Turbo codes for high order constellations

The feasibility of the extension of the original turbo codes to higher rate systems is investigated. Extension to the 8-PSK constellation is given as an example. The theoretical critical SNR to achieve one and two bits per 2-D symbol is calculated for 8-PSK with the Blahut-Arimoto algorithm, thus taking into consideration the additional loss due to selecting a finite signaling set. Codes for 8-PSK that achieve 2 bits/s/Hz, within a fraction of a decibel of the theoretic limit are presented. The decoder modifications described may be directly applied to constellations with large cardinality other than 8-PSK.