  Barcodes like QR Codes have made that encoded messages have entered our
everyday life, what suggests to attach them a second layer of information:
directly available to human receiver for informational or marketing purposes.
We will discuss a general problem of using codes with chosen statistical
constrains, for example reproducing given grayscale picture using halftone
technique. If both sender and receiver know these constrains, the optimal
capacity can be easily approached by entropy coder. The problem is that this
time only the sender knows them - we will refer to these scenarios as
constrained coding. Kuznetsov and Tsybakov problem in which only the sender
knows which bits are fixed can be seen as a special case, surprisingly
approaching the same capacity as if both sides would know the constrains. We
will analyze Correction Trees to approach analogous capacity in the general
case - use weaker: statistical constrains, what allows to apply them to all
bits. Finding satisfying coding is similar to finding the proper correction in
error correction problem, but instead of single ensured possibility, there are
now statistically expected some. While in standard steganography we hide
information in the least important bits, this time we create codes resembling
given picture - hide information in the freedom of realizing grayness by black
and white pixels using halftone technique. We will also discuss combining with
error correction and application to rate distortion problem.
