Runlength-Limited Sequences and Shift-Correcting Codes
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This work is motivated by the problem of error correction in bit-shift channels with the so-called (d,k) input constraints (where successive 1 's are required to be separated by at least d and at most k zeros, 0 ≤ d < k ≤∞ ). Bounds on the size of optimal (d,k) -constrained codes correcting a fixed number of bit-shifts are derived. The upper bound is obtained by a packing argument, while the lower bound follows from a construction based on a family of integer lattices. Several properties of (d, k) -constrained sequences that may be of independent interest are established as well; in particular, the capacity of the noiseless channel with (d, k) -constrained constant-weight inputs is characterized. The results are relevant for magnetic and optical storage systems, reader-to-tag RFID channels, and other communication models where bit-shift errors are dominant and where (d, k) -constrained sequences are used for modulation.
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