Paolo added file anytime_ISIT-02.aux  almost 9 years ago

Commit id: 0a0a9be0131670f710d101579d3679e874b9767d

deletions | additions      

         

\relax   \providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}  \HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined  \global\let\oldcontentsline\contentsline  \gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}  \global\let\oldnewlabel\newlabel  \gdef\newlabel#1#2{\newlabelxx{#1}#2}  \gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}  \AtEndDocument{\ifx\hyper@anchor\@undefined  \let\contentsline\oldcontentsline  \let\newlabel\oldnewlabel  \fi}  \fi}  \global\let\hyper@last\relax   \gdef\HyperFirstAtBeginDocument#1{#1}  \providecommand*\HyPL@Entry[1]{}  \citation{Franceschetti-Minero-2014}  \citation{matveed-savkin2007b}  \citation{Shannon1956}  \citation{Sahai2001}  \citation{Como-Fagnani-Zampieri2010,Sahai-Mitter2006,simsek-jain-varaija2004,Xu2005}  \citation{Wong-Brocket1999,Brocket-Liberzon2000,Liberzon2003,Delchamps1990,Martins-Dehleh-Elia2006,Nair-Evans-2004,Imer-etal-2006,Tatikonda-Mitter2004,Tatikonda-Mitter2004b,Gupta-Martins2010,Yuksel2010,Yuksel-Basar2011,Borkar-Mitter-1997,Minero-etal-2009,Coviello-etal2012,Gupta-etal-2007,Gupta-etal-2009,Schenato-etal-2007,Huang-Dey-2007,Elia2005,Mitter-Elia2001}  \citation{Minero-etal-2009,Coviello-etal2012}  \HyPL@Entry{0<>}  \@writefile{toc}{\contentsline {section}{\numberline {I}Introduction}{1}{section.1}}  \@writefile{toc}{\contentsline {section}{\numberline {II}Moment Stabilization over Markov Channels}{1}{section.2}}  \newlabel{sec:scalar}{{II}{1}{Moment Stabilization over Markov Channels\relax }{section.2}{}}  \@writefile{toc}{\contentsline {subsection}{\numberline {\unhbox \voidb@x \hbox {II-A}}System model}{1}{subsection.2.1}}  \newlabel{eq:scalsys}{{1}{1}{System model\relax }{equation.2.1}{}}  \citation{GoldsmithVaraiya1996}  \citation{Shannon1956}  \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Feedback loop model. The estimated state is quantized, encoded and sent to a decoder over a digital channel of state $R_k$ that evolves in time according to a Markov process. }}{2}{figure.1}}  \newlabel{fig:scheme}{{1}{2}{Feedback loop model. The estimated state is quantized, encoded and sent to a decoder over a digital channel of state $R_k$ that evolves in time according to a Markov process}{figure.1}{}}  \@writefile{toc}{\contentsline {subsection}{\numberline {\unhbox \voidb@x \hbox {II-B}}Channel Model}{2}{subsection.2.2}}  \newlabel{eq:support}{{2}{2}{Channel Model\relax }{equation.2.2}{}}  \newlabel{eq:P}{{3}{2}{Channel Model\relax }{equation.2.3}{}}  \newlabel{eq:Rdiag}{{4}{2}{Channel Model\relax }{equation.2.4}{}}  \newlabel{eq:shanc}{{7}{2}{Channel Model\relax }{equation.2.7}{}}  \newlabel{eq:shanz}{{8}{2}{Channel Model\relax }{equation.2.8}{}}  \@writefile{toc}{\contentsline {subsection}{\numberline {\unhbox \voidb@x \hbox {II-C}}Stability threshold function}{2}{subsection.2.3}}  \newlabel{eq:sta}{{9}{2}{Stability threshold function\relax }{equation.2.9}{}}  \newlabel{thm1}{{1}{2}{\relax }{theorem.1}{}}  \newlabel{eq:Rm}{{11}{2}{\relax }{equation.2.11}{}}  \newlabel{prop1}{{2}{2}{\relax }{theorem.2}{}}  \newlabel{eq:fact2}{{12}{2}{\relax }{equation.2.12}{}}  \newlabel{eq:fact3a}{{13}{2}{\relax }{equation.2.13}{}}  \citation{Sahai-Mitter2006}  \citation{Sahai-Mitter2006}  \citation{Sahai-Mitter2006}  \citation{matveed-savkin2007b}  \newlabel{eq:fact3b}{{14}{3}{\relax }{equation.2.14}{}}  \newlabel{eq:fact4}{{15}{3}{\relax }{equation.2.15}{}}  \newlabel{eq:fact4b}{{16}{3}{\relax }{equation.2.16}{}}  \@writefile{toc}{\contentsline {section}{\numberline {III}Anytime Capacity of Markov Channels}{3}{section.3}}  \newlabel{eq:relia}{{18}{3}{Anytime Capacity of Markov Channels\relax }{equation.3.18}{}}  \newlabel{thm2}{{3}{3}{Sahai, Mitter~\cite {Sahai-Mitter2006}\relax }{theorem.3}{}}  \newlabel{anytime2}{{19}{3}{Sahai, Mitter~\cite {Sahai-Mitter2006}\relax }{equation.3.19}{}}  \newlabel{th:combining}{{4}{3}{\relax }{theorem.4}{}}  \newlabel{anytime2}{{20}{3}{\relax }{equation.3.20}{}}  \newlabel{eq:par}{{21}{3}{\relax }{equation.3.21}{}}  \newlabel{anytime2b}{{22}{3}{\relax }{equation.3.22}{}}  \newlabel{eq:fact2}{{23}{3}{\relax }{equation.3.23}{}}  \newlabel{eq:fact3a1}{{24}{3}{\relax }{equation.3.24}{}}  \newlabel{eq:fact3a2}{{25}{3}{\relax }{equation.3.25}{}}  \newlabel{eq:fact3b}{{26}{3}{\relax }{equation.3.26}{}}  \citation{Sahai2001}  \citation{Xu2005}  \citation{Yuksel--Meyn2013}  \citation{Gupta-etal-2007}  \@writefile{toc}{\contentsline {section}{\numberline {IV}The Markov Erasure Channel}{4}{section.4}}  \newlabel{eq:bec}{{27}{4}{The Markov Erasure Channel\relax }{equation.4.27}{}}  \newlabel{th:anyerasure}{{5}{4}{\relax }{theorem.5}{}}  \newlabel{eq:anyMarkov}{{28}{4}{\relax }{equation.4.28}{}}  \@writefile{toc}{\contentsline {subsection}{\numberline {\unhbox \voidb@x \hbox {IV-A}}Special cases}{4}{subsection.4.1}}  \newlabel{eq:xu}{{30}{4}{Special cases\relax }{equation.4.30}{}}  \@writefile{toc}{\contentsline {section}{\numberline {V}Memoryless Channels}{4}{section.5}}  \newlabel{thm:memo}{{6}{4}{\relax }{theorem.6}{}}  \newlabel{eq:mmf3}{{32}{4}{\relax }{equation.5.32}{}}  \newlabel{ex4}{{V.1}{4}{\relax }{example.5.1}{}}  \newlabel{eq:xu2}{{35}{4}{\relax }{equation.5.35}{}}  \newlabel{ex4}{{V.2}{4}{\relax }{example.5.2}{}}  \newlabel{ex3}{{V.3}{4}{\relax }{example.5.3}{}}  \bibstyle{IEEEtran}  \bibdata{bib_control}  \bibcite{Franceschetti-Minero-2014}{1}  \bibcite{matveed-savkin2007b}{2}  \bibcite{Shannon1956}{3}  \bibcite{Sahai2001}{4}  \bibcite{Como-Fagnani-Zampieri2010}{5}  \bibcite{Sahai-Mitter2006}{6}  \bibcite{simsek-jain-varaija2004}{7}  \bibcite{Xu2005}{8}  \bibcite{Wong-Brocket1999}{9}  \bibcite{Brocket-Liberzon2000}{10}  \bibcite{Liberzon2003}{11}  \bibcite{Delchamps1990}{12}  \bibcite{Martins-Dehleh-Elia2006}{13}  \bibcite{Nair-Evans-2004}{14}  \bibcite{Imer-etal-2006}{15}  \bibcite{Tatikonda-Mitter2004}{16}  \bibcite{Tatikonda-Mitter2004b}{17}  \bibcite{Gupta-Martins2010}{18}  \bibcite{Yuksel2010}{19}  \bibcite{Yuksel-Basar2011}{20}  \bibcite{Borkar-Mitter-1997}{21}  \bibcite{Minero-etal-2009}{22}  \bibcite{Coviello-etal2012}{23}  \bibcite{Gupta-etal-2007}{24}  \bibcite{Gupta-etal-2009}{25}  \bibcite{Schenato-etal-2007}{26}  \bibcite{Huang-Dey-2007}{27}  \bibcite{Elia2005}{28}  \bibcite{Mitter-Elia2001}{29}  \bibcite{GoldsmithVaraiya1996}{30}  \bibcite{Yuksel--Meyn2013}{31}  \@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Comparison of the anytime capacity for different memoryless channels. For the uniform distribution the plot is obtained numerically.}}{5}{figure.2}}  \newlabel{fig:t3}{{2}{5}{Comparison of the anytime capacity for different memoryless channels. For the uniform distribution the plot is obtained numerically}{figure.2}{}}  \@writefile{toc}{\contentsline {section}{\numberline {VI}Proofs}{5}{section.6}}  \@writefile{toc}{\contentsline {section}{References}{5}{section*.1}}