MATLAB Implementation of TCM Modulation with 8PSK and 2/3 Rate Convolutional Code

TCM (Trellis Coded Modulation) is a communication technology that combines coding and modulation, capable of improving system performance without increasing bandwidth. The combination of 8PSK modulation and 2/3 rate convolutional code represents one of the classic implementations. Below is a brief explanation of its implementation approach.

At the modulation end, the input data first undergoes processing through a convolutional code encoder. A 2/3 rate convolutional code means that for every 2 input bits, the encoder outputs 3 bits, thereby introducing redundancy to enhance interference immunity. Convolutional codes are typically defined using specific generator polynomials, and their state transitions can be represented through trellis diagrams. In MATLAB implementation, the convolutional encoder can be realized using the poly2trellis function to define the trellis structure, followed by the convenc function for encoding.

Subsequently, the 3 encoded bits are mapped to 8PSK constellation points. 8PSK modulation maps every 3 bits to one complex symbol, with constellation points uniformly distributed on the unit circle with phase intervals of π/4. This mapping must satisfy the "set partitioning" principle, where symbols with high Euclidean distance correspond to different subsets to maximize coding gain. In code implementation, the mapping can be achieved using a lookup table or mathematical operations that convert binary triplets to corresponding phase angles.

When implementing in MATLAB, the following key steps are required: generating 3-bit output streams through convolutional encoding, grouping bits for mapping to 8PSK symbols, and adding white Gaussian noise to simulate channel conditions. The joint optimization of coding and modulation should reference Ungerboeck's set partitioning theory to ensure maximum minimum Euclidean distance between adjacent symbols. The MATLAB communication toolbox provides functions like pskmod for PSK modulation and awgn for noise addition.

Extension considerations: This scheme is suitable for bandwidth-constrained scenarios but requires balancing complexity and performance. For higher coding gain, constraint length can be increased or higher-order modulation (such as 16QAM combined with TCM) can be adopted, though this increases decoding complexity. The decoding process typically employs the Viterbi algorithm which searches the trellis diagram for the most likely transmitted sequence.