  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.
