Abstract: Information theory is the mathematic foundation for communication systems. The existing researches focus on low energy consumption bound analysis with the equivalent model of the symmetry circuits from the view point of information theory, and there are few works which focus on the analysis of the relationship among the information transmission, the reliability, and the supply voltage for the asymmetry circuits. The main contribution of this paper provides an analysis methodology for the reliability and supply voltage of asymmetry-based digital circuits with information theory. We use the new Markov random field (MRF) circuits, which can achieve ultra low power and high fault tolerance, as the analysis case. We demonstrate that the low supply voltage bound of MRF circuits is lower than that of traditional CMOS circuits through the proof of four lemmas of entropy, conditional entropy, and mutual information. This work can provide a theoretical basis for the research and design of the asymmetry-based MRF.