Two inequalities implied by unique decipherability

@article{McMillan1956TwoII,
  title={Two inequalities implied by unique decipherability},
  author={Brockway McMillan},
  journal={IRE Trans. Inf. Theory},
  year={1956},
  volume={2},
  pages={115-116}
}
  • B. McMillan
  • Published 1 December 1956
  • Mathematics
  • IRE Trans. Inf. Theory
Consider a list of b words, each word being a string of letters from a given fixed alphabet of a letters. If every string of words drawn from this list, when written out in letters without additional space marks to separate the words, is uniquely decipherable, then \begin{equation} a^{-l_1} + a^{-l_2} + \cdots + a^{-l_b} \leq 1, \qquad \qquad (1) \end{equation} where l_i, 1 \leq i \leq b , is the length of the i th word in the list. This result extends a remark of J. L. Doob, who derived the… 

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