Simulink Simulation of Convolutional Encoding and Decoding Working Principles

Convolutional encoding and decoding represents a widely adopted forward error correction (FEC) technique in digital communication systems. Its fundamental principle involves introducing redundant information to enhance system robustness against interference.

The convolutional encoder operates using shift registers to process input bit streams. At each timestamp, the output depends not only on the current input bit but also on several previous input bits. This memory characteristic endows convolutional codes with strong error-correction capabilities. Typical convolutional codes are defined by generator polynomials, which determine how input bits combine with register states to produce output bits.

Implementing a convolutional encoder in Simulink through S-Function requires designing a module that simulates shift register operations. This module accepts input bit streams and generates encoded outputs based on predefined constraint lengths and generator polynomials. The encoded data stream typically exhibits higher code rates, implying reduced transmission efficiency but significantly improved noise immunity.

Viterbi decoding employs a maximum likelihood sequence estimation algorithm to efficiently recover original information from noisy signals. Its core methodology involves representing all possible encoding state transitions through trellis diagrams and using dynamic programming to identify optimal paths. Implementing Viterbi decoding in Simulink via S-Function necessitates constructing state trellises, calculating path metrics, and performing traceback decoding operations.

The AWGN channel simulation component requires integration of additive white Gaussian noise modules. By adjusting signal-to-noise ratio (SNR) parameters, communication environments of varying quality can be simulated. After completing the system setup, Monte Carlo simulation methods can statistically analyze bit error rates (BER) under different SNR conditions.

BER versus SNR relationship curves visually demonstrate system performance. Typically, BER exhibits exponential decay as SNR increases. These curves serve as crucial tools for evaluating convolutional codec system performance metrics and validating results against theoretical benchmarks.