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Optimal coding with a single standard run length

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1 Author(s)

The optimum single standard run lengths for a binary first-order Markov source are derived and extended to multilevel first-order Markov sources. Maximization of the compression ratio is used as the criterion of optimality. When the output symbols are block coded, the optimal single standard run length n_i for each symbol is shown to satisfy an implicit equation of the form (n_i - 1)(-\ln q_{ii}) = 1 - q_{ii}^ {n_i} , where q_{ii} is a transition probability. An expression for the overall compression ratio is derived for the binary case, and a comparison is made with enumerative source encoding. Compression ratio maxima are found by computer search for the binary independent source when the output symbols are subsequently Huffman coded, and a comparison of this scheme with ordinary run-length and source-extension coding is given.

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IEEE Transactions on Information Theory  (Volume:20 ,  Issue: 3 )