DCP ruleset question

Hello Friends!
I hope you are well…
I want to write CVX code that solves the following expression(Entropy Rate):
max (x/x+y).(H(y,1-y))+(y/x+y).(H(x,1-x)) H(.):entropy
and gives me the optimal x,y to achieve the maximum of this function.
i know that this expression has a maximum value of 1 bit. and it occurs in x=y=1/2.
first i tried to write in DCP ruleset but i got an error:

cvx_begin 
    variable x
    variable y
    maximize (y/(x+y))*(entr(x)+entr(1-x))+(x/(x+y))* 
   (entr(y)+entr(1-y))
cvx_end

By reading more i got to know GP, but that didn’t work either!
can anyone help me pls…
thank u so much…

Can you write the expression in “illegal” CVX, i.e., with no regard for CVX"s rules, as you would write it in MATLABdouble precision, just using x, y, , log That way there will be no ,misinterpretation. And I presume you have proven the objective being maximized is concave? There have been many clever formulations in this forum using various combinations of rel_entr.