An optimized weighting algorithm for variations in PCM energy levels

The advantages of optimum weighted PCM for speech signals has been demonstrated by Sundberg [2]. Since the symbols in a PCM word have different sensitivities to digital transmission errors the relative signal energy used by each PCM word is matched accordingly. A near optimum performance may be achieved by transmitting groups of PCM symbols at the same energy level where the number of groups is less than the number of bits in the PCM word. A new dimension of the optimization problem is the determination as to which symbols should be allocated to a particular energy level for any given PCM word length while minimizing the digital noise. In this correspondence a general algorithm is developed for the judicious distribution of symbol energy which is optimum at every level.