Prior to this dissertation, a circular trellis coding with permuted state structure was invented to satisfy the state constraint without code rate loss.
This dissertation 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 algorithm for calculating the minimum distance of a trellis code always assumes a known starting state. This dissertation 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.
Conventional Viterbi decoder, which assumes a known starting state, is not suitable for HDCTCM. This dissertation explores the circular BCJR algorithm for decoding HDCTCM. Iterative circular shift BCJR is developed. In this decoding scheme, the starting state is statistically estimated using soft-output information, and the circular character of HDCTCM is incorporated to make the most reliable symbol in the received sequence as the starting point for decoding. Satisfactory bit error performance achieved by HDCTCM using this decoding algorithm is given.