this is for holding javascript data
Paolo added file anytime_ISIT-01.aux
almost 9 years ago
Commit id: c4579ff4b92673e3f4e6763383fc1e4aa655f19c
deletions | additions
diff --git a/anytime_ISIT-01.aux b/anytime_ISIT-01.aux
new file mode 100644
index 0000000..fb72708
--- /dev/null
+++ b/anytime_ISIT-01.aux
...
\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}{}}
\newlabel{eq:fact3b}{{14}{2}{\relax }{equation.2.14}{}}
\citation{Sahai-Mitter2006}
\citation{Sahai-Mitter2006}
\citation{Sahai-Mitter2006}
\citation{matveed-savkin2007b}
\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}
\bibcite{lutwav-etal2005}{32}
\bibcite{Friedland1981}{33}
\bibcite{Cohen1978}{34}
\bibcite{Costa-et-al-2004}{35}
\bibcite{fang--etal1994}{36}
\bibcite{El-Gamal--Kim2011}{37}
\@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}{References}{5}{section*.1}}
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Stability threshold function and anytime capacity for Example\nobreakspace {}\ref {ex1}}}{6}{figure.3}}
\newlabel{fig:t2}{{3}{6}{Stability threshold function and anytime capacity for Example~\ref {ex1}\relax }{figure.3}{}}
\@writefile{toc}{\contentsline {section}{Appendix\nobreakspace {}A: Stability threshold function examples}{6}{section*.2}}
\newlabel{ex1}{{A.1}{6}{\relax }{example.Appendix.A.1}{}}
\newlabel{eq:exP}{{42}{6}{\relax }{equation.Appendix.A.42}{}}
\newlabel{ex2}{{A.2}{6}{\relax }{example.Appendix.A.2}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Stability threshold function and anytime capacity for Example\nobreakspace {}\ref {ex2}.}}{6}{figure.4}}
\newlabel{fig:t1}{{4}{6}{Stability threshold function and anytime capacity for Example~\ref {ex2}}{figure.4}{}}
\citation{lutwav-etal2005}
\citation{Friedland1981}
\citation{Cohen1978}
\citation{Costa-et-al-2004}
\@writefile{toc}{\contentsline {section}{Appendix\nobreakspace {}B: Auxiliary Results}{7}{section*.3}}
\newlabel{lem:vme}{{1}{7}{\relax }{lemma.1}{}}
\newlabel{ref:eqqq}{{43}{7}{\relax }{equation.Appendix.B.43}{}}
\newlabel{eq:unde}{{44}{7}{\relax }{equation.Appendix.B.44}{}}
\newlabel{eq:Friedland}{{45}{7}{Friedland Theorem 4.2~\cite {Friedland1981}\relax }{equation.Appendix.B.45}{}}
\newlabel{eq:Friedland2}{{46}{7}{Friedland Theorem 4.2~\cite {Friedland1981}\relax }{equation.Appendix.B.46}{}}
\newlabel{thm:Friedland}{{2}{7}{Friedland Theorem 4.2~\cite {Friedland1981}\relax }{equation.Appendix.B.46}{}}
\newlabel{lem:cohen}{{3}{7}{Cohen Theorem 1~\cite {Cohen1978}\relax }{lemma.3}{}}
\newlabel{eq:Cohen}{{47}{7}{Cohen Theorem 1~\cite {Cohen1978}\relax }{equation.Appendix.B.47}{}}
\newlabel{eq:lim1}{{4}{7}{\relax }{lemma.4}{}}
\@writefile{toc}{\contentsline {section}{Appendix\nobreakspace {}C: Markov Jump Linear Systems. }{7}{section*.4}}
\newlabel{sec:mjls}{{C}{7}{\appendixname ~\thesectiondis \\* Markov Jump Linear Systems}{section*.4}{}}
\newlabel{eq:mjls}{{48}{7}{\appendixname ~\thesectiondis \\* Markov Jump Linear Systems}{equation.Appendix.C.48}{}}
\newlabel{eq:support}{{49}{7}{\appendixname ~\thesectiondis \\* Markov Jump Linear Systems}{equation.Appendix.C.49}{}}
\newlabel{eq:P}{{50}{7}{\appendixname ~\thesectiondis \\* Markov Jump Linear Systems}{equation.Appendix.C.50}{}}
\newlabel{eq:weak}{{51}{7}{\appendixname ~\thesectiondis \\* Markov Jump Linear Systems}{equation.Appendix.C.51}{}}
