High Dimensional Trellis Coded Modulation
Final rept. Mar 1999-Jun 2001
OHIO UNIV ATHENS DEPT OF ELECTRICAL AND COMPUTER ENGINEERING
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This work develops a high dimensional circular trellis-coded modulation with permuted state structure HDCTCM for power-limited spread spectrum channels. High dimensional simplex signal constellation is systematically developed to achieve the optimal energy efficiency and maximize the minimum distance among error events for any size trellis. By systematically analyzing the error events, sets of state transitions that should be assigned simplex are identified. Butterfly structure of circular trellis coding is successfully related to those state transitions and perfectly aligned into a multidimensional matrix. An algebraic representation of a simplex in a high dimensional space is introduced, and a corresponding signal constellation and symbol assignment procedure are built. A circular trellis code has an unknown starting state conventional algorithms for calculating the minimum distance of a trellis code always assume a known starting state. This work develops a computational algorithm to calculate minimum distance of circular trellis codes. The coding gain of HDCTCM is evaluated after the minimum distance is obtained. Tight upper and lower bonds on the minimum distance of HDCTCM codes are derived. Furthermore, a method to build codes that have the bounds of the minimum distance is developed. Whereas, in most coding schemes, the optimal distance codes can only be obtained through exhaustive search.
- Radio Communications