A Note on the Injection Distance
Stanislav Bulygin, Olav Geil, Diego Ruano
TL;DR
This paper demonstrates that Gabidulin codes are asymptotically optimal under the injection distance in noncoherent network coding, extending their known optimality from subspace distance.
Contribution
It establishes the asymptotic optimality of Gabidulin codes with respect to the injection distance in noncoherent network coding.
Findings
Gabidulin codes are asymptotically optimal for injection distance.
Extension of optimality from subspace distance to injection distance.
Supports the effectiveness of these codes in noncoherent network coding scenarios.
Abstract
Koetter and Kschischang showed in [R. Koetter and F.R. Kschischang, "Coding for Errors and Erasures in Random Network Coding," IEEE Trans. Inform. Theory, {54(8), 2008] that the network coding counterpart of Gabidulin codes performs asymptotically optimal with respect to the subspace distance. Recently, Silva and Kschischang introduced in [D. Silva and F.R. Kschischang, "On Metrics for Error Correction in Network Coding," To appear in IEEE Trans. Inform. Theory, ArXiv: 0805.3824v4[cs.IT], 2009] the injection distance to give a detailed picture of what happens in noncoherent network coding. We show that the above codes are also asymptotically optimal with respect to this distance.
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Taxonomy
TopicsCooperative Communication and Network Coding · Wireless Communication Security Techniques · Coding theory and cryptography