Exponential Strong Converse for Successive Refinement with Causal Decoder Side Information

We consider the $k$-user successive refinement problem with causal decoder side information and derive an exponential strong converse theorem. The rate-distortion region for the problem can be derived as a straightforward extension of the two-user case by Maor and Merhav (2008). We show that for any rate-distortion tuple outside the rate-distortion region of the $k$-user successive refinement problem with causal decoder side information, the joint excess-distortion probability approaches one exponentially fast. Our proof follows by judiciously adapting the recently proposed strong converse technique by Oohama using the information spectrum method, the variational form of the rate-distortion region and H\"older's inequality. The lossy source coding problem with causal decoder side information considered by El Gamal and Weissman is a special case ($k=1$) of the current problem. Therefore, the exponential strong converse theorem for the El Gamal and Weissman problem follows as a corollary of our result

Information Theoretic Security for Broadcasting of Two Encrypted Sources under Side-Channel Attacks

We consider the secure communication problem for broadcasting of two encrypted sources. The sender wishes to broadcast two secret messages via two common key cryptosystems. We assume that the adversary can use the side-channel, where the side information on common keys can be obtained via the rate constraint noiseless channel. To solve this problem we formulate the post encryption coding system. On the information leakage on two secrete messages to the adversary, we provide an explicit sufficient condition to attain the exponential decay of this quantity for large block lengths of encrypted sources.Comment: 13 pages, 4 figures. In the current version we we have corrected errors in Fig. 2 and Fig. 4. arXiv admin note: substantial text overlap with arXiv:1801.02563, arXiv:1801.0492

Modulation and Estimation with a Helper

The problem of transmitting a parameter value over an additive white Gaussian noise (AWGN) channel is considered, where, in addition to the transmitter and the receiver, there is a helper that observes the noise non-causally and provides a description of limited rate $R_\mathrm{h}$ to the transmitter and/or the receiver. We derive upper and lower bounds on the optimal achievable $\alpha$-th moment of the estimation error and show that they coincide for small values of $\alpha$ and for low SNR values. The upper bound relies on a recently proposed channel-coding scheme that effectively conveys $R_\mathrm{h}$ bits essentially error-free and the rest of the rate - over the same AWGN channel without help, with the error-free bits allocated to the most significant bits of the quantized parameter. We then concentrate on the setting with a total transmit energy constraint, for which we derive achievability results for both channel coding and parameter modulation for several scenarios: when the helper assists only the transmitter or only the receiver and knows the noise, and when the helper assists the transmitter and/or the receiver and knows both the noise and the message. In particular, for the message-informed helper that assists both the receiver and the transmitter, it is shown that the error probability in the channel-coding task decays doubly exponentially. Finally, we translate these results to those for continuous-time power-limited AWGN channels with unconstrained bandwidth. As a byproduct, we show that the capacity with a message-informed helper that is available only at the transmitter can exceed the capacity of the same scenario when the helper knows only the noise but not the message.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl