  We present a rate-compatible polar coding scheme that achieves the capacity
of any family of channels. Our solution generalizes the previous results [1],
[2] that provide capacity-achieving rate-compatible polar codes for a degraded
family of channels. The motivation for our extension comes from the fact that
in many practical scenarios, e.g., MIMO systems and non-Gaussian interference,
the channels cannot be ordered by degradation. The main technical contribution
of this paper consists in removing the degradation condition. To do so, we
exploit the ideas coming from the construction of universal polar codes.
  Our scheme possesses the usual attractive features of polar codes: low
complexity code construction, encoding, and decoding; super-polynomial scaling
of the error probability with the block length; and absence of error floors. On
the negative side, the scaling of the gap to capacity with the block length is
slower than in standard polar codes, and we prove an upper bound on the scaling
exponent.
