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1. Equivalence of ML decoding to a continuous optimization problem

   S. Sundararajan, S N. (January 2020, IEEE International Symposium on Information Theory (ISIT))

   Maximum likelihood (ML) and symbolwise maximum aposteriori (MAP) estimation for discrete input sequences play a central role in a number of applications that arise in communications, information and coding theory. Many instances of these problems are proven to be intractable, for example through reduction to NP-complete integer optimization problems. In this work, we prove that the ML estimation of a discrete input sequence (with no assumptions on the encoder/channel used) is equivalent to the solution of a continuous non-convex optimization problem, and that this formulation is closely related to the computation of symbolwise MAP estimates. This equivalence is particularly useful in situations where a function we term the expected likelihood is efficiently computable. In such situations, we give a ML heuristic and show numerics for sequence estimation over the deletion channel. 

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2. A New Formulation of Lossy Quantum-Classical and Classical Source Coding based on a Posterior Channel

   https://doi.org/10.1109/ISIT54713.2023.10206859  

   Sohail, Mohammad Aamir; Anwar Atif, Touheed; Pradhan, S. Sandeep (June 2023, IEEE)

   —In this work, we address the lossy quantum-classical (QC) source coding problem, where the task is to compress the classical information about a quantum source, obtained after performing a measurement, below the Shannon entropy of the measurement outcomes, while incurring a bounded reconstruction error. We propose a new formulation, namely, "rate-channel theory", for the lossy QC source coding problem based on the notion of a backward (posterior) channel. We employ a singleletter posterior channel to capture the reconstruction error in place of the single-letter distortion observable. The formulation requires the reconstruction of the compressed quantum source to satisfy a block error constraint as opposed to the average singleletter distortion criterion in the rate-distortion setting. We also develop an analogous formulation for the classical variant with respect to a corresponding posterior channel. Furthermore, we characterize the asymptotic performance limit of the lossy QC and classical source coding problems in terms of single-letter quantum mutual information and mutual information quantities of the given posterior channel, respectively. We provide examples for the above formulations. 

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3. Lattices from Linear Codes and Fine Quantization: General Continuous Sources and Channels

   Shirani, Farhad; Pradhan, Sandeep (June 2018, 2018 IEEE International Symposium on Information Theory (ISIT))

   In this paper we consider the information-theoretic characterization of performance limits of a broad class of multiterminal communication problems with general continuousvalued sources and channels. In particular, we consider point-topoint source coding and channel coding with side information, distributed source coding with distortion constraints and function reconstruction problems (two-help-one). We develop an approach that uses fine quantization of the source and the channel variables followed by random coding with unstructured as well as structured (linear) code ensembles. This approach leads to lattice-like codes for general sources and channels. 

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4. Secure computation of linear functions over linear discrete multiple-access wiretap channels

   https://doi.org/10.1109/ACSSC.2016.7869665  

   Goldenbaum, Mario; Boche, Holger; Poor, H. Vincent (November 2016, Proceedings of the 50th Annual Asilomar Conference on Signals, Systems, and Computers)

   In this paper, a joint source-channel coding approach is taken to the problem of securely computing a function of distributed sources over a multiple-access wiretap channel that is linear with respect to a finite field. It is shown that if the joint source distribution fulfills certain conditions and the function to be computed matches the linear structure of the channel, secrecy comes for free in the sense that the fundamental limit (i.e., the secrecy computation-capacity) is achieved without the need for stochastic encoding. Furthermore, the legitimate receiver does not need any advantage over the eavesdropper, which is in stark contrast to standard physical-layer security results. 

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5. FASURA: A Scheme for Quasi-Static Massive MIMO Unsourced Random Access Channels

   https://doi.org/10.1109/SPAWC51304.2022.9833940  

   Gkagkos, Michail; Narayanan, Krishna R; Chamberland, Jean-Francois; Georghiades, Costas N (July 2022, IEEE)

   This article considers the massive MIMO unsourced random access problem on a quasi-static Rayleigh fading channel. Given a fixed message length and a prescribed number of channel uses, the objective is to construct a coding scheme that minimizes the energy-per-bit subject to a fixed probability of error. The proposed scheme differs from other state-of-the-art schemes in that it blends activity detection, single-user coding, pilot-aided and temporary decisions-aided iterative channel estimation and decoding, minimum-mean squared error (MMSE) estimation, and successive interference cancellation (SIC). We show that an appropriate combination of these ideas can substantially outperform state-of-the-art coding schemes when the number of active users is more than 100, making this the best performing scheme known for this regime. 

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