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Error Exponents of Discrete MemorylessChannels Under Small Mismatch…
www-sigproc.eng.cam.ac.uk/foswiki/pub/Main/AG495/isit2024_exp.pdf20 Jun 2024: counterpart in Appendix A closely. Recall that weperformed a Taylor expansion of the cost function (23) andthus wish to solve (24). ... Upon applying the minimax theoremto (24), we cannot further move the minimization inside thelogarithm. -
Fixed-Memory Capacity Bounds for theGilbert-Elliott Channel Yutong…
www-sigproc.eng.cam.ac.uk/foswiki/pub/Main/AG495/isit2024_gec.pdf20 Jun 2024: by. PZi (1) =zi1. PZi2Zi1 (zi2zi1)qi(z. i2zi1) (24). zi1. PZi1 (zi1)qi(0i2zi1) (25). = ... p1 q(0). 1 q(0) q(01)(29). Similarly, by substituting the upper bound in (21) into (24),we get. -
Mismatched Decoding: Generalized MutualInformation under Small…
www-sigproc.eng.cam.ac.uk/foswiki/pub/Main/AG495/izs2024_gmi.pdf29 Jan 2024: IGMI(QX,Ŵ,r). = minWB(QX,Ŵ ,r). sups0. EQXW [is(X,Y )] (24). = sups0. ... minWB(QX,Ŵ ,r). EQXW [is(X,Y )] (25). The minimax theorem [5] is applied to switch the order ofthe optimizations from (24) to (25) since EQXW [is(X,Y )]. is -
Coding for the Gilbert-Elliott Channel: AMismatched Decoding…
www-sigproc.eng.cam.ac.uk/foswiki/pub/Main/AG495/izs2024_gec.pdf29 Jan 2024: nGnGG=0. enD(Φ‖Γ|F) (22). = maxnGG[0,nG]. enD(Φ‖Γ|F) (23). = enD(Φ‖Γ|F) (24). where we denote D(Φ‖Γ|F) , minfGG[0,fG] D( ... Applying the LogSumExp(LSE) inequality maxi ai logni=1 exp(ai) log n+ maxi ai and substituting (24) into. -
Nearest Neighbor Decodingfor a Class of Compound Channels Francesc ...
www-sigproc.eng.cam.ac.uk/foswiki/pub/Main/AG495/isit2024_cont.pdf20 Jun 2024: 24). When r is sufficiently small, the o() term can beomitted from the constraint, penalizing the cost functionas o(d(ŴW |QX)) = o(r) using the new constraintd(ŴW |QX) r. -
Fixed Composition Arguments andLower Bounds to Error Probability…
www-sigproc.eng.cam.ac.uk/foswiki/pub/Main/AG495/fixed_composition_notes.pdf24 Jun 2024: Pe en(Esp(Q,Rδn)δn) (23). whereEsp(Q,R) = min. P̂ :I(Q;P̂ )RD(P̂‖P |Q) (24). ... and. δn (JK 1) log(n 1) log 2. n. Note that the rate R in (24) corresponds to R δn in (22); this allows us to make aclean definition of -
Error Exponents of Block Codesfor Finite-State Sources with Mismatch…
www-sigproc.eng.cam.ac.uk/foswiki/pub/Main/AG495/izs2024_source.pdf29 Jan 2024: 24)We thus write the first term in brackets in (21) as. -
Universal Neyman–Pearson classification with a partially known…
www-sigproc.eng.cam.ac.uk/foswiki/pub/Main/AG495/univ_imaiai.pdf20 Jun 2024: engineering, signal processing, medicine and finance among others [24]. ... 1–31. 24. LEHMANN, E. L. & ROMANO, J. P. (2005) Testing statistical hypotheses, Springer Texts in Statistics, 3rd edn.
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