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....deleting the first row from the previous database. In the enlarged database scheme discussed in this section, the compression ratio r can be approximated by r = length of the overhead information length of repeated subword = log n log L n L n : 2) However, Kieffer in a private correspondence [15] pointed out that a precise estimation of the compression ratio is more complicated. Indeed, let X (k) be the database after the kth application of the above procedure. Observe that X (k 1) X (k) X jX (k) j L jX (k) jX (k) j 1 (3) where denotes concatenation. Then, the ....

.... first and second moment methods along the lines of arguments used in [19] The almost sure convergence of log N = is proved in [29] while the lack of almost sure convergence of L n = log n is established in [19] Finally, 10) is a simple consequence of (2) and (8) We conjecture after Kieffer [15] that the compression ratio as defined in (4) also converges almost surely to r 0 (D) In [18, 19] the R enyi entropy r 0 (D) was computed for memoryless sources and Hamming distance. In Figure 1 we compared it to the optimal rate distortion R(D) h D log D (1 Gamma D) log(1 Gamma D) where ....

J.C. Kieffer, Private Correspondence.

....deleting the first row from the previous database. In the enlarged database scheme discussed in this section, the compression ratio r can be approximated by r = length of the overhead information length of repeated subword = log n log L n L n : 2) However, Kieffer in a private correspondence [15] pointed out that a precise estimation of the compression ratio is more complicated. Indeed, let X (k) be the database after the kth application of the above procedure. Observe that X (k 1) X (k) X jX (k) j L jX (k) jX (k) j 1 (3) where denotes concatenation. Then, the ....

.... first and second moment methods along the lines of arguments used in [19] The almost sure convergence of log N = is proved in [29] while the lack of almost sure convergence of L n = log n is established in [19] Finally, 10) is a simple consequence of (2) and (8) We conjecture after Kieffer [15] that the compression ratio as defined in (4) also converges almost surely to r 0 (D) In [18, 19] the R enyi entropy r 0 (D) was computed for memoryless sources and Hamming distance. In Figure 1 we compared it to the optimal rate distortion R(D) h D log D (1 Gamma D) log(1 Gamma D) where ....

J.C. Kieffer, Private Correspondence.

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