\newlabel{eq:Adiag}{{52}{7}{\appendixname ~\thesectiondis \\* Markov Jump Linear Systems}{equation.Appendix.C.52}{}}
\newlabel{lemmamjls}{{7}{7}{\relax }{theorem.7}{}}
\newlabel{eq:pp}{{53}{7}{\relax }{equation.Appendix.C.53}{}}
\citation{Costa-et-al-2004}
\citation{fang--etal1994}
\citation{El-Gamal--Kim2011}
\citation{Minero-etal-2009}
\newlabel{eq:sub}{{54}{8}{\appendixname ~\thesectiondis \\* Markov Jump Linear Systems}{equation.Appendix.C.54}{}}
\newlabel{eq:0}{{55}{8}{\appendixname ~\thesectiondis \\* Markov Jump Linear Systems}{equation.Appendix.C.55}{}}
\@writefile{toc}{\contentsline {section}{Appendix\nobreakspace {}D: Proofs}{8}{section*.5}}
\@writefile{toc}{\contentsline {subsection}{\numberline {\unhbox \voidb@x \hbox {D-A}}Theorem\nobreakspace {}\ref {thm1}}{8}{subsection.Appendix.D.1}}
\newlabel{eq:lbstate2}{{58}{8}{Theorem~\ref {thm1}\relax }{equation.Appendix.D.58}{}}
\newlabel{eq:zzzz}{{59}{8}{Theorem~\ref {thm1}\relax }{equation.Appendix.D.59}{}}
\newlabel{eq:in_0}{{60}{8}{Theorem~\ref {thm1}\relax }{equation.Appendix.D.60}{}}
\newlabel{eq:ineq1}{{61}{8}{Theorem~\ref {thm1}\relax }{equation.Appendix.D.61}{}}
\newlabel{lem_min}{{62}{8}{Theorem~\ref {thm1}\relax }{equation.Appendix.D.62}{}}
\newlabel{eq:ineq2}{{63}{8}{Theorem~\ref {thm1}\relax }{equation.Appendix.D.63}{}}
\newlabel{eq:in_1}{{64}{8}{Theorem~\ref {thm1}\relax }{equation.Appendix.D.64}{}}
\newlabel{eq:in_2}{{65}{8}{Theorem~\ref {thm1}\relax }{equation.Appendix.D.65}{}}
\citation{Cohen1978}
\newlabel{eq:in_3}{{66}{9}{Theorem~\ref {thm1}\relax }{equation.Appendix.D.66}{}}
\newlabel{eq:in_4}{{67}{9}{Theorem~\ref {thm1}\relax }{equation.Appendix.D.67}{}}
\newlabel{eq:nec_mjls22}{{68}{9}{Theorem~\ref {thm1}\relax }{equation.Appendix.D.68}{}}
\newlabel{eq:in_}{{69}{9}{Theorem~\ref {thm1}\relax }{equation.Appendix.D.69}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {\unhbox \voidb@x \hbox {D-B}}Proposition\nobreakspace {}\ref {prop1}}{9}{subsection.Appendix.D.2}}
\newlabel{App1}{{\unhbox \voidb@x \hbox {D-B}}{9}{Proposition~\ref {prop1}\relax }{subsection.Appendix.D.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {\unhbox \voidb@x \hbox {D-C}}Theorem\nobreakspace {}\ref {th:combining}}{10}{subsection.Appendix.D.3}}
\newlabel{eq:any1}{{73}{10}{Theorem~\ref {th:combining}\relax }{equation.Appendix.D.73}{}}
\newlabel{eq:any2}{{74}{10}{Theorem~\ref {th:combining}\relax }{equation.Appendix.D.74}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {\unhbox \voidb@x \hbox {D-D}}Theorem\nobreakspace {}\ref {th:anyerasure}}{10}{subsection.Appendix.D.4}}
\newlabel{eq:bec2a}{{76}{10}{Theorem~\ref {th:anyerasure}\relax }{equation.Appendix.D.76}{}}
\newlabel{eq:bec2}{{77}{10}{Theorem~\ref {th:anyerasure}\relax }{equation.Appendix.D.77}{}}
\newlabel{eq:bec3}{{78}{10}{Theorem~\ref {th:anyerasure}\relax }{equation.Appendix.D.78}{}}
\newlabel{bec4}{{79}{10}{Theorem~\ref {th:anyerasure}\relax }{equation.Appendix.D.79}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {\unhbox \voidb@x \hbox {D-E}}Theorem\nobreakspace {}\ref {thm:memo}}{10}{subsection.Appendix.D.5}}
\newlabel{eq:mmf}{{80}{10}{Theorem~\ref {thm:memo}\relax }{equation.Appendix.D.80}{}}
\newlabel{eq:mmf2}{{81}{10}{Theorem~\ref {thm:memo}\relax }{equation.Appendix.D.81}{}}
