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The number of different possible compact codes (Corresp.)

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For a source with a given number q of messages and an unspecified set of probabilities, the number X(q) of non-trivially different compact codes that are possible increases in a predictable fashion as q increases. Distinct binary compact codes of q messages correspond to distinct oriented binary trees with q terminal nodes. The theorem of this correspondence shows that, by using a recursion relation, and given that there is one compact code tree for q = 2 , all compact code trees for any q > 2 can be automatically constructed. This is done by splitting, for all integers s \geq 1, s bottom level nodes of all compact code trees which have q - s terminal nodes and which end in s or more bottom level nodes.

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Information Theory, IEEE Transactions on  (Volume:13 ,  Issue: 4 )