Multicomponent Network Codes for a Channel with Random Linear Transformations and Packet Errors

Abstract : This work is related to new multicomponent network codes for a channel with random linear transformations and packet errors. New code construction is a generalization of Gabidulin-Pilipchuk codes, and similarly uses rank codes with restrictions as subcodes. Usage of a greedy algorithm, when selecting the code components, allows us to increase code cardinality compared with the previously known constructions. We provide the conditions under which the described multicomponent code can correct both erasures and packet errors in the channel. Finally, we present an efficient algorithm of decoding both types of errors and give some examples.