High dimensional circular trellis-coded modulation

Circular trellis-coded modulation (CTCM) is a trellis coding with a state permutation structure which not only retains the properties of traditional trellis-coded modulation (TCM) but also allows more efficient systematic trellis construction. The embedded state-permuted characteristic guarantees that the starting and ending states for a given input symbol block are the same. This property is termed the "state constraint". The state transitions form a wrap-around path which depends on each distinct input sequence. However, a cyclic shift of the input sequence compels a cyclic shift of its state transition sequence. The grouping of these cyclically shifting state-transition sets reduces the encoding speed and simplifies performance analysis.