Self-checking principle and design of ternary Berger code

With the gradual maturity of the hardware and programming platform of Ternary optical computer (TOC), TOC gradually enters the practical application stage. Its reliability is becoming a research hotspot. The liquid crystal is used to change the polarization direction in the TOC to realize the three-state conversion of light. So the data is ternary and the classical binary detection/correction schemes are ineffective. In this paper, the ternary Berger code is proposed for ternary code-word of the form m = mnmn−1…m2m1 with symbols \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0,1,\overline{1}$$\end{document}, and a principle of error detection based on the ternary Berger code is presented for the error schemes x → y, where x ≠ y and x, y ∈{\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0,1,\overline{1}$$\end{document}}. Then a photoelectric structure of error detection based on ternary Berger code is designed, which can detect single error for huge-bit data with high efficiency and low cost and lower delay.