Efficient implementation of a Viterbi decoder for geometrically uniform TCM codes

Presents a procedure to design maximum likelihood decoders for the new class of geometrically uniform (GU) TCM codes, with an efficient VLSI implementation. The design of the decoders for the GUTCM codes is different and more complicated in comparison to the standard convolutional code decoders because between any pair of states in the trellis diagram of a GUTCM code, there is usually a large number of parallel transitions, and the trellis diagram of the code has a much higher degree of connectivity in comparison to binary convolutional codes, making routing a more critical problem. The authors present a novel technique for solving the parallel transitions using the algebraic structure of the GUTCM codes, which represents a significant reduction in complexity with respect to the direct approach. The proposed technique is applied to the design of an efficient Viterbi decoder (VD) for a 64-state nonbinary GUTCM code defined over (Z₈)⁴ with 5.46 dB of asymptotic coding gain with respect to uncoded QPSK and 2 information bits per two dimensions. For this example, they obtain a 50 fold reduction in complexity in comparison to the direct implementation