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Chaoping Xing

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FOCS Conference 2024 Conference Paper

Random Gabidulin Codes Achieve List Decoding Capacity in the Rank Metric

  • Zeyu Guo 0001
  • Chaoping Xing
  • Chen Yuan 0003
  • Zihan Zhang 0001

Gabidulin codes, serving as the rank-metric counterpart of Reed-Solomon codes, constitute an important class of maximum rank distance (MRD) codes. However, unlike the fruitful positive results about the list decoding of Reed-Solomon codes, results concerning the list decodability of Gabidulin codes in the rank metric are all negative so far. For example, in contrast to Reed-Solomon codes, which are always list decodable up to the Johnson bound in the Hamming metric, Raviv and Wachter-Zeh (IEEE TIT, 2016 and 2017) constructed a class of Gabidulin codes that are not even combinatorially list decodable beyond the unique decoding radius in the rank metric. Proving the existence of Gabidulin codes with good combinatorial list decodability in the rank metric has remained a long-standing open problem. In this paper, we resolve the aforementioned open problem by showing that, with high probability, random Gabidulin codes over sufficiently large alphabets attain the optimal generalized Singleton bound for list decoding in the rank metric. In particular, they achieve list decoding capacity in the rank metric. Our work is significantly influenced by the recent break-throughs in the combinatorial list decodability of Reed-Solomon codes, especially the work by Brakensiek, Gopi, and Makam (STOC 2023). Our major conceptual and technical contributions, which may hold independent interest, consist of the following: (1) We initiate the study of “higher order MRD codes” and provide a novel unified theory, which runs parallel to the theory of “higher order MDS codes” developed by Brakensiek, Gopi, and Makam. (2) We prove a natural analog of the GM-MDS theorem, proven by Lovett (FOCS 2018) and Yildiz and Hassibi (IEEE TIT, 2019), which we call the GM-MRD theorem. In particular, our GMMRD theorem for Gabidulin codes is strictly stronger than the GM-MDS theorem for Gabidulin codes proven by Yildiz and Hassibi.

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IS Journal 2020 Journal Article

A Secure Federated Transfer Learning Framework

  • Yang Liu
  • Yan Kang
  • Chaoping Xing
  • Tianjian Chen
  • Qiang Yang

Machine learning relies on the availability of vast amounts of data for training. However, in reality, data are mostly scattered across different organizations and cannot be easily integrated due to many legal and practical constraints. To address this important challenge in the field of machine learning, we introduce a new technique and framework, known as federated transfer learning (FTL), to improve statistical modeling under a data federation. FTL allows knowledge to be shared without compromising user privacy and enables complementary knowledge to be transferred across domains in a data federation, thereby enabling a target-domain party to build flexible and effective models by leveraging rich labels from a source domain. This framework requires minimal modifications to the existing model structure and provides the same level of accuracy as the nonprivacy-preserving transfer learning. It is flexible and can be effectively adapted to various secure multiparty machine learning tasks.

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