Finite-Length Empirical Comparison of Polar, PAC, and Invertible-Extractor Secrecy Codes over the Wiretap BSC
This work addresses secure communication over noisy channels for applications like wireless networks, but it is incremental as it compares existing methods without introducing new ones.
The paper empirically compares three secrecy-coding schemes for the degraded wiretap binary symmetric channel in the finite-blocklength regime, finding that polar and PAC codes provide tighter security guarantees than the invertible-extractor framework, with PAC codes improving reliability without compromising secrecy.
We compare three secrecy-coding schemes for the degraded wiretap binary symmetric channel (BSC) in the finite-blocklength regime: (i) polar wiretap coset codes, (ii) PAC codes used as wiretap coset codes, and (iii) the invertible-extractor (IE) framework of Bellare-Tessaro. Our comparison is empirical and uses a common semantic-secrecy metric (distinguishing advantage). For polar coset codes, we compute Eve's polarized bit-channel capacities (via the Tal-Vardy construction) to obtain explicit finite-length upper bounds on mutual-information leakage, yielding strong secrecy bounds. For PAC coset codes, we prove that Eve's synthesized bit-channels are equivalent to those of polar codes (up to a permutation), so the same leakage bounds apply; we then convert these strong-secrecy bounds into semantic-secrecy guarantees for symmetric wiretap channels. For the IE scheme, we use the closed-form semantic-secrecy bounds given in the reference work. Finally, we report finite-length results that jointly characterize (a) semantic-secrecy guarantees against Eve and (b) frame-error-rate performance at Bob, illustrating that PAC codes can significantly improve reliability without changing the secrecy bounds inherited from polar coding. Moreover, under the finite-length bounds considered in this work, polar/PAC secrecy codes provide tighter security guarantees than the invertible-extractor framework.