MATLAB Implementation of TCM Encoding with (3,2,3) Convolutional Code and 8-PSK Modulation

This MATLAB program implements Trellis-Coded Modulation (TCM) encoding by combining (3,2,3) convolutional coding with 8-PSK modulation. The implementation involves selecting output codewords from convolutional encoding and mapping them to corresponding points on the 8-PSK constellation diagram to maximize Euclidean distance, thereby improving system performance in noisy channels.

To achieve this objective, we first develop a function for (3,2,3) convolutional code encoding using MATLAB's poly2trellis function to define the trellis structure, followed by convenc function for encoding binary input sequences. The convolutional encoder takes 2-bit input blocks and generates 3-bit output codewords with a constraint length of 3. Subsequently, we create an 8-PSK modulation function that maps the 3-bit convolutional encoder outputs to 8-PSK constellation points using Gray coding for optimal bit error performance. The mapping algorithm calculates constellation points with uniform angular spacing of 45 degrees to ensure maximum Euclidean distance between adjacent symbols.

By integrating these two functions through systematic bit-to-symbol mapping, we create a complete TCM encoder that leverages MATLAB's computational capabilities to implement sophisticated coding techniques. This approach enhances reliability and performance in communication systems by providing approximately 3 dB coding gain compared to uncoded modulation schemes, making it particularly suitable for bandwidth-efficient digital communications.