Composition Check Codes

We present composition check codes for noisy storage and transmission channels with unknown gain and/or offset. In the proposed composition check code, like in systematic error correcting codes, the encoding of the main data into a constant composition code is completely avoided. To the main data, a coded label is appended that carries information regarding the composition vector of the main data. Slepian’s optimal detection technique of codewords that are taken from a constant composition code is applied for detection. A first Slepian detector detects the label and subsequently restores the composition vector of the main data. The composition vector, in turn, is used by a second Slepian detector to optimally detect the main data. We compute the redundancy and error performance of the new method, and results of computer simulations are presented.

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

[2]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

[3]  John Riordan,et al.  Introduction to Combinatorial Analysis , 1959 .

[4]  Jos H. Weber,et al.  Efficient balancing of q-ary sequences with parallel decoding , 2009, 2009 IEEE International Symposium on Information Theory.

[5]  Kees A. Schouhamer Immink,et al.  Error propagation assessment of enumerative coding schemes , 1999, IEEE Trans. Inf. Theory.

[6]  Bella Bose,et al.  m-ary Balanced Codes With Parallel Decoding , 2015, IEEE Trans. Inf. Theory.

[7]  William Ryan,et al.  Channel Codes by William Ryan , 2009 .

[8]  Thomas M. Cover,et al.  Enumerative source encoding , 1973, IEEE Trans. Inf. Theory.

[9]  Bane V. Vasic,et al.  Permutation (d, k) codes: Efficient enumerative coding and phrase length distribution shaping , 2000, IEEE Trans. Inf. Theory.

[10]  Jos H. Weber,et al.  Knuth's Balanced Codes Revisited , 2010, IEEE Transactions on Information Theory.

[11]  Yue Li,et al.  Data archiving in 1x-nm NAND flash memories: Enabling long-term storage using rank modulation and scrubbing , 2016, 2016 IEEE International Reliability Physics Symposium (IRPS).

[12]  Ugo Vaccaro,et al.  Efficient m-ary Balanced Codes , 1999, Discret. Appl. Math..

[13]  Helmut Prodinger,et al.  Positional number systems with digits forming an arithmetic progression , 2008 .

[14]  Luisa Gargano,et al.  Efficient q-ary immutable codes , 1991, Discret. Appl. Math..

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

[16]  William Ryan,et al.  Channel Codes: Classical and Modern , 2009 .

[17]  Donald E. Knuth,et al.  Efficient balanced codes , 1986, IEEE Trans. Inf. Theory.

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

[19]  J. Pieter M. Schalkwijk,et al.  An algorithm for source coding , 1972, IEEE Trans. Inf. Theory.

[20]  G. David Forney,et al.  Maximum-likelihood sequence estimation of digital sequences in the presence of intersymbol interference , 1972, IEEE Trans. Inf. Theory.

[21]  Shu Lin,et al.  Channel Codes: Classical and Modern , 2009 .

[22]  Steven W. McLaughlin,et al.  An enumerative method for runlength-limited codes: permutation codes , 1999, IEEE Trans. Inf. Theory.