Projective Space Codes for the Injection Metric
Azadeh Khaleghi, Frank R. Kschischang
TL;DR
This paper introduces new codes for error correction in network coding using the injection metric, deriving bounds and constructing codes that outperform existing subspace metric codes.
Contribution
It develops a Gilbert-Varshamov bound for injection metric codes and constructs new non-constant-dimension codes with more codewords than previous subspace metric codes.
Findings
Derived a Gilbert-Varshamov bound for injection metric codes
Constructed new non-constant-dimension codes with improved size
Codes outperform comparable subspace metric codes
Abstract
In the context of error control in random linear network coding, it is useful to construct codes that comprise well-separated collections of subspaces of a vector space over a finite field. In this paper, the metric used is the so-called "injection distance", introduced by Silva and Kschischang. A Gilbert-Varshamov bound for such codes is derived. Using the code-construction framework of Etzion and Silberstein, new non-constant-dimension codes are constructed; these codes contain more codewords than comparable codes designed for the subspace metric.
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Taxonomy
TopicsCooperative Communication and Network Coding · Coding theory and cryptography · Advanced Wireless Communication Technologies