Turbo Decoding Theory: Derivation and Performance Evaluation

Turbo codes are among the most effective error correction codes currently in use, providing outstanding performance and a vast array of applications. Even though Turbo codes have the theoretical capacity to approximate the limiting code rate of Shannon's theorem through iterations, the substantial computational complexity of the decoding process poses challenges for the optimization of Turbo codes performance in practical applications. Additionally, the computational delay hampers its use in communication systems that require low latency, such as mobile phones. This paper delves into the coding process of Turbo codes, scrutinizes the decoding concepts, and summarizes Soft Output Viterbi Algorithm, Maximum A Posteriori, and Logarithmic Maximum A Posteriori decoding methods through a systematic review approach. It also compares the decoding performance of these diverse methods considering parameters such as time delay, computational complexity, storage space, and Bit Error Rate. Through our analysis, we found that the Maximum A Posteriori algorithm is the most complex, the Logarithmic Maximum A Posteriori algorithm is somewhat simplified in comparison, and the Soft Output Viterbi Algorithm possesses the least computational complexity. Regarding decoding performance, the Maximum A Posteriori algorithm has the lowest Bit Error Rate, followed by the Logarithmic Maximum A Posteriori algorithm, with the Soft Output Viterbi Algorithm performing the worst. This study provides valuable insights into the key factors for enhancing the performance of Turbo codes from a theoretical perspective. It holds substantial significance for the practical application and future development of Turbo codes.