Convolutional Coding: A Memory-Based Encoding Technique with Code Implementation Insights

Convolutional code is an encoding method with inherent memory properties. At any given time unit, the encoder's n outputs depend both on the current k input bits and the previous m input bits stored in memory registers. Conventionally represented as (n, k, m), this simulation specifically uses a (2, 1, 3) convolutional code configuration. Implementation typically involves shift registers to maintain state memory and generator polynomials to compute parity bits.

As a widely adopted encoding scheme, convolutional codes enhance data transmission reliability and fault tolerance. By incorporating memory elements, they perform redundant encoding on input data streams, significantly improving error detection and correction capabilities. In practical applications, convolutional codes are extensively used in communication systems, wireless sensor networks, and storage systems, often implemented through algorithms like Viterbi decoding for optimal path recovery.

For this simulation, the (2, 1, 3) convolutional code was selected due to its balanced trade-off between error correction performance and decoding complexity. The encoding process involves convolving input bits with predetermined generator polynomials (e.g., g1 = [1 1 1 1] and g2 = [1 0 1 1] for constraint length 4), producing two output bits per input bit. This structure enables reliable data transmission, while the decoding process employs algorithms such as the Viterbi algorithm to efficiently detect and correct errors at the receiver end.

Experimental results from this simulation validate the superiority of convolutional codes in channel transmission scenarios. The implementation demonstrates the complete encoding and decoding workflow of (2, 1, 3) convolutional codes, including state transitions, branch metric calculations, and path metric updates. These findings provide valuable insights into convolutional code principles and applications, serving as a reference for future research and engineering practices in channel coding techniques.