Irregular Channel Polarization and Its Applications to Static Adversarial Wiretap Channel
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The problem of achieving the secrecy capacity of static adversarial wiretap channel with discrete memoryless channels is studied in this paper. To construct the explicit secure coding scheme, an irregular channel polarization operation is proposed which is the extension of Arıkan's channel polarization. As theoretically proofed, for N independent initial channels with different transition probabilities, channels generated by the operation G_N are also polarized into full noise channels and noiseless channels, same as the regular channel polarization. Then for the adversarial behaviors including directly reading and rewriting, equivalent channels are constructed by channel cascading with full noise or noiseless binary erase channels. Finally by applying the irregular channel polarization to the equivalent channels, a secure polar coding scheme is constructed which successfully achieves the secrecy capacity of static adversarial wiretap channel with discrete memoryless channels under the reliability and strong security criterions.
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