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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
Flexible Fractional Repetition Codes for Distributed Stor...
Imad Ahmad, Chih-Chun Wang · 2016-04-28 · via cs.IT updates on arXiv.org

Consider the following fundamental question of distributed storage networks: Given any arbitrary $(n,k,d)$ values, whether there exists an intelligent helper selection scheme (assuming unlimited memory and computing power) that can strictly improve the storage-bandwidth (S-B) tradeoff. Ahmad et al. 18' answered this question by proving that for a subset of $(n,k,d)$ values, no helper selection scheme can ever improve the S-B tradeoff, and for the $(n,k,d)$ not in that subset, a new scheme called family helper selection (FHS) can strictly improve the S-B tradeoff over a blind helper selection scheme. Nonetheless, the analysis of FHS is done by a min-cut analysis with no actual code construction. This work fills this gap between pure min-cut analysis and actual code construction by pairing FHS with a new, generalized version of the existing fractional repetition (FR) codes. Specifically, existing FR codes are exact-repair codes that admit the highly-desirable repair-by-transfer property, but its unique construction limits the application to a restricted set of $(n,k,d)$ values. In contrast, our new construction, termed flexible fractional repetition codes, can be applied to arbitrary $(n,k,d)$ while retaining most of the practical benefits of FR codes, i.e., admitting small repair bandwidth, being exact-repair, and being almost repairable-by-transfer.