On Successive Refinement of the Binary Symmetric Markov Source

We show that for every
$n ≫ 2$
the standard
$ n$
th-order approximation
$R_n(D)$
, to the rate-distortion function of the binary-symmetric Markov source (BSMS) is not successively refineable under the Hamming distortion measure in an open interval of the form
$D_n !≪ ! D !≪ !1/2 ! = !D_max $
.