A Comparative Study Between Subspace and Matrix-Based Error Control Solutions

Abstract

Subspace codes are codes in which codewords are subspaces from a given vector space over a finite field $\mathbb{F}_{q}$. Their use for error correction in Random Linear Network Coding (RLNC)-based networks has been first proposed by Kötter and Kschischang. The rationale of their application in RLNC stems from the fact that information in RLNC is basically a vector space and as long as its basis is preserved, information will not be lost. Those codes share a set of similarities with rank metric codes, which are codes with codewords being $m \times n$ matrices from the space $\mathbb{F}_{q}^{m \times n}$. In this paper, we compare the two codes and we provide insights and guidelines to follow when choosing between them for error correction. Particularly, we show that when a choice is possible for a given application, it will always be a tradeoff between code cardinality and correction capability.