Abstract: A digital transmitter/receiver communications system transmits audio voice signals over a channel with increased quality for a specified bit rate. The method of encoding takes advantage of spherical symmetry of error vectors associated with encoding Line Spectral Frequency (LSF) coefficients, to reduce the information transmitted. Errors in encoding the LSF coefficient sets, vectors J, are modeled by a number of vectors J.sub.p having all positive components, and a sign vector s indicating the polarity of each component of the vector. Each LSF vector J intended to be transmitted is approximated by a positive vector J.sub.p and a sign vector s. An index I.sub.p of the positive vector J.sub.p and the sign vector corresponding to vector J are transmitted, along with other audio information to a receiver/decoder where the signal is decoded into an audio signal closely representing the original signal intended to be transmitted.