# Multishot Codes for Network Coding Using Rank-Metric Codes

@article{Nbrega2010MultishotCF, title={Multishot Codes for Network Coding Using Rank-Metric Codes}, author={Roberto Wanderley da N{\'o}brega and Bartolomeu F. Uch{\^o}a Filho}, journal={2010 Third IEEE International Workshop on Wireless Network Coding}, year={2010}, pages={1-6} }

The multiplicative-additive finite-field matrix channel arises as an adequate model for linear network coding systems when links are subject to errors and erasures, and both the network topology and the network code are unknown. In a previous work we proposed a general construction of multishot codes for this channel based on the multilevel coding theory. Herein we apply this construction to the rank-metric space, obtaining multishot rank-metric codes which, by lifting, can be converted to…

## 79 Citations

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## References

SHOWING 1-10 OF 13 REFERENCES

### Multishot codes for network coding: Bounds and a multilevel construction

- Computer Science2009 IEEE International Symposium on Information Theory
- 2009

This paper explores the idea of using the subspace channel more than once and investigates the so called multishot subspace codes, and presents definitions for the problem, a motivating example, lower and upper bounds for the size of Codes, and a multilevel construction of codes based on block-coded modulation.

### On Metrics for Error Correction in Network Coding

- Computer ScienceIEEE Transactions on Information Theory
- 2009

It is shown that universal network error correcting codes achieving the Singleton bound can be easily constructed and efficiently decoded and the decoder associated with the injection metric is shown to correct more errors then a minimum-subspace-distance decoder.

### A Rank-Metric Approach to Error Control in Random Network Coding

- Computer ScienceIEEE Transactions on Information Theory
- 2008

The problem of error control in random linear network coding is addressed from a matrix perspective that is closely related to the subspace perspective of Rotter and Kschischang and an efficient decoding algorithm is proposed that can properly exploit erasures and deviations.

### Coding for Errors and Erasures in Random Network Coding

- Computer ScienceIEEE Transactions on Information Theory
- 2008

A Reed-Solomon-like code construction, related to Gabidulin's construction of maximum rank-distance codes, is described and a Sudan-style ldquolist-1rdquo minimum-distance decoding algorithm is provided.

### Multilevel codes and multistage decoding

- Computer ScienceIEEE Trans. Commun.
- 1989

The author extends the coding method to coset codes and shows how to calculate minimum squared distance and path multiplicity in terms of the norms and multiplicities of the different cosets.

### Author's Reply to Comments on 'Maximum-rank array codes and their application to crisscross error correction'

- Computer ScienceIEEE Trans. Inf. Theory
- 1992

It is shown that the dimension of such array codes must satisfy the Singleton-like bound k, which is a k-dimensional linear space of n*n matrices over F such that every nonzero matrix in C has rank mu.

### A new multilevel coding method using error-correcting codes

- Computer ScienceIEEE Trans. Inf. Theory
- 1977

A new multilevel coding method that uses several error-correcting codes that makes effective use of soft-decisions to improve the performance of decoding and is superior to other multileVEL coding systems.

### Error control coding

- Computer Science
- 2001

The basic goal in digital communications is to transport bits of information without losing too much information along the way. The level of information loss that is tolerable/acceptable varies for…

### A Rank-Metric Approach to Error Control in Random Network Coding

- Computer Science2007 IEEE Information Theory Workshop on Information Theory for Wireless Networks
- 2007

The problem of error control in random network coding is considered, and a formulation of the problem is given in terms of rank-metric codes. This formulation allows many of the tools developed for…

### Theory of codes with maximum rank dista nce

- Problemy Peredachi Informatsii , vol. 21, no. 1, pp. 3–16, 1985.
- 1985