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arXiv:1405.7441 · IEEE International Symposium on Information Theory (ISIT)

Key capacity with limited one-way communication for product sources

Jingbo Liu, Paul Cuff, Sergio Verdú

Published Jun 1, 2014• 8 citations
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Abstract

We show that for product sources, rate splitting is optimal for secret key agreement using limited one-way communication at two terminals. This yields an alternative proof of the tensorization property of a strong data processing inequality originally studied by Erkip and Cover and amended recently by Anantharam et al. We derive a `water-filling' solution of the communication rate-key rate tradeoff for two arbitrarily correlated vector Gaussian sources, for the case with an eavesdropper, and for stationary Gaussian processes.

DOI
10.1109/isit.2014.6875012

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We show that for product sources, rate splitting is optimal for secret key agreement using limited one-way communication at two terminals. This yields an alternative proof of the tensorization property of a strong data processing inequality originally studied by Erkip and Cover and amended recently by Anantharam et al. We derive a `water-filling' solution of the communication rate-key rate tradeoff for two arbitrarily correlated vector Gaussian sources, for the case with an eavesdropper, and for stationary Gaussian processes.
We show that for product sources, rate splitting is optimal for secret key agreement using limited one-way communication between two terminals. This yields an alternative proof of the tensorization property of a strong data processing inequality originally studied by Erkip and Cover and amended recently by Anantharam et al. We derive a water-filling solution of the communication-rate-key-rate tradeoff for a wide class of discrete memoryless vector Gaussian sources which subsumes the case without an eavesdropper. Moreover, we derive an explicit formula for the maximum secret key per bit of communication for all discrete memoryless vector Gaussian sources using a tensorization property and a variation on the enhanced channel technique of Weingarten et al. Finally, a one-shot information spectrum achievability bound for key generation is proved from which we characterize the communication-rate-key-rate tradeoff for stationary Gaussian processes.
We investigate the secret key agreement from correlated vector Gaussian sources in which legitimate parties can use public communication with limited rate. For the class of protocols with one-way public communication, we show that the optimal trade-off between the rate of key generation and the rate of the public communication is characterized as an optimization problem of a Gaussian random variable. The characterization is derived by using the enhancement technique introduced by Weingarten for multiple-input-multiple-output (MIMO) Gaussian broadcast channel.
We investigate the secret key agreement from correlated vector Gaussian sources in which the legitimate parties can use the public communication with limited rate. For the class of protocols with the one-way public communication, we show that the optimal trade-off between the rate of key generation and the rate of the public communication is characterized as an optimization problem of a Gaussian random variable. The characterization is derived by using the enhancement technique introduced by Weingarten et. al. for MIMO Gaussian broadcast channel.
Secret key generation by multiple terminals is considered based on their observations of jointly distributed Gaussian signals, followed by public communication among themselves. Exploiting an inherent connection between secrecy generation and lossy data compression, two main contributions are made. The first is a characterization of strong secret key capacity, and entails a converse proof technique that is valid for real-valued (and not necessarily Gaussian) as well as finite-valued signals. The capacity formula acquires a simple form when the terminals observe “symmetrically correlated” jointly Gaussian signals. For the latter setup with two terminals, considering schemes that involve quantization at one terminal, the best rate of an achievable secret key is characterized as a function of quantization rate; secret key capacity is attained as the quantization rate tends to infinity. Structured codes are shown to attain the optimum tradeoff between secret key rate and quantization rate, constituting our second main contribution.
We consider secret key (SK) generation by two terminals, each of which observes an i.i.d. source which is correlated with the other; the two sources are jointly Gaussian with known distribution. The terminals are then allowed to communicate with each other, possibly interactively in many rounds and without rate restrictions, over a noiseless two-way public channel. Randomization is permitted at each terminal. The goal is for the terminals to generate a SK comprising discrete common randomness which is concealed from an eavesdropper that has access to the public interterminal communication. We establish that this maximum rate of SK generation, i.e., SK capacity, is, as expected, the per-symbol mutual information I of the correlated sources. Our main technical contribution is a new scheme for achieving SK capacity using structured codes. In our scheme, vector quantization at rate R nats/source symbol of the source at terminal 1 is performed by employing nested lattice codes with dithering. Then, a SK is generated by the terminals from the quantized random sequence at terminal 1 and the (unquantized) Gaussian source at terminal 2, using both lossy and lossless data compression techniques. Our algorithm, using a rate-R lattice quantizer, achieves a maximum SK rate of 1/2 log 1/(e-2I+(1-e-2I)e-2R), which tends to the SK capacity I with increasing R. Thus, our result also specifies the associated tradeoff between quantization rate R and the maximum achievable SK rate. This tradeoff is shown to be optimum among a certain restricted class of schemes for SK generation that involve quantization at rate R of a Gaussian source at one terminal.