Feedback-Based Collaborative Secrecy Encoding over Binary Symmetric Channels

In this paper we propose a feedback scheme for transmitting secret messages between two legitimate parties, over an eavesdropped communication link. Relative to Wyner’s traditional encoding scheme \cite{wyner1}, our feedback-based encoding often yields larger rate-equivocation regions and achievable secrecy rates. More importantly, by exploiting the channel randomness inherent in the feedback channels, our scheme achieves a strictly positive secrecy rate even when the eavesdropper’s channel is less noisy than the legitimate receiver’s channel. All channels are modeled as binary and symmetric (BSC). We demonstrate the versatility of our feedback-based encoding method by using it in three different configurations: the stand-alone configuration, the mixed configuration (when it combines with Wyner’s scheme \cite{wyner1}), and the reversed configuration. Depending on the channel conditions, significant improvements over Wyner’s secrecy capacity can be observed in all configurations.

💡 Research Summary

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The paper introduces a novel feedback‑driven collaborative secrecy encoding scheme for binary symmetric channels (BSCs) and demonstrates that it can substantially enlarge the achievable rate‑equivocation region compared with Wyner’s classic wiretap coding. The authors begin by recalling Wyner’s model, where a transmitter (Alice) sends a binary sequence X over a BSC to a legitimate receiver (Bob) with crossover probability p_R, while an eavesdropper (Eve) observes the same transmission through a possibly noisier BSC with crossover probability p_E. Wyner’s secrecy capacity is C_s^W = max{0, H(p_E) – H(p_R)}; consequently, if Eve’s channel is less noisy (p_E < p_R), the secrecy capacity collapses to zero.

The core contribution of this work is to exploit a feedback link from Bob to Alice, also modeled as a BSC with crossover probability p_F. In each transmission round Bob sends a single‑bit feedback that encodes his current observation (or a function thereof). Alice uses this feedback to adaptively flip or retain the next data bit. Because Bob knows both his own observation and the (possibly corrupted) feedback, he can perfectly recover the original message, while Eve, who observes both the forward channel (with noise p_E) and the feedback channel (with noise p_F), faces a compounded uncertainty. The authors formalize this intuition by deriving an achievable secrecy rate for the stand‑alone feedback scheme:

 R_s^FB = max_{0≤α≤1}