Secure Cascade Channel Synthesis

TL;DR

This paper studies secure distributed generation of correlated random variables over a cascade network, characterizing the optimal tradeoff between common randomness and communication rates, and proposing an efficient superposition coding scheme.

Contribution

It introduces the first characterization of the optimal tradeoff between common randomness and communication rates for secure cascade channel synthesis, using a superposition codebook approach.

Findings

Optimal tradeoff between common randomness and communication rates established.

Superposition codebook scheme achieves the most efficient synthesis.

Shared randomness exceeds the communication rate requirements.

Abstract

We consider the problem of generating correlated random variables in a distributed fashion, where communication is constrained to a cascade network. The first node in the cascade observes an i.i.d. sequence $X^n$ locally before initiating communication along the cascade. All nodes share bits of common randomness that are independent of $X^n$. We consider secure synthesis - random variables produced by the system appear to be appropriately correlated and i.i.d. even to an eavesdropper who is cognizant of the communication transmissions. We characterize the optimal tradeoff between the amount of common randomness used and the required rates of communication. We find that not only does common randomness help, its usage exceeds the communication rate requirements. The most efficient scheme is based on a superposition codebook, with the first node selecting messages for all downstream nodes. We also provide a fleeting view of related problems, demonstrating how the optimal rate region may shrink or expand.