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cs.IT updates on arXiv.org

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
Scalable Block-Wise Product BCH Codes
Yingquan Wu, Eyal En Gad · 2018-12-18 · via cs.IT updates on arXiv.org

In this paper we comprehensively investigate block-wise product (BWP) BCH codes, wherein raw data is arranged in the form of block-wise matrix and each row and column BCH codes intersect on one data block. We first devise efficient BCH decoding algorithms, including reduced-1-bit decoding, extra-1-bit list decoding, and extra-2-bit list decoding. We next present a systematic construction of BWP-BCH codes upon given message and parity lengths that takes into account for performance, implementation and scalability, rather than focusing on a regularly defined BWP-BCH code. It can easily accommodate different message length or parity length at minimal changes. It employs extended BCH codes instead of BCH codes to reduce miscorrection rate and an inner RS code to lower error floor. We also describe a high-speed scalable encoder. We finally present a novel iterative decoding algorithm which is divided into three phases. The first phase iteratively applies reduced BCH correction capabilities to correct lightly corrupted rows/columns while suppressing miscorrection, until the process stalls. The second phase iteratively decodes up to the designed correction capabilities, until the process stalls. The last phase iteratively applies the proposed list decoding in a novel manner which effectively determines the correct candidate. The key idea is to use cross decoding upon each list candidate to pick the candidate which enables the maximum number of successful cross decoding. Our simulations show that the proposed algorithm provides a significant performance boost compared to the state-of-the-art algorithms.