Investigation of Turbo Code Polynimials under Constraints Length Four and Deterministic Interleaver

Abstract

Turbo coding Technique is one from very powerful error correction techniques that have made a tremendous impact on channel coding in the last few years. It had been recommended for increased capacity at higher transmission rates due to their superior performance over conventional codes. Recursive systematic convolutional (RSC) turbo code uses two polynomials in its encoding circuit which are feed-forward and feed-back polynomials. Those polynomials make great effects on performance of turbo codes in all regions. In this paper, the primitive and non-primitive polynomials will be investigated which are not clarified until now. Their effects on the performance in water-fall region and error floor regions will be elaborated. The minimum Hamming distance and their multiplicities are the criteria for comparison. Simulation results over the AWGN channel show that primitive polynomials in the Feed-back and feed-forward can achieve better performance at high SNR by improving the minimum distance (large minimum distance) which leads to decrease BER in the region of high signal to noise ratio to be used in the satellites new missions. Moreover, the results give a larger minimum distance by factor of 1.12dB compared with the CCSDS interleaver. The simulation is applied for frame length 1784, and code rate 1/2.