Group theoretic description of circular trellis coded modulation

James E. Curry; Alan R. Lindsey; Jeffrey C. Dill; Sergio Lopez-Permouth

doi:10.1117/12.438294

28 August 2001 Group theoretic description of circular trellis coded modulation

James E. Curry, Alan R. Lindsey, Jeffrey C. Dill, Sergio Lopez-Permouth

Proceedings Volume 4395, Digital Wireless Communication III; (2001) https://doi.org/10.1117/12.438294
Event: Aerospace/Defense Sensing, Simulation, and Controls, 2001, Orlando, FL, United States

Abstract

Circular Trellis Coded Modulation (CTCM) defines a family of (block) trellis codes which use a unique algebraic constraint, imposed on the start state, to produce a strong tail-biting property without the inefficiency of driving the encoder state to zero, using a sequence of input zeroes. Previous papers have investigated specific practical results in the case of binary and 4-ary signaling, using the elements of the Galois field GF(2^m) to label the trellis. The `4-fly' has proven to be the central feature of the trellis structure, allowing exceptional performance. The present paper generalizes the 4-fly structure, naturally related to GF(2^m), to the case of p^j-flies, which support efficient p^j-ary signaling using trellises labeled by the field GF(p^m), valid both for p equals 2 and for odd characteristic. This opens numerous practical system design options, allows greater flexibility for the transmitter design, and lays the mathematical groundwork required to support a much more systematic and general analysis of the CTCM trellis structure. This paper gives the general definitions and records the first elements of the structural analysis. Detailed knowledge of the trellis structure is key to the minimization of decoder complexity.

Citation Download Citation

James E. Curry, Alan R. Lindsey, Jeffrey C. Dill, and Sergio Lopez-Permouth "Group theoretic description of circular trellis coded modulation", Proc. SPIE 4395, Digital Wireless Communication III, (28 August 2001); https://doi.org/10.1117/12.438294

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