
Error-correcting codes over the real field are studied which can locate outlying computational errors when performing approximate computing of real vector--matrix multiplication on resistive crossbars. Prior work has concentrated on locating a single outlying error and, in this work, several classes of codes are presented which can handle multiple errors. It is first shown that one of the known constructions, which is based on spherical codes, can in fact handle multiple outlying errors. A second family of codes is then presented with $\zeroone$~parity-check matrices which are sparse and disjunct; such matrices have been used in other applications as well, especially in combinatorial group testing. In addition, a certain class of the codes that are obtained through this construction is shown to be efficiently decodable. As part of the study of sparse disjunct matrices, this work also contains improved lower and upper bounds on the maximum Hamming weight of the rows in such matrices.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
