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Issue No.06 - June (1970 vol.19)
pp: 548-551
K.L. Doty , IEEE
ABSTRACT
The concept of lossless state or system is generalized by the definition of k-losslessness. If k>N( N-1)/2 for an N-state machine, k-lossless implies lossless. The series connection of a set of discrete time systems {Ai}, where Ai is ki-lossless, results in a system which is min{ki}-lossless. This result is a simple verification of the intuitive notion that a noiseless communication channel is only as lossless as the most lossy system in the channel. By means of input- output pair analysis, systems with the decomposition property (one of the necessary but not sufficient conditions for linearity) are shown to be information-lossless of finite order m, when one state has finite order m. Further, every state must have exactly the same order. For an N-state system with decomposition and zero-state linearity, information-lossless implies information-lossless of finite order m=N. As a consequence, all information-lossless linear sequential machines used as encoders allow decoding to begin after m received symbols, provided that the encoder's starting state is known in advance.
INDEX TERMS
Decomposition property, encoders, information- lossless machines, invertible, linear.
CITATION
K.L. Doty, "On Information-Lossless Discrete-Time Systems", IEEE Transactions on Computers, vol.19, no. 6, pp. 548-551, June 1970, doi:10.1109/T-C.1970.222974
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