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1. Ozarow-Type Outer Bounds for Memoryless Sources and Channels

   Kochman, Yuval; Ordentlich, Or; Polyanskiy, Yury (June 2018, 2018 IEEE Int. Symp. Inf. Theory (ISIT))

   Two problems, namely multiple-description source coding and joint source-channel broadcasting of a common source, are addressed. For the multiple-description problem, we revisit Ozarow’s technique for establishing impossibility results, and extend it to general sources and distortion measures. For the problem of sending a source over a broadcast channel, we revisit the bounding technique of Reznik, Feder and Zamir, and extend it to general sources, distortion measures and broadcast channels. Although the obtained bounds do not improve over existing results in the literature, they are relatively easy to evaluate, and their derivation reveals the similarities between the two bounding techniques. 

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2. On the Duality Between the BSC and Quantum PSC

   https://doi.org/10.1109/ISIT45174.2021.9518034  

   Rengaswamy, Narayanan; Pfister, Henry D. (July 2021, 2021 IEEE International Symposium on Information Theory (ISIT))

   null (Ed.)

   In 2018, Renes [IEEE Trans. Inf. Theory, vol. 64, no. 1, pp. 577-592 (2018)] developed a general theory of channel duality for classical-input quantum-output channels. His result shows that a number of well-known duality results for linear codes on the binary erasure channel can be extended to general classical channels at the expense of using dual problems which are intrinsically quantum mechanical. One special case of this duality is a connection between coding for error correction on the quantum pure-state channel (PSC) and coding for wiretap secrecy on the classical binary symmetric channel (BSC). Similarly, coding for error correction on the BSC is related to wire-tap secrecy on the PSC. While this result has important implications for classical coding, the machinery behind the general duality result is rather challenging for researchers without a strong background in quantum information theory. In this work, we leverage prior results for linear codes on PSCs to give an alternate derivation of the aforementioned special case by computing closed-form expressions for the performance metrics. The noted prior results include the optimality of square-root measurement for linear codes on the PSC and the Fourier duality of linear codes. 

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3. 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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4. Information transmission with continuous variable quantum erasure channels

   https://doi.org/10.22331/q-2023-03-06-939  

   Zhong, Changchun; Oh, Changhun; Jiang, Liang (March 2023, Quantum)

   Quantum capacity, as the key figure of merit for a given quantum channel, upper bounds the channel's ability in transmitting quantum information. Identifying different types of channels, evaluating the corresponding quantum capacity, and finding the capacity-approaching coding scheme are the major tasks in quantum communication theory. Quantum channel in discrete variables has been discussed enormously based on various error models, while error model in the continuous variable channel has been less studied due to the infinite dimensional problem. In this paper, we investigate a general continuous variable quantum erasure channel. By defining an effective subspace of the continuous variable system, we find a continuous variable random coding model. We then derive the quantum capacity of the continuous variable erasure channel in the framework of decoupling theory. The discussion in this paper fills the gap of a quantum erasure channel in continuous variable setting and sheds light on the understanding of other types of continuous variable quantum channels. 

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5. Channel Coding at Low Capacity

   Fereydounian Mohammad; Jamali, Mohammad Vahid; Hassani, Hamed; Mahdavifar, Hessam (January 2019, 2019 IEEE Information Theory Workshop (ITW))

   Low-capacity scenarios have become increasingly important in the technology of Internet of Things (IoT) and the next generation of mobile networks. Such scenarios require efficient and reliable transmission of information over channels with an extremely small capacity. Within these constraints, the performance of state-of-the-art coding techniques is far from optimal in terms of either rate or complexity. Moreover, the current non-asymptotic laws of optimal channel coding provide inaccurate predictions for coding in the low-capacity regime. In this paper, we provide the first comprehensive study of channel coding in the low-capacity regime. We will investigate the fundamental non-asymptotic limits for channel coding as well as challenges that must be overcome for efficient code design in low-capacity scenarios. 

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