Abstract
The model in Chapter 8 is for the noiseless channel; no errors are allowed. The basic notion needed for the three theorems of the chapter is that of the residual quotient set of a pair of sets of sequences over some alphabet. The notion is defined and then certain residual quotient sets are characterized in Propositions 2 and 4, the latter being the more useful formulation. Unique decipherability is characterized in Theorem I, unique decipherability with bounded delay (= decodability with bounded delay) in Theorem II, and synchronizability (= error-limitation) in Theorem III. All proofs involve residual quotient sets. The chapter closes with the establishment of numerical bounds concerning the algorithms described in the three theorems.
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© 1974 D. Reidel Publishing Company, Dordrecht, Holland
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Hartnett, W.E. (1974). Overview. In: Hartnett, W.E. (eds) Foundations of Coding Theory. Episteme, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-2298-9_9
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DOI: https://doi.org/10.1007/978-94-010-2298-9_9
Publisher Name: Springer, Dordrecht
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Online ISBN: 978-94-010-2298-9
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