Yung-Cheng Lo

Circular Trellis-Coded Modulation with Permuted-State Structure

Trellis-coded modulation (TCM) encoders are emphasized two design aspects, searching for a good code (increasing trellis depth) and developing signal constellations (maximizing Euclidean distance). However, the analysis of permutation property for TCM is lack of papers. Until turbo codes were developed, trellis termination and short frame transmission systems were addressed. By assuming all zero input as initial state, all of TCM inherited from traditional convolutional code encode the message from this given initial state. To transmit in block, the encoder needs to set the last tail information bits to zeros in order to drive the encoder to the all zero state. In this paper, we present a new trellis code named circular trellis-coded modulation (CTCM) which assures an unique initial state satisfied the same starting state and ending state for any legal transmission message in certain block length. The proposal CTCM has the property of state permutation and is developed by using Zech's logarithm. Instead of brute-force search, algebraic formula for the initial state is also developed. Once state table for a good code is constructed, transmission symbol table for signal constellations is easily to build. The source sequence is mapped to channel transmission sequence. For power-limited channel, we expand the bandwidth by increase of transmission symbol dimensions. To utilize trellis transition, a bi-orthogonal signaling set is used to assign to be a set of channel symbol. The distinct bi-orthogonal signaling partitioning is employed to achieve the maximum Euclidean distance for spread spectrum communication.