Information Bytes

Matthieu Bloch
School of Electrical and Computer Engineering
Georgia Institute of Technology

Recent works

  1. I. A. Kadampot, M. Tahmasbi, and M. R. Bloch, “Multilevel-Coded Pulse-Position Modulation for Covert Communications over Binary-Input Discrete Memoryless Channels,” IEEE Transactions on Information Theory, vol. 66, no. 10, pp. 6001–6023, Oct. 2020.
    DOI arXiv

    We consider the problem of coding to ensure covert communication, which involves ensuring reliable communication between two legitimate parties while simultaneously guaranteeing a low probability of detection by an eavesdropper. Specifically, we develop an optimal low-complexity coding scheme that achieves the information-theoretic limits of covert communications over binary-input discrete memoryless channels (BI-DMCs). To justify our design, we first consider a regime in which information theory proves the possibility of covert communication without shared secret key and show the impossibility of achieving information-theoretic limits using linear codes without secret key. We then circumvent this impossibility by introducing non-linearity into the coding scheme through the use of pulse position modulation (PPM) and multilevel coding (MLC). This MLC-PPM scheme exhibits several appealing properties; in particular, for an appropriate decoder, the channel at a given level is independent of the total number of levels and the codeword length. We exploit these properties to show how one can use families of channel capacity- and channel resolvability-achieving codes to concretely instantiate a covert communication scheme.

    @article{Kadampot2018a,
      author = {Kadampot, Ishaque Ashar and Tahmasbi, Mehrdad and Bloch, Matthieu R},
      journal = {IEEE Transactions on Information Theory},
      title = {Multilevel-Coded Pulse-Position Modulation for Covert Communications over Binary-Input Discrete Memoryless Channels},
      year = {2020},
      month = oct,
      number = {10},
      pages = {6001-6023},
      volume = {66},
      doi = {10.1109/TIT.2020.3019996},
      eprint = {1811.09695},
      file = {:2020-Kadampot-IEEETransIT.pdf:PDF}
    }
    

  2. N. Helal, M. Bloch, and A. Nosratinia, “Cooperative Resolvability and Secrecy in the Cribbing Multiple-Access Channel,” IEEE Transactions on Information Theory, vol. 66, no. 9, pp. 5429–5447, Sep. 2020.
    DOI arXiv

    We study channel resolvability for the discrete memoryless multiple-access channel with cribbing, i.e., the characterization of the amount of randomness required at the inputs to approximately produce a chosen i.i.d. output distribution according to Kullback-Leibler divergence. We analyze resolvability rates when one encoder cribs (i) the input of the other encoder; or the output of the other encoder, (ii) non-causally, (iii) causally, or (iv) strictly-causally. For scenarios (i)-(iii), we exactly characterize the channel resolvability region. For (iv), we provide inner and outer bounds for the channel resolvability region; the crux of our achievability result is to handle the strict causality constraint with a block-Markov coding scheme in which dependencies across blocks are suitably hidden. Finally, we leverage the channel resolvability results to derive achievable secrecy rate regions for each of the cribbing scenarios under strong secrecy constraints.We study channel resolvability for the discrete memoryless multiple-access channel with cribbing, i.e., the characterization of the amount of randomness required at the inputs to approximately produce a chosen i.i.d. output distribution according to Kullback-Leibler divergence. We analyze resolvability rates when one encoder cribs (i) the input of the other encoder; or the output of the other encoder, (ii) non-causally, (iii) causally, or (iv) strictly-causally. For scenarios (i)-(iii), we exactly characterize the channel resolvability region. For (iv), we provide inner and outer bounds for the channel resolvability region; the crux of our achievability result is to handle the strict causality constraint with a block-Markov coding scheme in which dependencies across blocks are suitably hidden. Finally, we leverage the channel resolvability results to derive achievable secrecy rate regions for each of the cribbing scenarios under strong secrecy constraints.

