Quantiser design for AWGN and Rayleigh fading BPSK channels with soft output decoding

A new method of combined source-channel coding for the scalar quantisation of a discrete memoryless source is presented that takes advantage of the channel soft output values produced by the demodulator. The case of transmitting a memoryless Gaussian source using binary phase shift keying (BPSK) modulation over over an additive white Gaussian noise (AWGN) channel with and without Rayleigh fading is studied. Numerical results using some closed form expressions are presented, showing up to 1 dB improvement in the end-to-end distortion with respect to a traditional channel optimised scalar quantiser.