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Theoretical Limits of Language Model Alignment $f$-Divergence Regularized RLHF: Two Tales of Sampling and Unified Analyses A Unified Measure-Theoretic View of Diffusion, Score-Based, and Flow Matching Generative Models When Can Voting Help, Hurt, or Change Course? Exact Structure of Binary Test-Time Aggregation When Semantic Communication Meets Queueing: Cross-Layer Latency and Task Fidelity Optimization Convexity in Disguise: A Theoretical Framework for Nonconvex Low-Rank Matrix Estimation Conditional Diffusion Under Linear Constraints: Langevin Mixing and Information-Theoretic Guarantees Sharp Capacity Thresholds in Linear Associative Memory: From Winner-Take-All to Listwise Retrieval Expert Routing for Communication-Efficient MoE via Finite Expert Banks Contextual Memory-Enhanced Source Coding for Low-SNR Communications Realizable Bayes-Consistency for General Metric Losses Leveraging Code Automorphisms for Improved Syndrome-Based Neural Decoding A Hierarchical Sampling Framework for bounding the Generalization Error of Federated Learning Dueling DDQN-Based Adaptive Multi-Objective Handover Optimization for LEO Satellite Networks The Causal Description Gap: Information-Theoretic Separations Across Pearl's Hierarchy Optimization of CV-QKD Under Practical Constraints Benchmarking Wireless Representations: High-Dimensional vs. Compressed Embeddings for Efficiency and Robustness Real-Time Text Transmission via LLM-Based Entropy Coding over Fixed-Rate Channels SwiftChannel: Algorithm-Hardware Co-Design for Deep Learning-Based 5G Channel Estimation Evolving Token Communication with Parametric Memory Network Remote Action Generation: Remote Control with Minimal Communication The (Marginal) Value of a Search Ad: An Online Causal Framework for Repeated Second-price Auctions Stabilizing Private LASSO under Heterogeneous Covariates via Anisotropic Objective Perturbation Linear-Readout Floors and Threshold Recovery in Computation in Superposition Soft Graph Diffusion Transformer for MIMO Detection Hierarchical Federated Learning for Networked AI: From Communication Saving to Architecture-Aware Design Exponential families from a single KL identity MIFair: A Mutual-Information Framework for Intersectionality and Multiclass Fairness Diffusion-OAMP for Joint Image Compression and Wireless Transmission Decoupled Descent: Exact Test Error Tracking Via Approximate Message Passing
An Error-Code Perspective on Metzner--Kapturowski-like De...
Thomas Jerkovits, Felicitas Hörmann, Hannes Bartz · 2024-09-27 · via cs.IT updates on arXiv.org

In this paper we consider a Metzner-Kapturowski-like decoding algorithm for high-order interleaved sum-rank-metric codes, offering a novel perspective on the decoding process through the concept of an error code. The error code, defined as the linear code spanned by the vectors forming the error matrix, provides a more intuitive understanding of the decoder's functionality and new insights. The proposed algorithm can correct errors of sum-rank weight up to $d-2$, where $d$ is the minimum distance of the constituent code, given a sufficiently large interleaving order. The decoder's versatility is highlighted by its applicability to any linear constituent code, including unstructured or random codes. The computational complexity is $O(\max\{n^3, n^2 s\})$ operations over $\mathbb{F}_{q^m}$, where $n$ is the code length and $s$ is the interleaving order. We further explore the success probability of the decoder for random errors, providing an efficient algorithm to compute an upper bound on this probability. Additionally, we derive bounds and approximations for the success probability when the error weight exceeds the unique decoding radius, showing that the decoder maintains a high success probability in this regime. Our findings suggest that this decoder could be a valuable tool for the design and security analysis of code-based cryptosystems using interleaved sum-rank-metric codes. The new insights into the decoding process and the high success probability of the algorithm even beyond the unique decoding radius underscore its potential to contribute to various coding-related applications.