Multistage coding and decoding for a M-PSK system

Punctured convolutional codes are applied to a sequence of subsets of the signal set which is coded using block and/or convolutional codes in the Gaussian channel. The maximum-likelihood metric for the different stages of multistage decoding are derived. Simulation results and bounds for coded 4-PSK (phase-shift keying) show a gain over classical coding at the same bit-error rate (BER) and the same coding rate. It can also be shown that the BER of the first decoded stage is far away from its asymptotic limit at moderate BER (10^-4-10^-6). Therefore the simple gain formula used in the literature is not useful in this range