Closed-System Quantum Logic Network Implementation of the Viterbi Algorithm

New convolution-based multiple-stream error-control coding and decoding schemes are introduced. The new coding method applies the reversibility property in the convolution-based encoder for multiple-stream erro r-control encoding and im- plements the reversibility property in the new reversible Viterbi decoding algorithm for multiple-stream error-correction decoding. The compl ete design of quantum cir- cuits for the quantum realization of the new quantum Viterbi cell in the quantum do- main is also introduced. In quantum mechanics, a closed system is an isolated system that can't exchange energy or matter with its surroundings a nd doesn't interact with other quantum systems. In contrast to open quantum systems, closed quantum sys- tems obey the unitary evolution and thus they are reversible . Reversibility property in error-control coding can be important for the following mai n reasons: (1) reversibility is a basic requirement for low-power circuit design in futur e technologies such as in quantum computing (QC), (2) reversibility leads to super-speedy encoding/decoding operations because of the superposition and entanglement properties that emerge in the quantum computing systems that are naturally reversible and therefore very high performance is obtained, and (3) it is shown in this paper tha t the reversibility rela- tionship between multiple-streams of data can be used for further correction of errors that are uncorrectable using the implemented decoding algorithm such as in the case of triple-errors that are uncorrectable using the classica l irreversible Viterbi algorithm.