Capacity-Achieving Rate-Compatible Polar Codes for General Channels

TL;DR

This paper introduces a universal rate-compatible polar coding scheme that achieves channel capacity without requiring channel degradation, suitable for diverse practical scenarios like MIMO and interference-limited systems.

Contribution

It extends capacity-achieving polar codes to general channels by removing the degradation condition, leveraging universal polar code ideas.

Findings

Achieves capacity for any family of channels

Maintains low complexity encoding and decoding

Provides an upper bound on the scaling exponent

Abstract

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.