Abstract
Random Linear Network Coding (RLNC) is a technique to disseminate information in a network. Various error scenarios require algebraic code constructions with high error-correcting capability in order to transmit packets reliably through such a network. It was shown that subspace codes, in particular lifted rank-metric codes, are suitable for this purpose, in contrast to Hamming metric in the case of a classical transmission. The mainly used codes are Gabidulin codes. In this contribution, we will introduce Gabidulin codes and describe several error-erasure decoding algorithms. Further, an extension of Gabidulin codes is introduced which allows to decode beyond half the minimum rank distance, the interleaved Gabidulin codes. Further, we will introduce (partial) unit memory codes based on Gabidulin codes. Such convolutional codes are of particular interest in so-called multi-shot transmissions since memory between different transmission is introduced. Finally, we will show a significant difference of Gabidulin and Reed-Solomon codes in case of list decoding. Namely, that the list size can grow exponentially for a decoding radius below the Johnson bound for rank metric codes.
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