Abstract
Standard runlength-limiting codes — nonlinear codes defined by trellises — have the disadvantage that they disconnect the outer errorcorrecting code from the bit-by-bit likelihoods that come out of the channel. I present two methods for creating transmissions that, with probability extremely close to 1, both are runlength-limited and are codewords of an outer linear error-correcting code (or are within a very small Hamming distance of a codeword). The cost of these runlength-limiting methods, in terms of loss of rate, is significantly smaller than that of standard runlength-limiting codes. The methods can be used with any linear outer code; low-density parity-check codes are discussed as an example.
The cost of the method, in terms of additional redundancy, is very small: a reduction in rate of less than 1% is sufficient for a code with blocklength 4376 bits and maximum runlength 14.
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References
John Byers, Michael Luby, Michael Mitzenmacher, and Ashu Rege. A digital fountain approach to reliable distribution of bulk data. In Proceedings of ACM SIGCOMM’ 98, September 2–4, 1998, 1998.
R. H. Deng and M. A. Herro. DC-free coset codes. IEEE Trans. Inf. Th., 34:786–792, 1988.
R. G. Gallager. Low Density Parity Check Codes. Number 21 in Research monograph series. MIT Press, Cambridge, Mass., 1963.
K. A. S. Immink. Constructions of almost block-decodable runlength-limited codes. IEEE Transactions on Information Theory, 41(1), January 1995.
K. A. S. Immink. A practical method for approaching the channel capacity of constrained channels. IEEE Trans. Inform. Theory, 43(5):1389–1399, Sept 1997.
K. A. S. Immink. Weakly constrained codes. Electronics Letters, 33(23), Nov. 1997.
D. J. C. MacKay and M. C. Davey. Evaluation of Gallager codes for short block length and high rate applications. In B. Marcus and J. Rosenthal, editors, Codes, Systems and Graphical Models, volume 123 of IMA Volumes in Mathematics and its Applications, pages 113–130. Springer-Verlag, New York, 2000.
B. H. Marcus, P. H. Siegel, and J. K. Wolf. Finite-state modulation codes for data storage. IEEE Journal on Selected Areas in Communication, 10(1):5–38, January 1992.
G. S. Markarian, M. Naderi, B. Honary, A. Popplewell, and J. J. O’Reilly. Maximum likelihood decoding of RLL-FEC array codes on partial response channels. Electronics Letters, 29(16):1406–1408, 1993.
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© 2001 Springer-Verlag Berlin Heidelberg
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MacKay, D.J.C. (2001). Almost-Certainly Runlength-Limiting Codes. In: Honary, B. (eds) Cryptography and Coding. Cryptography and Coding 2001. Lecture Notes in Computer Science, vol 2260. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45325-3_13
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DOI: https://doi.org/10.1007/3-540-45325-3_13
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