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1. Channel Coding at Low Capacity

   https://doi.org/10.1109/ITW44776.2019.8989142  

   Fereydounian, Mohammad; Jamali, Mohammad Vahid; Hassani, Hamed; Mahdavifar, Hessam (August 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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2. Channel coding at low capacity

   Fereydounian, Mohammad; Hassani, Hamed; Jamal, Vahid; Mahdavifar, Hessam (August 2023, IEEE journal on selected areas in information theory)

   Low-capacity scenarios have become increasingly important in the technology of the In- ternet of Things (IoT) and the next generation of wireless networks. Such scenarios require efficient and reliable transmission over channels with an extremely small capacity. Within these constraints, the state-of-the-art coding techniques may not be directly applicable. More- over, the prior work on the finite-length analysis of optimal channel coding provides inaccurate predictions of the limits in the low-capacity regime. In this paper, we study channel coding at low capacity from two perspectives: fundamental limits at finite length and code construc- tions. We first specify what a low-capacity regime means. We then characterize finite-length fundamental limits of channel coding in the low-capacity regime for various types of channels, including binary erasure channels (BECs), binary symmetric channels (BSCs), and additive white Gaussian noise (AWGN) channels. From the code construction perspective, we charac- terize the optimal number of repetitions for transmission over binary memoryless symmetric (BMS) channels, in terms of the code blocklength and the underlying channel capacity, such that the capacity loss due to the repetition is negligible. Furthermore, it is shown that capacity- achieving polar codes naturally adopt the aforementioned optimal number of repetitions. 

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3. Fundamental Limits of Thermal-noise Lossy Bosonic Multiple Access Channel

   Anderson, Evan; Bash, Boulat A. (December 2022, 2022 IEEE Globecom Workshops (GC Wkshps))

   Bosonic channels describe quantum-mechanically many practical communication links such as optical, microwave, and radiofrequency. We investigate the maximum rates for the bosonic multiple access channel (MAC) in the presence of thermal noise added by the environment and when the transmitters utilize Gaussian state inputs. We develop an outer bound for the capacity region for the thermal-noise lossy bosonic MAC. We additionally find that the use of coherent states at the transmitters is capacity-achieving in the limits of high and low mean input photon numbers. Furthermore, we verify that coherent states are capacity-achieving for the sum rate of the channel. In the non-asymptotic regime, when a global mean photon-number constraint is imposed on the transmitters, coherent states are the optimal Gaussian state. Surprisingly however, the use of single-mode squeezed states can increase the capacity over that afforded by coherent state encoding when each transmitter is photon number constrained individually. 

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4. On finite-length analysis and channel dispersion for broadcast packet erasure channels with feedback

   https://doi.org/10.1109/ISIT45174.2021.9517889  

   Lin, Shih-Chun; Wang, Chih-Chun; Wang, I-Hsiang; Huang, Yu-Chih; Lai, Yi-Chun (July 2021, 2021 IEEE International Symposium on Information Theory (ISIT))

   Motivated by the applications for low-delay communication networks, the finite-length analysis, or channel dispersion identification, of the multi-user channel is very important. Recent studies also incorporate the effects of feedback in point-to-point and common-message broadcast channels (BCs). However, with private messages and feedback, finite-length results for BCs are much more scarce. Though it is known that feedback can strictly enlarge the capacity, the ultimate feedback capacity regions remain unknown for even some classical channels including Gaussian BCs. In this work, we study the two-user broadcast packet erasure channel (PEC) with causal feedback, which is one of the cleanest feedback capacity results and the capacity region can be achieved by elegant linear network coding (LNC). We first derive a new finite-length outer bound for any LNCs and then accompanying inner bound by analyzing a three-phase LNC. For the outer-bound, we adopt a linear-space-based framework, which can successfully find the LNC capacity. However, naively applying this method in finite-length regime will result in a loose outer bound. Thus a new bounding technique based on carefully labelling each time slot according to the type of LNC transmitted is proposed. Simulation results show that the sum-rate gap between our inner and outer bounds is within 0.02 bits/channel use. Asymptotic analysis also shows that our bounds bracket the channel dispersion of LNC feedback capacity for broadcast PEC to within a factor of Q-l (E/2)/Q-l (E). 

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5. Neural Compress-and-Forward for the Relay Channel

   https://doi.org/10.1109/SPAWC60668.2024.10694419  

   Özyılkan, Ezgi; Carpi, Fabrizio; Garg, Siddharth; Erkip, Elza (September 2024, IEEE)

   The relay channel, consisting of a source-destination pair and a relay, is a fundamental component of cooperative communications. While the capacity of a general relay channel remains unknown, various relaying strategies, including compress-and-forward (CF), have been proposed. For CF, given the correlated signals at the relay and destination, distributed compression techniques, such as Wyner–Ziv coding, can be harnessed to utilize the relay-to-destination link more efficiently. In light of the recent advancements in neural network-based distributed compression, we revisit the relay channel problem, where we integrate a learned one-shot Wyner–Ziv compressor into a primitive relay channel with a finite-capacity and orthogonal (or out-of-band) relay-to-destination link. The resulting neural CF scheme demonstrates that our task-oriented compressor recovers binning of the quantized indices at the relay, mimicking the optimal asymptotic CF strategy, although no structure exploiting the knowledge of source statistics was imposed into the design. We show that the proposed neural CF scheme, employing finite order modulation, operates closely to the capacity of a primitive relay channel that assumes a Gaussian codebook. Our learned compressor provides the first proof-of-concept work toward a practical neural CF relaying scheme. Published in: 2024 IEEE 25th Intern 

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