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