Coding schemes for multi-level channels with unknown gain and/or offset

We will present coding techniques for transmission and storage channels with unknown gain and/or offset. It will be shown that a codebook of length-n q-ary codewords, S, where all codewords in S have equal balance and energy show an intrinsic resistance against unknown gain and/or offset. Generating functions for evaluating the size of S will be presented. We will present an approximate expression for the code redundancy for asymptotically large values of n.

[1]  Luca G. Tallini,et al.  Efficient m-ary balanced codes which are invariant under symbol permutation , 2006, IEEE Transactions on Computers.

[2]  Kees A. Schouhamer Immink.  Prefixless q-ary Balanced Codes , 2013 .

[3]  Paul H. Siegel,et al.  Perspectives on Balanced Sequences , 2013, ArXiv.

[4]  Tetsunao Matsuta,et al.  国際会議開催報告:2013 IEEE International Symposium on Information Theory , 2013 .

[5]  Anxiao Jiang,et al.  Balanced Modulation for Nonvolatile Memories , 2012, ArXiv.

[6]  Bella Bose,et al.  Variable Length Unordered Codes , 2012, IEEE Transactions on Information Theory.

[7]  Anxiao Jiang,et al.  Rank modulation for flash memories , 2008, 2008 IEEE International Symposium on Information Theory.

[8]  Kees A. Schouhamer Immink,et al.  Binary transmission codes with higher order spectral zeros at zero frequency , 1987, IEEE Trans. Inf. Theory.

[9]  Ugo Vaccaro,et al.  On efficient m-ary balanced codes , 1997, Proceedings of IEEE International Symposium on Information Theory.

[10]  D. Slepian.  Permutation Modulation , 1965, Encyclopedia of Wireless Networks.

[11]  K. Schouhamer Immink,et al.  Principles of Optical Disc Systems , 1985 .

[12]  P. Flajolet,et al.  Analytic Combinatorics: RANDOM STRUCTURES , 2009 .

[13]  Philippe Flajolet,et al.  Analytic Combinatorics , 2009 .

[14]  Charles J. Colbourn,et al.  On constant composition codes , 2006, Discret. Appl. Math..

[15]  W T Welford,et al.  Principles of Optical Disc Systems , 1986 .