Error Performance Analysis of Maximum Rank Distance Codes

In this paper, we first introduce the concept of elementary linear subspace, which has similar properties to those of a set of coordinates. We then use elementary linear subspaces to derive properties of maximum rank distance (MRD) codes that parallel those of maximum distance separable (MDS) codes. Using these properties, we show that, for MRD codes with error correction capability t, the decoder error probability of bounded distance decoders decreases exponentially with t based on the assumption that all errors with the same rank are equally likely. Finally, our simulation results show that our bounds seem applicable to other error models as well and that MRD codes are more resilient against crisscross errors than MDS codes.