By Giuseppe Longo

ISBN-10: 3211811540

ISBN-13: 9783211811542

ISBN-10: 3709129613

ISBN-13: 9783709129616

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Extra info for Coding for Markov Sources: Course Held at the Department for Automation and Information June 1971

Example text

_ . 00) J12. 2. Application to coding for discrete memoryless sources. 1. Consider theorem 2. ::{l, ... l}insteadof k k with the usual meaning of the notations. 59') (2. 59' 1) ii) Y' ;. E(~ (L) E. e. ) is the usual product probability of the sequence p2 ln) L -length Y. • In other words, probable sequences of length L (L) E • is the set of the most p whose overall probability is 1 - PCl The I (L) U -measure of a set E c 0. is proportion (L) al to the number J E (IJ of elements in E. (~' is equivalent to finding the minimum of IE{IJ I· The proportionality coefficient is Now eq.

7) will be called a 'codeword 11 of length N Now the task of the Coder ( ~~) can be described (*) Apart from the information processing for securing prote£ tion against transmission errors, which is neglected here. J. 9) N~ the , whose length N ~ (L) u~ (L) = N~ (u·~ ). 8), it outputs a sequence (L) ( 2. ) ) q, ( y 2 ) = is the ''code mapping", which defines the rule bywhich a codeword is associated to a Source sequence. If we wish to decrease the transmission cost, we should decrease the average length of the codewords, which can be done, roughly, by choosing such a + which associates probable Source sequences with short codewords and unprobable Source sequences with long codewords, while respecting some specific rules for granting unique decipherability (such as the prefix property and the like}.

A L of size made up with letters K into codewords of length N made up with letters taken from the alphabet tf. of size 0 . 11) or equivalently N :? 12) Eq. 12) sets a lower bound on the codeword length, and if it is satisfied, a one-one correspondence between Source sequences and codewords is granted, which makes it possible (if transmission errors have no effect) to recover the information emitted by the Source with zero error probability. Seen from Shannon Theorem 34 this viewpoint, fixed length techniques are not very attractive, since the lower bound of eq.

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Coding for Markov Sources: Course Held at the Department for Automation and Information June 1971 by Giuseppe Longo

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