Unequal Bit-Error Protection in Coherent M-ary PSK

This paper addresses the problem of evaluating the bit-error probability of the individual bits of a symbol in a communication system using coherent M-ary phase shift keying. Exact expressions are provided, and these are evaluated for seven different mappings from bits to symbols, including five Gray mappings, for a 32-PSK system. It is shown that the highly varying error performance obtained with a common binary reflected Gray mapping can be restored by using a balanced Gray mapping