Gallager error-correcting codes for binary asymmetric channels
نویسندگان
چکیده
Abstract. We derive critical noise levels for Gallager codes on asymmetric channels as a function of the input bias and the temperature. Using a statistical mechanics approach we study the space of codewords and the entropy in the various decoding regimes. We further discuss the relation of the convergence of the message passing algorithm with the endogenous property and complexity, characterizing solutions of recursive equations of distributions for cavity fields.
منابع مشابه
Good Error-Correcting Codes Based On Very Sparse Matrices - Information Theory, IEEE Transactions on
We study two families of error-correcting codes defined in terms of very sparse matrices. “MN” (MacKay–Neal) codes are recently invented, and “Gallager codes” were first investigated in 1962, but appear to have been largely forgotten, in spite of their excellent properties. The decoding of both codes can be tackled with a practical sum-product algorithm. We prove that these codes are “very good...
متن کاملErrata for "Good error-correcting codes based on very sparse matrices"
We study two families of error-correcting codes defined in terms of very sparse matrices. “MN” (MacKay–Neal) codes are recently invented, and “Gallager codes” were first investigated in 1962, but appear to have been largely forgotten, in spite of their excellent properties. The decoding of both codes can be tackled with a practical sum-product algorithm. We prove that these codes are “very good...
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We study two families of error-correcting codes deened in terms of very sparse matrices. `MN' (MacKay{Neal) codes are recently invented, and`Gallager codes' were rst investigated in 1962, but appear to have been largely forgotten, in spite of their excellent properties. The decoding of both codes can be tackled with a practical sum{product algorithm. We prove that these codes arèvery good', in ...
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