Abstract: 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 error-control encoding and implements the reversibility property in the new reversible Viterbi decoding algorithm for multiple-stream error-correction decoding. The complete design of quantum circuits for the quantum realization of the new quantum Viterbi cell in the quantum domain is also introduced. In quantum mechanics, a closed system is an isolated system that can't exchange energy or matter with its surroundings and doesn't interact with other quantum systems. In contrast to open quantum systems, closed quantum systems obey the unitary evolution and thus they are reversible. Reversibility property in error-control coding can be important for the following main reasons: (1) reversibility is a basic requirement for low-power circuit design in future 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 that the reversibility relationship 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 classical irreversible Viterbi algorithm.
Keywords: Error-Correcting Codes, Error-Control Coding, Coding, Low-Power Computing, Low-Power Circuits and Systems, Noise, Quantum Circuits, Quantum Computing, Reversible Circuits, Reversible Logic.