On Code Parameters and Coding Vector Representation for Practical RLNC

Random Linear Network Coding (RLNC) provides a theoretically efficient method for coding. The drawbacks associated with it are the complexity of the decoding and the overhead resulting from the encoding vector. Increasing the field size and generation length presents a fundamental trade-off between packet-based throughput and operational overhead. On the one hand, decreasing the probability of redundant packets' being transmitted is beneficial for throughput and, consequently, reduces transmission energy. On the other hand, the decoding complexity and amount of header overhead increase with field size and generation length, leading to higher energy consumption. The main findings of this work are bounds for the transmission overhead due to linearly dependent packets. The optimal trade-off is system and topology dependent, as it depends on the cost in energy of performing coding operations versus transmitting data. We show that moderate field sizes are the correct choice when trade-offs are considered. The results show that sparse binary codes perform the best, unless the generation size is very low.Cooperation and Network Coding Project (CONE) (Grant 09-066549/FTP

Fulcrum: Flexible Network Coding for Heterogeneous Devices

Producción CientíficaWe introduce Fulcrum, a network coding framework that achieves three seemingly conflicting objectives: 1) to reduce the coding coefficient overhead down to nearly n bits per packet in a generation of n packets; 2) to conduct the network coding using only Galois field GF(2) operations at intermediate nodes if necessary, dramatically reducing computing complexity in the network; and 3) to deliver an end-to-end performance that is close to that of a high-field network coding system for high-end receivers, while simultaneously catering to low-end receivers that decode in GF(2). As a consequence of 1) and 3), Fulcrum has a unique trait missing so far in the network coding literature: providing the network with the flexibility to distribute computational complexity over different devices depending on their current load, network conditions, or energy constraints. At the core of our framework lies the idea of precoding at the sources using an expansion field GF(2 h ), h > 1, to increase the number of dimensions seen by the network. Fulcrum can use any high-field linear code for precoding, e.g., Reed-Solomon or Random Linear Network Coding (RLNC). Our analysis shows that the number of additional dimensions created during precoding controls the trade-off between delay, overhead, and computing complexity. Our implementation and measurements show that Fulcrum achieves similar decoding probabilities as high field RLNC but with encoders and decoders that are an order of magnitude faster.Green Mobile Cloud project (grant DFF-0602-01372B)Colorcast project (grant DFF-0602-02661B)TuneSCode project (grant DFF - 1335-00125)Danish Council for Independent Research (grant DFF-4002-00367)Ministerio de Economía, Industria y Competitividad - Fondo Europeo de Desarrollo Regional (grants MTM2012-36917-C03-03 / MTM2015-65764-C3-2-P / MTM2015-69138-REDT)Agencia Estatal de Investigación - Fondo Social Europeo (grant RYC-2016-20208)Aarhus Universitets Forskningsfond Starting (grant AUFF-2017-FLS-7-1