Working Principles of Convolutional Encoding and Viterbi Decoding with Simulink Implementation

This document details the operational principles of convolutional encoding and decoding systems. It presents a methodology for implementing convolutional encoding via Simulink simulations and corresponding decoding using the Viterbi algorithm. All encoding and decoding components are programmed through custom S-Functions, emphasizing hands-on implementation rather than built-in blocks. The communication system is tested under Additive White Gaussian Noise (AWGN) channel conditions, with comprehensive analysis of Bit Error Rate (BER) versus Signal-to-Noise Ratio (SNR) characteristics through plotted performance curves. Key implementation aspects include: 1. Convolutional Encoder S-Function: Designed using shift registers and generator polynomials (e.g., [7, 5] in octal) to produce coded outputs based on finite-state machine transitions 2. Viterbi Decoder S-Function: Implements trellis path metrics calculation, survivor path selection, and traceback decoding with minimum path metric identification 3. AWGN Channel Modeling: Incorporates noise injection using Gaussian random number generation scaled according to SNR values 4. BER-SNR Curve Generation: Automated data collection through multiple simulation runs with varying SNR parameters, followed by logarithmic-scale plotting This approach provides deeper insight into convolutional codec operations and enables observation of BER performance degradation under different channel noise conditions, demonstrating typical coding gain improvements in digital communication systems.