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：我们考虑旨在纠正/检测模拟向量-矩阵乘法实现中离群错误的模拟纠错码。模拟纠错码的纠错/检错能力可通过其高度轮廓来表征，该高度轮廓期望尽可能小。本文研究校验矩阵列具有单位欧几里得范数的模拟纠错码。首先，我们给出此类代码高度轮廓的上界，以及用于纠正单个错误的简单解码器。随后，我们构造了一族针对任意码长具有三冗余的单个错误纠正模拟纠错码，其高度轮廓较已知的$[n,n-2]$ MDS构造更小。