On encoding and decoding maps for group codes (Corresp.)

The problem of minimizing mean-square error when digital data is encoded into the elements of a group code via an encoding map a and the received elements of the group code are decoded via a decoding map
\beta
is considered. This problem has been solved under the restriction that
\beta = \alpha^{-1}
. It is shown that the same solution still obtains when this restriction is removed.