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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 Why Self-Supervised Encoders Want to Be Normal Statistical Channel Fingerprint Construction for Massive MIMO: A Unified Tensor Learning Framework Adaptive Transform Coding for Semantic Compression Lightweight Quantum Agent for Edge Systems: Joint PQC and NOMA Resource Allocation Rethinking KV Cache Eviction via a Unified Information-Theoretic Objective Information bottleneck for learning the phase space of dynamics from high-dimensional experimental data MEG-RAG: Quantifying Multi-modal Evidence Grounding for Evidence Selection in RAG Generalising maximum mean discrepancy: kernelised functional Bregman divergences Improving Robustness of Tabular Retrieval via Representational Stability Information-Theoretic Measures in AI: A Practical Decision Guide A Unified Fractional Regularization Framework for Sparse Recovery Shape of Memory: a Geometric Analysis of Machine Unlearning in Second-Order Optimizers The Exact Replica Threshold for Nonlinear Moments of Quantum States Semantic Error Correction and Decoding for Short Block Codes Null-Space Flow Matching for MIMO Channel Estimation in Latency-Constrained Systems Directional Confusions Reveal Divergent Inductive Biases Through Rate-Distortion Geometry in Human and Machine Vision MambaCSP: Hybrid-Attention State Space Models for Hardware-Efficient Channel State Prediction Amortized Vine Copulas for High-Dimensional Density and Information Estimation Decentralized Machine Learning with Centralized Performance Guarantees via Gibbs Algorithms Secure Rate-Distortion-Perception: A Randomized Distributed Function Computation Approach for Realism RateQuant: Optimal Mixed-Precision KV Cache Quantization via Rate-Distortion Theory FB-NLL: A Feature-Based Approach to Tackle Noisy Labels in Personalized Federated Learning Ultrametric OGP - 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On the Symmetry of Polar Codes for Symmetric Binary-Input Discrete Memoryless Channels
Qiming Wang, Liping Li · 2015-04-20 · via cs.IT updates on arXiv.org

In this paper, we study the symmetry of polar codes on symmetric binary-input discrete memoryless channels (B-DMC). The symmetry property of polar codes is originally pointed out in Arikan's work for general B-DMC channels. With the symmetry, the output vector $y_1^N$ ($N$ be the block length) can be divided into equivalence classes in terms of their transition probabilities. In this paper, we present a new frame of analysis on the symmetry of polar codes for B-DMC channels. Theorems are provided to characterize the symmetries among the received vectors.

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