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Molecular electronics such as silicon nanowires (NW) and carbon nanotubes (CNT) demonstrate great potential for continuing the technology advances toward future nano-computing paradigm. However, excessive defects from bottom-up stochastic assembly have emerged as a fundamental obstacle for achieving reliable computation using molecular electronics. In this paper, we present an information-theoretic approach to investigate the intrinsic relationship between defect tolerance and inherence redundancy in molecular crossbar systems. By modeling defect-prone molecular crossbars as a non-ideal information processing medium, we determine the information transfer capacity, which can be interpreted as the bound on reliability that a molecular crossbar system can achieve. The proposed method allows us to evaluate the effectiveness of redundancy-based defect tolerance in a quantitative manner. Employing this method, we derive the gap of reliability between redundancy-based defect tolerance and ideal defect-free molecular systems. We also show the implications to the related design optimization problem.