1. A method implemented by a computer system of searching a signed codebook to quantize an input vector representative of a portion of a signal, the signed codebook including a set of shape codevectors, each shape codevector being associated with a positive signed codevector and a negative codevector, comprising: (a) weighting, by a processor of the computer system, a shape codevector in the set of shape codevectors with a weighting function for a weighted mean square error (WMSE) criteria, to produce a weighted shape codevector; (b) correlating the weighted shape codevector with an input vector to produce a weighted correlation term; (c) determining based on a sign of the weighted term, a preferred one of the positive and negative signed codevectors associated with the shape codevector; and (d) deriving a single minimization term for the shape codevector that corresponds to the preferred signed codevector.