A reduced-state SISO algorithm for multilevel modulation in turbo equalization

Turbo equalization is an iterative equalization decoding scheme for detecting encoded data transmitted over channels that introduce intersymbol interference. In such a scheme, the complexity of the optimal soft-input soft-output (SISO) equalizer, which implements the BCJR a posteriori probability computation algorithm, is one of the major concerns. We extend the reduced state sequence detection (RSSD) algorithm to a BCJR-SISO equalizer matched to a non binary modulation. The resulting reduced-state SISO (RS-SISO) algorithms can take full advantage from the flexibility offered by RSSD in reducing the number of trellis states. However, extension of RSSD algorithm for obtaining the RS-SISO equalizers requires attention in the recombination procedure of the forward and backward metrics.