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arXiv:2609.32074

The Transmitter Trojan Channel: Achievable Rates and Error Exponents

Maryam Farahnak-Ghazani, Aria Nosratinia

Published Sep 25, 2026• 0 citations
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Abstract

Experiments have shown that modifications in communication hardware can enable unauthorized exfiltration of data from transmitters. We study the resulting Transmitter Trojan channel, in which a malicious encoder embedded within a legitimate transmitter perturbs the transmitted codeword on a symbol-by-symbol basis. The model reflects the limited footprint, delay, and computational complexity available to such hardware modifications. We derive achievable rogue message rate and achievable rates for the legitimate message under the mismatch induced by the Trojan. We also analyze decoding error exponents for the legitimate and rogue receivers, including operational exponent lower bounds obtained through channel-resolvability transfer arguments. Finally, we study Trojan detection at the legitimate receiver under different levels of statistical knowledge, including likelihood-ratio detection when the ensemble-averaged induced channel is known and goodness-of-fit detection when only the nominal channel is known. The resulting detection error exponents, together with the achievable rate and decoding error exponents, quantify tradeoffs among rogue message rate, legitimate message rate, decoding reliability, and Trojan detectability. We specialize the analysis to the binary symmetric channel and the additive white Gaussian noise channel, and illustrate the resulting tradeoffs numerically.

DOI
10.48550/arxiv.2609.32074

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This paper investigates the achievable message transmission rate of covert communication over slow fading channels where the channel coefficient remains unchanged over a finite transmission block. Such communication is often implemented with an extremely low transmission power aiming to achieve low probability of detection by the eavesdropper and under tolerable probability of decoding error for the legitimate receiver. The exact expression of achievability and asymptotic covert bounds are derived, which are shown in accordance with the square root law in AWGN (Additive White Gaussian Noise) channels with large transmission blocks. The case that the eavesdropper has unknown channel state information is also studied in the paper.
RF fingerprinting exploits the variations in the RF chain of radios to uniquely identify transmitters, and distinguish adversarial transmissions from transmissions of legitimate nodes. We provide a systematic approach rooted from information theory to evaluate basic performance limits of RF fingerprinting. We develop a novel channel model for RF fingerprinting, where the imperfections in the RF chain are modeled as a fingerprint channel, cascaded to the actual physical channel. We address the authentication problem in the presence of an adversary, where both the legitimate transmitter and the adversary are equipped with unique fingerprint channels, in addition to a possible secret key available at the legitimate nodes. We provide achievable bounds for the error exponents for reliable communication of the legitimate nodes, and the success exponent for impersonation and substitution attacks of the adversary, as a function of certain parameters based on their RF-fingerprints, and the shared key rate. We illustrate that keyless authentication is possible via RF fingerprints when the legitimate channel is not simulatable.
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Or a given linear code, a lower bound on the error exponent under maximum likelihood decoding is investigated at low rates. or a given linear code, a lower bound on the error exponent under maximum likelihood decoding is investigated at low rates. F In the analysis of the decoding error probability, it is important to characterize the error exponent, since it indicates how fast the probability of decoding error converges to zero asymptotically. Over a symmetric memoryless channel, an error exponent is derived for a given linear code. A sufficient condition for achieving the expurgated exponent, which is the best among known error exponents at low rates, is given. Over a general discrete memoryless channel, the same analysis shows the expected error exponent of an ensemble of coset codes generated by a given linear code.
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