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Sliding-block joint source/noisy-channel coding theorems. (English) Zbl 0348.94019
Author’s summary: “Sliding-block codes are nonblock coding structures consisting of discrete-time time-invariant possibly nonlinear filters. They are equivalent to time-invariant trellis codes. The coupling of Forney’s rigorization of Shannon’s random-coding/typical-sequence approach to block coding theorems with the strong Rohlin-Kakutani Theorem of ergodic theory is used to obtain a sliding-block coding theorem for ergodic sources and discrete memoryless noisy channels. Combining this result with a theorem on sliding-block source coding with a fidelity criterion yields a sliding-block information transmission theorem. Thus, the basic existence theorems of information theory hold for stationary nonblock structures, as well as for block codes.”
The reader will find “Forney’s” 1972 rigorization in the reviewer’s “Coding theorems of information theory” Berlin etc.: Springer (1961; Zbl 0102.34501); second ed. (1964; Zbl 0132.39704).
Reviewer: Jacob Wolfowitz

94A24 Coding theorems (Shannon theory)
94A29 Source coding
94B12 Combined modulation schemes (including trellis codes) in coding theory
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