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A coding scheme for single peak-shift correction in (d, k)-constrained channels

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2 Author(s)
A. V. Kuznetsov ; Inst. for Problems of Inf. Transmission, Acad. of Sci., Moscow, Russia ; A. J. H. Vinck

A two step coding scheme for peak-shift correction in (d, k)-constrained sequences is described. The first step is based on q-ary (q=k-d+1 is a prime) block codes that allow correction of specific types of double errors caused by single peak-shifts. The second step is a simple conversion of q-ary symbols to binary strings of the type 00. . .01. The concatenation of these strings satisfies the (d,k)-constraint within the codeword and in concatenation with neighboring words. The length of the codewords is controlled and, if necessary, can be fixed. The rate R1 of the overall encoding approaches (2 log2 (k-d+1)/(k+d+2) for large codeword lengths. Codes for correction of peak-shift, deletions, and insertions of zeros are presented as well. Encoding and decoding are done by simple algorithms without using look-up tables, enumeration or denumeration procedures and, therefore, the codelength may be large

Published in:

IEEE Transactions on Information Theory  (Volume:39 ,  Issue: 4 )