Multishot codes for network coding using rank-metric codes

Computing Research Repository, 2007

It is shown that the error control problem in random network coding can be reformulated as a generalized decoding problem for rank-metric codes. This result allows many of the tools developed for rank-metric codes to be applied to random network coding. In the generalized decoding problem induced by random network coding, the channel may supply partial information about the error in the form of erasures (knowledge of an error location but not its value) and deviations (knowledge of an error value but not its location). For Gabidulin codes, an important family of maximum rank distance codes, an efficient decoding algorithm is proposed that can fully exploit the correction capability of the code; namely, it can correct any pattern of errors, µ erasures and δ deviations provided

2007 10th Canadian Workshop on Information Theory (CWIT), 2007

The idea of priority encoding transmission (PET), although very useful to provide graceful degradation of performance in the presence of packet loss, presents a challenge when one tries to apply it in a random network coding environment. So far, the only solution proposed relies on the rateless feature of network coding and is therefore not suitable for delay-constrained applications. In this paper, a PET system based on rank-metric codes is proposed. This system can provide strict combinatorial guarantees of recovery. The system is also able to provide forward error correction of corrupt packets that could potentially be introduced by malicious users. Application of the system to streaming media broadcasting is proposed, illustrating the potential practical utility of this approach.

IEEE Transactions on Information Theory, 2015

By extending the notion of minimum rank distance, this paper introduces two new relative code parameters of a linear code C 1 of length n over a field extension F q m and its subcode C 2 C 1 . One is called the relative dimension/intersection profile (RDIP), and the other is called the relative generalized rank weight (RGRW). We clarify their basic properties and the relation between the RGRW and the minimum rank distance. As applications of the RDIP and the RGRW, the security performance and the error correction capability of secure network coding, guaranteed independently of the underlying network code, are analyzed and clarified. We propose a construction of secure network coding scheme, and analyze its security performance and error correction capability as an example of applications of the RDIP and the RGRW. Silva and Kschischang showed the existence of a secure network coding in which no part of the secret message is revealed to the adversary even if any dim C 1 -1 links are wiretapped, which is guaranteed over any underlying network code. However, the explicit construction of such a scheme remained an open problem. Our new construction is just one instance of secure network coding that solves this open problem.

2016

In this paper is we establish the role of Rank-metric Codes for error correction in Random network Coding. For this, first we try to understand the process of communication and its components. Thereafter, describing the problem in achieving error free communication and making necessary assumptions, we arrive at the conclusion.

ArXiv, 2022

The rank metric measures the distance between two matrices by the rank of their difference. Codes designed for the rank metric have attracted considerable attention in recent years, reinforced by network coding and further motivated by a variety of applications. In code-based cryptography, the hardness of the corresponding generic decoding problem can lead to systems with reduced public-key size. In distributed data storage, codes in the rank metric have been used repeatedly to construct codes with locality, and in coded caching, they have been employed for the placement of coded symbols. This survey gives a general introduction to rank-metric codes, explains their most important applications, and highlights their relevance to these areas of research.