Abstract
We consider codes coming from systems of sparse linear equations. (These low-density parity check codes are examples of what are called Gallager codes.) We suggest how non-linear equations very elose to the given linear equations might be used to improve decoding properties while retaining the same level of coding and decoding complexity.
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Much of this work was done under the auspices of Lawrence University’s sabbatical program.
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References
R.G. Gallager, Low-Density Parity-Check Codes, no. 21 in Research Monograph Series, Cambridge MA: MIT Press, 1963.
D.J.C. MacKay, Good Error-Correcting Codes Based on Very Sparse Matrices, IEEE Transactions on Information Theory, Vol. 45, no. 2, March 1999.
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© 2001 Springer-Verlag New York, Inc.
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Parks, A. (2001). Mildly Non-Linear Codes. In: Marcus, B., Rosenthal, J. (eds) Codes, Systems, and Graphical Models. The IMA Volumes in Mathematics and its Applications, vol 123. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0165-3_8
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DOI: https://doi.org/10.1007/978-1-4613-0165-3_8
Publisher Name: Springer, New York, NY
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