    @article{Helhal2018a,
      author = {Helal, Noha and Bloch, Matthieu and Nosratinia, Aria},
      title = {Cooperative Resolvability and Secrecy in the Cribbing Multiple-Access Channel},
      journal = {IEEE Transactions on Information Theory},
      year = {2020},
      volume = {66},
      number = {9},
      pages = {5429-5447},
      month = sep,
      doi = {10.1109/TIT.2020.2995565},
      eprint = {1811.11649},
      file = {:2020-Helal-IEEETransIT.pdf:PDF},
      howpublished = {accepted for \emph{IEEE Transactions on Information Theory}}
    }
    

  3. M. Tahmasbi and M. R. Bloch, “Steganography Protocols for Quantum Channels,” Journal of Mathematical Physics, vol. 61, no. 8, p. 082201, Aug. 2020.
    DOI arXiv

    We study several versions of a quantum steganography problem in which two legitimate parties attempt to conceal a cypher in a quantum cover transmitted over a quantum channel without arising suspicion from a warden who intercepts the cover. In all our models, we assume that the warden has an inaccurate knowledge of the quantum channel and we formulate several variations of the steganography problem depending on the tasks used as the cover and the cypher task. In particular, when the cover task is classical communication, we show that the cypher task can be classical communication or entanglement sharing; when the cover task is entanglement sharing and the main channel is noiseless, we show that the cypher task can be randomness sharing; when the cover task is quantum communication and the main channel is noiseless, we show that the cypher task can be classical communication. In the latter case, our results improve earlier ones by relaxing the need for a shared key between the transmitter and the receiver and hold under milder assumptions on the cover quantum communication code. We study several versions of a quantum steganography problem in which two legitimate parties attempt to conceal a cypher in a quantum cover transmitted over a quantum channel without arising suspicion from a warden who intercepts the cover. In all our models, we assume that the warden has an inaccurate knowledge of the quantum channel and we formulate several variations of the steganography problem depending on the tasks used as the cover and the cypher task. In particular, when the cover task is classical communication, we show that the cypher task can be classical communication or entanglement sharing; when the cover task is entanglement sharing and the main channel is noiseless, we show that the cypher task can be randomness sharing; when the cover task is quantum communication and the main channel is noiseless, we show that the cypher task can be classical communication. In the latter case, our results improve earlier ones by relaxing the need for a shared key between the transmitter and the receiver and hold under milder assumptions on the cover quantum communication code.

    @article{Tahmasbi2020a,
      author = {Tahmasbi, Mehrdad and Bloch, Matthieu R},
      title = {Steganography Protocols for Quantum Channels},
      journal = {Journal of Mathematical Physics},
      year = {2020},
      volume = {61},
      number = {8},
      pages = {082201},
      month = aug,
      doi = {10.1063/5.0004731},
      eprint = {1907.09602},
      file = {:2020-Tahmasbi-JMP.pdf:PDF},
      howpublished = {accepted to \emph{Journal of Mathematical Physics}}
    }
    

  4. G. Cervia, L. Luzzi, M. Le Treust, and M. Bloch, “Strong Coordination of Signals and Actions over Noisy Channels with two-sided State Information,” IEEE Transactions on Information Theory, vol. 66, no. 8, pp. 4681–4708, Aug. 2020.
    DOI arXiv

    We consider a network of two nodes separated by a noisy channel with two-sided state information, in which the input and output signals have to be coordinated with the source and its reconstruction. In the case of non-causal encoding and decoding, we propose a joint source-channel coding scheme and develop inner and outer bounds for the strong coordination region. While the inner and outer bounds do not match in general, we provide a complete characterization of the strong coordination region in three particular cases: i) when the channel is perfect; ii) when the decoder is lossless; and iii) when the random variables of the channel are independent from the random variables of the source. Through the study of these special cases, we prove that the separation principle does not hold for joint source-channel strong coordination. Finally, in the absence of state information, we show that polar codes achieve the best known inner bound for the strong coordination region, which therefore offers a constructive alternative to random binning and coding proofs.

    @article{Cervia2018,
      author = {Cervia, Giulia and Luzzi, Laura and {Le Treust}, Ma\"el and Bloch, Matthieu},
      title = {Strong Coordination of Signals and Actions over Noisy Channels with two-sided State Information},
      journal = {IEEE Transactions on Information Theory},
      year = {2020},
      volume = {66},
      number = {8},
      pages = {4681-4708},
      month = aug,
      doi = {10.1109/TIT.2020.2984345},
      eprint = {1801.10543},
      file = {:2020-Cervia-IEEETransIT.pdf:PDF},
      howpublished = {accepted to \emph{IEEE Transactions on Information Theory}}
    }
    


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