Rayleigh Channel Simulation of (2, 1, 3) Convolutional Code

This simulation investigates the performance of (2, 1, 3) convolutional code over Rayleigh fading channels to generate bit error rate curves. The implementation typically involves generating random binary data, encoding it using a convolutional encoder with generator polynomials (e.g., [5, 7] in octal notation for constraint length 3), and modulating the encoded bits using BPSK or QPSK. The Rayleigh channel model is implemented by multiplying the transmitted signal with complex Gaussian random variables to simulate multi-path fading effects, followed by adding AWGN with varying SNR levels. Key algorithmic components include the Viterbi decoder for maximum likelihood sequence estimation, which uses trellis decoding to recover the original data from the corrupted received signal. The simulation calculates bit error rates by comparing decoded bits with original transmitted bits across multiple Monte Carlo iterations. Performance analysis involves plotting BER versus Eb/N0 curves to evaluate coding gain and analyze how the convolutional code mitigates fading effects. This simulation provides crucial insights into the code's performance characteristics and optimization strategies for wireless communication systems, demonstrating practical applications of error correction coding in realistic channel conditions.