In this work, we investigate the performance of polar codes with the assistance of feedback in communication systems. Although it is well known that feedback does not improve the capacity of memoryless channels, we show that the finite length performance of polar codes can be significantly improved as feedback enables genie-aided decoding and allows more flexible thresholds for the polar coding construction. To analyze the performance under the new construction, we then propose an accurate characterization of the distribution of the error event under the genie-aided successive cancellation (SC) decoding. This characterization can be also used to predict the performance of the standard SC decoding of polar codes with rates close to capacity.

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