One of the main obstacles to the wider use of the modern error-correction codes is that, due to the complex behavior of their decoding algorithms, no systematic method which would allow characterization of the BitError-Rate (BER) is known. This is especially true at the weak noise where many systems operate and where coding performance is difficult to estimate because of the diminishingly small number of errors. We show how the instanton method of physics allows one to solve the problem of BER analysis in the weak noise range by recasting it as a computationally tractable minimization problem. PACS numbers: 89.70.+c, Modern technologies, as well as many natural and sociological systems, rely heavily on a wide range of error-correction mechanisms to compensate for their inherent unreliability and to ensure faithful transmission, processing and storage of information. There has been a great deal of research activity in coding theory in the last half a century that has culminated in the recent discovery of coding schemes [1,2,3] that approach a reliability limit set by classical information theory [4]. The problem considered in this paper is of a special interest because of a unique feature of the modern coding schemes, which is referred to as an error floor [5,6]. Error floor is a phenomenon characterized by an abrupt degradation of the coding scheme performance, as measured by the BER, from the so-called water-fall regime of moderate Signal-to-Noise Ratio (SNR) to the absolutely different error-floor asymptotic achieved at high SNR. To estimate the error-floor asymptotic in the modern high-quality systems is a notoriously difficult task. Typical required BER values are 10 −12 for an optical communication system, 10 −15 for hard drive systems in personal computers and as small as 10 −20 for storage systems used in banks and financial institutions. However, direct numerical methods, e.g. Monte Carlo, cannot be used to determine BER below 10 −9 .To address this challenge we suggest a physics-inspired approach that ultimately solves the problem of the error-floor analysis. The method is coined the "instanton" method, after a theoretical particle in quantum physics that lasts for only an instant, occupying a localized portion of space-time [7]. Statistical physics uses the word instanton to describe a microscopic configuration which, in spite of its rare occurrence, contributes most to the macroscopic behavior of the system [8]. Our instanton is the most probable configuration of the noise to cause a decoding error.We consider a model of a general communication system with error correction [4]. Data originating from an information source are parsed into fixed length words. Each word is encoded into a longer codeword and transmitted through a noisy channel (e.g., radio or optical link, magnetic or optical data storage system, etc.). The decoder tries to reconstruct the original codeword using the knowledge of the noise statistics and the structure of the code. Error resilience is achieved at the expense of introduced r...