w*log2(1+p/w) = -rel_entr(w,w+p)/log(2).
See x\log(1+1/x) using CVX , including the warning there. Note that mcg’s May 27, 2013 answer has a typo, and should be -rel_entr(x,x+1), not -rel_entr(x+1,x).
Edit: Didn’t see mcg’s comment before posting, but this is what he was referring to.
Edit 2: Corrected to -rel_entr(w,w+p)/log(2), rather than -rel_entr(w+p,w)/log(2)