Analog error-correcting codes (analog ECCs) introduced by Roth are designed to correct outlying errors arising in analog implementations of vector-matrix multiplication. The error-detection/correction 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 MDS constructions.

翻译：Roth 提出的模拟纠错码旨在纠正向量-矩阵乘法的模拟实现中产生的离群误差。模拟纠错码的检错/纠错能力可由其高度轮廓表征，该轮廓期望尽可能小。本文考虑其奇偶校验矩阵的列具有单位欧几里得范数的模拟纠错码。我们首先给出了此类码的高度轮廓的一个上界，以及一个用于纠正单个误差的简单译码器。随后，我们为任意码长构造了一族冗余度为三的单个误差可纠正模拟纠错码，其高度轮廓相较于已知的 MDS 构造更小。