Reduced-state representations for trellis codes using constellation symmetry

This paper presents a symmetry-based technique for trellis-code state-diagram reduction that has more general applicability than the quasi-regularity technique of Rouanne et al. and Zehavi et al. for trellis codes using standard constellations and labelings. For a 2^νx-state trellis code, the new technique reduces the 2^2νx state diagram to 2^νx+νq-state diagram where 0≤ν_q≤ν_x. The particular value of ν_q depends on the constellation labeling and the convolutional encoder. For standard rate-k/(k+1) set-partitioned trellis codes, ν_q=0, and the overall number of states is the same with the new technique as with quasi-regularity. For codes that are not quasi-regular (and thus not amenable to the quasi-regularity technique), the new technique often provides some improvement (when ν_q<ν_x). For 8-phase-shift-keying trellis codes, the new technique always yields ν_q=0.