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1. On Caching with Finite Blocklength Coding for Secrecy over the Binary Erasure Wiretap Channel

   https://doi.org/10.1109/WTS51064.2021.9433710  

   Harrison, Willie K.; Shoushtari, Morteza (April 2021, 2021 Wireless Telecommunications Symposium (WTS))

   null (Ed.)

   In this paper, we show that caching can aid in achieving secure communications by considering a wiretap scenario where the transmitter and legitimate receiver share access to a secure cache, and an eavesdropper is able to tap transmissions over a binary erasure wiretap channel during the delivery phase of a caching protocol. The scenario under consideration gives rise to a new channel model for wiretap coding that allows the transmitter to effectively choose a subset of bits to erase at the eavesdropper by caching the bits ahead of time. The eavesdropper observes the remainder of the coded bits through the wiretap channel for the general case. In the wiretap type-II scenario, the eavesdropper is able to choose a set of revealed bits only from the subset of bits not cached. We present a coding approach that allows efficient use of the cache to realize a caching gain in the network, and show how to use the cache to optimize the information theoretic security in the choice of a finite blocklength code and the choice of the cached bit set. To our knowledge, this is the first work on explicit algorithms for secrecy coding in any type of caching network. 

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2. Smoothing of Binary Codes, Uniform Distributions, and Applications

   https://doi.org/10.3390/e25111515  

   Pathegama, Madhura; Barg, Alexander (November 2023, Entropy)

   The action of a noise operator on a code transforms it into a distribution on the respective space. Some common examples from information theory include Bernoulli noise acting on a code in the Hamming space and Gaussian noise acting on a lattice in the Euclidean space. We aim to characterize the cases when the output distribution is close to the uniform distribution on the space, as measured by the Rényi divergence of order α∈(1,∞]. A version of this question is known as the channel resolvability problem in information theory, and it has implications for security guarantees in wiretap channels, error correction, discrepancy, worst-to-average case complexity reductions, and many other problems. Our work quantifies the requirements for asymptotic uniformity (perfect smoothing) and identifies explicit code families that achieve it under the action of the Bernoulli and ball noise operators on the code. We derive expressions for the minimum rate of codes required to attain asymptotically perfect smoothing. In proving our results, we leverage recent results from harmonic analysis of functions on the Hamming space. Another result pertains to the use of code families in Wyner’s transmission scheme on the binary wiretap channel. We identify explicit families that guarantee strong secrecy when applied in this scheme, showing that nested Reed–Muller codes can transmit messages reliably and securely over a binary symmetric wiretap channel with a positive rate. Finally, we establish a connection between smoothing and error correction in the binary symmetric channel. 

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3. MIMO wiretap channel with ISI heterogeneity — Achieving secure DoF with no CSI

   https://doi.org/10.1109/ACSSC.2017.8335647  

   de Dieu Mutangana, Jean; Kumar, Deepak; Tandon, Ravi (October 2017, 51st Asilomar Conference on Signals, Systems, and Computers)

   We consider the multiple-input multiple-output (MIMO) wiretap channel with intersymbol interference (ISI) in which a transmitter (Alice) wishes to securely communicate with a receiver (Bob) in presence of an eavesdropper (Eve). We focus on the practically relevant setting in which there is no channel state information (CSI) at Alice about either of the channels to Bob or Eve, except statistical information about the ISI channels (i.e., Alice only knows the effective number of ISI taps). The key contribution of this work is to show that even with no CSI at Alice, positive secure degrees of freedom (SDoF) are achievable by carefully exploiting a) the heterogeneity of the ISI links to Bob and Eve, and b) the relative number of antennas at all the three terminals. To this end, we propose a novel achievable scheme that carefully mixes information and artificial noise symbols in order to exploit ISI heterogeneity to achieve positive SDoF. To the best of our knowledge, this is the first work to explore the idea of exploiting ISI channel length heterogeneity to achieve positive SDoF for the MIMO wiretap channel with no CSI at the legitimate transmitter. 

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4. Quantifying equivocation for finite blocklength wiretap codes

   https://doi.org/10.1109/ICC.2017.7996925  

   Pfister, Jack; Gomes, Marco A.; Vilela, Joao P.; Harrison, Willie K. (May 2017, International Conference on Communications)

   This paper presents a new technique for providing the analysis and comparison of wiretap codes in the small blocklength regime over the binary erasure wiretap channel. A major result is the development of Monte Carlo strategies for quantifying a code's equivocation, which mirrors techniques used to analyze forward error correcting codes. For this paper, we limit our analysis to coset-based wiretap codes, and give preferred strategies for calculating and/or estimating the equivocation in order of preference. We also make several comparisons of different code families. Our results indicate that there are security advantages to using algebraic codes for applications that require small to medium blocklengths. 

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5. The Fading Gaussian Broadcast Channel with Channel State Information and Output Feedback

   https://doi.org/10.1109/ISIT44484.2020.9173934  

   Li, Siyao; Tuninetti, Daniela; Devroye, Natasha (June 2020, International Symposium on Information Theory)

   null (Ed.)

   The fading broadcast channel (BC) with additive white Gaussian noise (AWGN) channel, channel output feedback (COF) and channel state information (CSI) is considered. Perfect CSI is available at the receivers, and unit delayed CSI along with COF at the transmitter. Under the assumption of memoryless fading, a posterior matching scheme that incorporates the additional CSI feedback into the coding scheme is presented. With COF, the achievable rates depend on the joint distribution of the fading process. Numerical examples show that the capacity region of two-user fading AWGN-BC is enlarged by COF. The coding scheme is however suboptimal since some parts of the achievable rate region are outperformed by superposition coding without COF. 

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