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1. Threshold-Secure Coding with Shared Key

   https://doi.org/10.1109/ALLERTON.2019.8919868  

   Aldaghri, Nasser; Mahdavifar, Hessam (September 2019, 2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton))

   Cryptographic protocols are often implemented at upper layers of communication networks, while error-correcting codes are employed at the physical layer. In this paper, we consider utilizing readily-available physical layer functions, such as encoders and decoders, together with shared keys to provide a threshold-type security scheme. To this end, the effect of physical layer communication is abstracted out and the channels between the legitimate parties, Alice and Bob, and the eaves-dropper Eve are assumed to be noiseless. We introduce a model for threshold-secure coding, where Alice and Bob communicate using a shared key in such a way that Eve does not get any information, in an information-theoretic sense, about the key as well as about any subset of the input symbols of size up to a certain threshold. Then, a framework is provided for constructing threshold-secure codes form linear block codes while characterizing the requirements to satisfy the reliability and security conditions. Moreover, we propose a threshold-secure coding scheme, based on Reed-Muller (RM) codes, that meets security and reliability conditions. Furthermore, it is shown that the encoder and the decoder of the scheme can be implemented efficiently with quasi-linear time complexity. In particular, a low-complexity successive cancellation decoder is shown for the RM-based scheme. Also, the scheme is flexible and can be adapted given any key length. 

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2. A Low-Density Parity-Check Coding Scheme for LoRa Networking

   https://doi.org/10.1145/3665928  

   Yang, Kang; Du, Wan (July 2024, ACM Transactions on Sensor Networks)

   This article presents a novel system,LLDPC,¹which brings Low-Density Parity-Check (LDPC) codes into Long Range (LoRa) networks to improve Forward Error Correction, a task currently managed by less efficient Hamming codes. Three challenges in achieving this are addressed: First, Chirp Spread Spectrum (CSS) modulation used by LoRa produces only hard demodulation outcomes, whereas LDPC decoding requires Log-Likelihood Ratios (LLR) for each bit. We solve this by developing a CSS-specific LLR extractor. Second, we improve LDPC decoding efficiency by using symbol-level information to fine-tune LLRs of error-prone bits. Finally, to minimize the decoding latency caused by the computationally heavy Soft Belief Propagation (SBP) algorithm typically used in LDPC decoding, we apply graph neural networks to accelerate the process. Our results show thatLLDPCextends default LoRa’s lifetime by 86.7% and reduces SBP algorithm decoding latency by 58.09×. 

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3. Quantum spherical codes

   https://doi.org/10.1038/s41567-024-02496-y  

   Jain, Shubham P; Iosue, Joseph T; Barg, Alexander; Albert, Victor V (August 2024, Nature Physics)

   As with classical computers, quantum computers require error-correction schemes to reliably perform useful large-scale calculations. The nature and frequency of errors depends on the quantum computing platform, and although there is a large literature on qubit-based coding, these are often not directly applicable to devices that store information in bosonic systems such as photonic resonators. Here, we introduce a framework for constructing quantum codes defined on spheres by recasting such codes as quantum analogues of the classical spherical codes. We apply this framework to bosonic coding, and we obtain multimode extensions of the cat codes that can outperform previous constructions but require a similar type of overhead. Our polytope-based cat codes consist of sets of points with large separation that, at the same time, form averaging sets known as spherical designs. We also recast concatenations of Calderbank–Shor–Steane codes with cat codes as quantum spherical codes, which establishes a method to autonomously protect against dephasing noise. 

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4. Extracting Topological Orders of Generalized Pauli Stabilizer Codes in Two Dimensions

   https://doi.org/10.1103/PRXQuantum.5.030328  

   Liang, Zijian; Xu, Yijia; Iosue, Joseph T; Chen, Yu-An (August 2024, PRX Quantum)

   In this paper, we introduce an algorithm for extracting topological data from translation invariant generalized Pauli stabilizer codes in two-dimensional systems, focusing on the analysis of anyon excitations and string operators. The algorithm applies to ${\mathbb{Z}}_d$qudits, including instances where $d$is a nonprime number. This capability allows the identification of topological orders that differ from the ${\mathbb{Z}}_d$toric codes. It extends our understanding beyond the established theorem that Pauli stabilizer codes for ${\mathbb{Z}}_p$qudits (with $p$being a prime) are equivalent to finite copies of ${\mathbb{Z}}_p$toric codes and trivial stabilizers. The algorithm is designed to determine all anyons and their string operators, enabling the computation of their fusion rules, topological spins, and braiding statistics. The method converts the identification of topological orders into computational tasks, including Gaussian elimination, the Hermite normal form, and the Smith normal form of truncated Laurent polynomials. Furthermore, the algorithm provides a systematic approach for studying quantum error-correcting codes. We apply it to various codes, such as self-dual CSS quantum codes modified from the two-dimensional honeycomb color code and non-CSS quantum codes that contain the double semion topological order or the six-semion topological order. Published by the American Physical Society2024 

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5. Multiple Timescale Online Learning Rules for Information Maximization with Energetic Constraints

   https://doi.org/10.1162/neco_a_01182  

   Yi, Peng; Ching, ShiNung (May 2019, Neural Computation)

   A key aspect of the neural coding problem is understanding how representations of afferent stimuli are built through the dynamics of learning and adaptation within neural networks. The infomax paradigm is built on the premise that such learning attempts to maximize the mutual information between input stimuli and neural activities. In this letter, we tackle the problem of such information-based neural coding with an eye toward two conceptual hurdles. Specifically, we examine and then show how this form of coding can be achieved with online input processing. Our framework thus obviates the biological incompatibility of optimization methods that rely on global network awareness and batch processing of sensory signals. Central to our result is the use of variational bounds as a surrogate objective function, an established technique that has not previously been shown to yield online policies. We obtain learning dynamics for both linear-continuous and discrete spiking neural encoding models under the umbrella of linear gaussian decoders. This result is enabled by approximating certain information quantities in terms of neuronal activity via pairwise feedback mechanisms. Furthermore, we tackle the problem of how such learning dynamics can be realized with strict energetic constraints. We show that endowing networks with auxiliary variables that evolve on a slower timescale can allow for the realization of saddle-point optimization within the neural dynamics, leading to neural codes with favorable properties in terms of both information and energy. 

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