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Optimal communication systems with noiseless feedback for a binary source and white Gaussian channel

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The sequential and nonsequential feedback systems for a binary source, first proposed by Turin, are considered. It is shown that in both cases the optimal signals belong to the familypm A (y)[1 + exp (pm y)]^{-1}, whereA(y)is arbitrary. In the sequential scheme the bound on transmission rate is achieved for anyP_{e}by all members of this family, and in the nonsequential scheme for smallP_{e}only. The optimal signals within this family, i.e., signals for whichalpha =peak power/average power is minimal, result ifA(y) = pm sqrt{alpha P_{av}} (1 -b e^{-|y|}). In the sequential case, the optimal scheme is compared with two suboptimal schemes, and the advantages of the first are demonstrated. Finally, the problem of sequential detection with time-varying thresholds is presented, and its equivalence to a problem with fixed thresholds is proved.

Published in:

Information Theory, IEEE Transactions on  (Volume:15 ,  Issue: 1 )

Date of Publication:

Jan 1969

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