Linear Analog Codes: The Good and The Bad

Abstract

This paper studies the theory of linear analog error correction coding. Since classical concepts of minimum Hamming distance and minimum Euclidean distance fail in the analog context, a new metric, termed the "minimum (squared Euclidean) distance ratio," is defined. It is shown that linear analog codes that achieve the largest possible value of minimum distance ratio also achieve the smallest possible mean square error (MSE). Based on this achievability, a concept of "maximum distance ratio expansible (MDRE)" is established, in a spirit similar to maximum distance separable (MDS). Existing codes are evaluated, and it is shown that MDRE and MDS can be simultaneously achieved through careful design.