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The proposed system deals with Non-binary error control coding of the TCM scheme for transmissions over the AWGN channel. The idea of Non-binary codes has been extended for symbols defined over rings of integers, which outperform binary codes with only a small increase in decoding complexity. The basic mathematical concepts are necessary for working with Non-binary error-correcting codes are Groups, Rings and Fields. A new non-binary decoding method, Yaletharatalhussein decoding algorithm, is designed and implemented for decoding non-binary convolutional codes which is based on the trellis diagram representing the convolutional encoder. Yaletharatalhussein decoding algorithm outperforms the Viterbi algorithm and other algorithms in its simplicity, very small computational complexity, and easy to implement with real-time applications. The simulation results show that the performance of the non-binary TCM-based Yaletharatalhussein decoding algorithm outperforms the binary and non-binary decoding methods.

A Non-Binary Trellis Code Modulation-based Novel Decoding Algorithm