Bit geometrically uniform encoders: a systematic approach to the design of serially concatenated TCM

We introduce a class of encoders, called bit geometrically uniform (BGU) encoders, for which the bit error probability does not depend on the transmitted sequence. Strong connections between the symmetry groups of geometrically uniform signal constellations and those of the binary Hamming spaces are involved. Both uncoded modulation and infinitely long trellis codes are considered, and connections with the code linearity discussed. The theory of BGU encoders proves very useful for the analysis and design of codes aimed at minimizing the bit, rather than symbol, or sequence error probability. We apply the theory to the design of good serially concatenated trellis-coded modulation schemes.