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.
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
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