We consider analog error-correcting codes (analog ECCs) that are designed to correct/detect outlying errors arising in analog implementations of vector-matrix multiplication. The error-correction/detection capability of an analog ECC can be characterized by its height profile, which is expected to be as small as possible. In this paper, we consider analog ECCs whose parity check matrix has columns of unit Euclidean norm. We first present an upper bound on the height profile of such codes as well as a simple decoder for correcting a single error. We then construct a family of single error-correcting analog ECCs with redundancy three for any code length, which has smaller height profile compared to the known $[n,n-2]$ MDS constructions.

翻译：我们考虑用于纠正/检测向量-矩阵乘法模拟实现中出现的离群误差的模拟纠错码（analog ECCs）。模拟纠错码的纠错/检测能力可通过其高度轮廓（height profile）来表征，该轮廓期望尽可能小。本文研究其奇偶校验矩阵列向量具有单位欧几里得范数的模拟纠错码。首先，我们给出了此类码高度轮廓的上界，以及一种用于纠正单个误差的简单译码器。随后，我们构造了一族针对任意码长、冗余度为三的单纠错模拟纠错码，其高度轮廓优于已知的$[n,n-2]$ MDS构造。