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Effects of floating-point arithmetic in enumerative coding

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Let S be a given subset of binary n-sequences. We provide an explicit scheme for calculating the index of any sequence in S according to its position in the lexicographic ordering of S . A simple inverse algorithm is also given. Particularly nice formulas arise when S is the set of all n -sequences of weight k and also when S is the set of all sequences having a given empirical Markov property. Schalkwijk and Lynch have investigated the former case. The envisioned use of this indexing scheme is to transmit or store the index rather than the sequence, thus resulting in a data compression of (logmidSmid)/n .
Traditional schemes for encoding and decoding runlength-constrained sequences using the enumeration principle require two sets of weighting coefficients. A new enumeration is presented requiring only one set of coefficients
Runlength limited sequences
  • Tj
  • Tjalkens
Tj. Tjalkens, 'Runlength limited sequences', IEEE Trans. Inform. Theory, vol. IT-40, no. 3, pp. 934-940, 1994.