Performance Analysis of Four Dimensional Turbo Code (4D-TC) Using Moment Based Simplified Augmented State Diagram (MSASD) Approach: Extension to LTE System

Thought provoking “Turbo Code” (TC) is found to be as one of the competent error control coding schemes not only for its amazing “Bit Error Rate” (BER) act but also for its proficiency in secured data transmission with least errors. However, “TC” is incapable of lessening the knocking down effect because of low “Minimum Hamming Distance (MHD)” \(d_{\hbox{min} }\). This problem can be resolved either by designing greater memory driven “TCs” or by conniving a coding system driven by higher number of encoding units. Moreover, the evaluation of “constricted and accurate upper bound” on “BER” can be considered as another interesting scope of research in this regard. Inspired by this research orientation, in this article, the Moment based Simplified Augmented State Diagram (MSASD) has been proposed to evaluate the “Transfer Function” for the assessment of the “upper bound” on the “BER” act of the “4D-TC” scheme. For this purpose, “BER” act of the two memories driven “4D-TC” model has been inspected using “simulation”, “Augmented State Diagram” (ASD) and “MSASD” techniques. Moreover, a qualified investigation has been done on the “BER” performances of the “4D-TC” for different code rates. Furthermore, the “BER” behavior of the “4D-TC” has been compared with “3D-TC” using three different approaches namely, “simulation”, “ASD” and “MSASD”. Finally, a comprehensive BER comparison among different forms of TCs has been performed in LTE system under different fading channel conditions.