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We report weaknesses in two algebraic constructions of low-density parity-check codes based on expander graphs. The Margulis construction gives a code with nearcodewords, which cause problems for the sum-product decoder; The RamanujanMargulis construction gives a code with low-weight codewords, which produce an error-floor.

- James William Harrington, John Preskill, +61 authors Frank Reyes
- 2004

Quantum information theory is concerned with identifying how quantum mechanical resources (such as entangled quantum states) can be utilized for a number of information processing tasks, including data storage, computation, communication, and cryptography. Efficient quantum algorithms and protocols have been developed for performing some tasks (e.g.,… (More)

- Michael S. Postol
- IEEE Trans. Circuits Syst. Video Techn.
- 2002

- David J. C. MacKay, Michael S. Postol
- Electr. Notes Theor. Comput. Sci.
- 2002

We report weaknesses in two algebraic constructions of low-density parity-check codes based on expander graphs. The Margulis construction gives a code with nearcodewords, which cause problems for the sum-product decoder; The RamanujanMargulis construction gives a code with low-weight codewords, which produce an error-floor.

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