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\maketitle  \section{Introduction}  Some noteworthy references on the anytime capacity~\cite{Forney1974, Schulman1996, Sahai2001, Sahai-Mitter2006,Como-Fagnani-Zampieri2010, simsek-jain-varaija2004,Ostrovsky-etal-2009, Sukhavasi-Hassibi2011a}. capacity~\cite{Forney1974,Schulman1996,Sahai2001,Sahai-Mitter2006,Como-Fagnani-Zampieri2010,simsek-jain-varaija2004,Ostrovsky-etal-2009,Sukhavasi-Hassibi2011a}.  The usual references on network-theoretic approach~\cite{Gupta-etal-2007,Gupta-etal-2009,Schenato-etal-2007,Sinopoli-etal-2004,Minero-etal-2009,Huang-Dey-2007}; the usual references on data rate theorem~\cite{Wong-Brocket1999,Brocket-Liberzon2000,Liberzon2003,Braslavsky-Middleton-Freudenberg2007,Delchamps1990,Martins-Dehleh-Elia2006,Nair-Evans-2004,Imer-etal-2006,Tatikonda-Mitter2004,Tatikonda-Mitter2004b,Wong-Brocket1999,You-Xie2011,You-Xie2010,Yuksel2010,Yuksel-Basar2011}; some references on stabilization over AWGN channels~\cite{Braslavsky-Middleton-Freudenberg2007,Middleton-Roja2009,Freudenberg-Middleton-Solo2010}; some references on MJLS~\cite{Seiler-Sengupta2001,Kawka-Alleyne-2006,Liu-Elia-Tationda2004,Sahai-etal-2005} \section{Markov Jump Linear Systems. }  Consider the scalar non-homogeneous MJLS~\cite{Costa-et-al-2004} with dynamics