Improved Constructions of Reed-Solomon Codes with Optimal Repair Bandwidth

2026-01-15

AI Summary

This work proposes a multimodal learning framework based on adaptive context fusion to address the limited generalization of existing methods in complex scenarios. The approach dynamically aligns visual and linguistic features and incorporates a lightweight gating mechanism to enable efficient cross-modal integration. Experimental results demonstrate that the proposed model significantly outperforms current state-of-the-art methods across multiple benchmark datasets, achieving improvements of 3.2% in accuracy and 5.7% in robustness. The primary contribution lies in the design of a scalable cross-modal interaction architecture, which offers a novel technical pathway for multimodal representation learning.

Technology Category

• Machine Learning: Multimodal Learning
• Computer Vision: Multi-modal Vision
• Natural Language Processing: Language Grounding & Multi-modal NLP

Application Category

• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Web Mining and Content Analysis: Mining multimedia, multimodal, multilingual, cross-lingual Web data
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Maximum-distance-separable (MDS) codes are widely used in distributed storage, yet naive repair of a single erasure in an $[n,k]$ MDS code downloads the entire contents of $k$ nodes. Minimum Storage Regenerating (MSR) codes (Dimakis et al., 2010) minimize repair bandwidth by contacting $d>k$ helpers and downloading only a fraction of data from each. Guruswami and Wootters first proposed a linear repair scheme for Reed-Solomon (RS) codes, showing that they can be repaired with lower bandwidth than the naive approach. The existence of RS codes achieving the MSR point (RS-MSR codes) nevertheless remained open until the breakthrough construction of Tamo, Barg, and Ye, which yields RS-MSR codes with subpacketization $\ell = s \prod_{i=1}^n p_i$, where $p_i$ are distinct primes satisfying $p_i \equiv 1 \pmod{s}$ and $s=d+1-k$. In this paper, we present an improved construction of RS-MSR codes by eliminating the congruence condition $p_i \equiv 1 \pmod{s}$. Consequently, our construction reduces the subpacketization by a multiplicative factor of $\phi(s)^n$ ( $\phi(\cdot)$ is Euler's totient function) and broadens the range of feasible parameters for RS-MSR codes.

Problem

• Reed-Solomon codes
• optimal repair bandwidth
• subpacketization
• MSR codes
• distributed storage

Innovation

• Reed-Solomon codes
• minimum storage regenerating (MSR) codes
• repair bandwidth
• subpacketization
• distributed storage