Explicit Codes for the Wiretap Channel: A Unified Design Framework
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A construction of explicit codes for the wiretap channel is proposed. Appropriate choices of the construction parameters yield, within a unified design framework, the achievability of the secrecy capacity of (i) Wyner's wiretap channel, (ii) the wiretap channel of type II, (iii) the wiretap channel of type II with noisy main channel, (iv) the hybrid Wyner's/type II wiretap channel, and the best known single-letter achievable secrecy rates for (v) the wiretap channel when uncertainties hold on the eavesdropper's channel statistics (compound model), (vi) the wiretap channel when the eavesdropper's channel statistics are arbitrarily varying. Results are obtained for strong secrecy, do not require any symmetry or degradation assumptions on the channel, and do not require a pre-shared secret between the legitimate users. The underlying construction idea is an efficient emulation of random binning via polar codes to obtain reliability, coupled with universal hashing implemented via invertible extractors to ensure strong secrecy.
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