In this paper, we present a general method for determining the capacity of low-density parity-check (LDPC) codes under message-passing decoding when used over any binary-input memoryless channel with discrete or continuous output alphabets. Transmitting at rates below this capacity, a randomly

Low-density parity-check (LDPC) codes can be considered serious competitors to turbo codes in terms of performance and complexity and they are based on a similar philosophy: constrained random code ensembles and iterative decoding algorithms. In this paper, we consider the encoding problem

This article presents EXE, an effective bug-finding tool that automatically generates inputs that crash real code. Instead of running code on manually or randomly constructed input, EXE runs it on symbolic input initially allowed to be anything. As checked code runs, EXE tracks the constraints

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Multi-model ensemble simulations of

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Abstract—This paper studies a random coding ensemble in which each codeword is constrained to satisfy multiple cost constraints. Using this ensemble, an achievable second-order coding rate is presented for the mismatched single-user channel. Achievable error exponents are given for the mismatched

When economic capital is calculated using a portfolio model of credit value-at-risk, the marginal capital requirement for an instrument depends, in general, on the properties of the portfolio in which it is held. By contrast, ratings-based capital rules, including both the current Basel Accord and its proposed revision, assign a capital charge to an instrument based only on its own characteristics. I demonstrate that ratingsbased capital rules can be reconciled with the general class of credit VaR models. Contributions to VaR are portfolio-invariant only if (a) there is only a single systematic risk factor driving correlations across obligors, and (b) no exposure in a portfolio accounts for more than an arbitrarily small share of total exposure. Analysis of rates of convergence to asymptotic VaR leads to a simple and accurate portfolio-level add-on charge for undiversified idiosyncratic risk. There is no similarly simple way to address violation of the single factor assumption.

We address the problem of evaluating the asymptotic, normalized distributions of a class of combinatorial configurations in random, regular and irregular binary low-density parity-check (LDPC) code ensembles. Among the configurations considered are trapping and stopping sets 1; these sets represent