Simple systematic Pearson coding

The recently proposed Pearson codes offer immunity against channel gain and offset mismatch. These codes have very low redundancy, but efficient coding procedures were lacking. In this paper, systematic Pearson coding schemes are presented. The redundancy of these schemes is analyzed for memoryless uniform sources. It is concluded that simple coding can be established at only a modest rate loss.

[1]  D. R. Heath-Brown,et al.  An Introduction to the Theory of Numbers, Sixth Edition , 2008 .

[2]  J. Wolfowitz,et al.  An Introduction to the Theory of Statistics , 1951, Nature.

[3]  Jos H. Weber,et al.  Minimum Pearson Distance Detection for Multilevel Channels With Gain and/or Offset Mismatch , 2014, IEEE Transactions on Information Theory.

[4]  Jos H. Weber,et al.  Hybrid Minimum Pearson and Euclidean Distance Detection , 2015, IEEE Transactions on Communications.

[5]  Kees A. Schouhamer Immink Coding schemes for multi-level channels with unknown gain and/or offset , 2013, 2013 IEEE International Symposium on Information Theory.

[6]  Anxiao Jiang,et al.  Error-correcting schemes with dynamic thresholds in nonvolatile memories , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.

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

[8]  Jos H. Weber,et al.  Pearson Codes , 2015, IEEE Transactions on Information Theory.

[9]  Frederic Sala,et al.  Error Control Schemes for Modern Flash Memories: Solutions for Flash deficiencies , 2015, IEEE Consumer Electronics Magazine.

[10]  Jos H. Weber,et al.  Very Efficient Balanced Codes , 2010, IEEE Journal on Selected Areas in Communications.

[11]  E. Wright,et al.  An Introduction to the Theory of Numbers , 1939 .

[12]  K.A.S. Immink Coding schemes for multi-level Flash memories that are intrinsically resistant against unknown gain and/or offset using reference symbols , 2014 .

[13]  H. J. Larson,et al.  Introduction to the Theory of Statistics , 1973 .