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The simplest coding problem
The optimum rate of information transmission
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amount of information arbitrary cost sequence assumption average code word basic inequality blocks of length Bog2 channel capacity code g code g(u code word cost conservation of entropy converges in probability cost of transmission cost satisfies 1.16 define different cost different sequences encoded source entropy rate Eog2 Eog2p(u fixed positive numbers implies inequality 1.12 information theory INFORMATION TRANSMISSION Lemma lower bound mapping g memoryless channels messages of length noiseless channel number of different number of sequences number of symbols point representing possibly small cost prefix code prefix property principle of conservation probability assignement probability to q quences rate H(X sense decodable code sequences of letters sequences transmissible sequences U eX Shannon-Fano method Shannon's entropy source X strict sense decodable Suppose symbol costs transmissible with cost TRANSMISSION WITH SIMBOLS trivial cost sequence Udine uniformly integrable upper bounded valued random variables variable length encod void sequence