On Code Parameters and Coding Vector Representation for Practical RLNC

Abstract

Abstract-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 size presents a fundamental trade-off between packetbased throughput and operational overhead. On the one hand, decreasing the probability of transmitting redundant packets 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. Therefore, 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.

Providing Reliable Services over Wireless Networks Using a Low Overhead Random Linear Coding Scheme

“…Intraflow network coding schemes have two main issues: (1) overhead due to the transmission of the random coefficients used by the protocol to combine the different packets; (2) the computational cost of the coding/decoding tasks. On the one hand, some works have proposed to use coding patterns, [11,22], in order to reduce complexity in the decoding process or, on the other hand, to codify a fewer number of packets on each transmission, for instance [6,10]. In the latter case, the authors also discussed the reduction on the required overhead.…”

“…We analytically study the additional gain brought by this reduced header, following an approach similar to that used by Trullols et al [28]. It is expected that the improvement would be more relevant for larger finite fields and this is quite significant, since it is known that larger finite fields reduce the number of meaningless transmissions (linearly dependent combinations) [10]. In any case, it is quite important to study the impact of the finite field size, since larger values would also lead to longer decoding operations and a trade-off between these performance indicators would be therefore required.…”

On the Effectiveness of Recoding-based Repair in Network Coded Distributed Storage

“…To verify the assumption we made based on prior work [14] that recoding does not introduce a significant amount of linear dependence for RLNC given a large enough field for calculations, we have conducted further simulations with different fields. We chose four fields of practical interest.…”

“…When working over a small finite field, there is a possibility that the values for the α ij are selected in such a way that the q recoded packets are not linearly independent. The probability for this to happen is reduced significantly by selecting a larger field [14]. Our model assumes the use of a high field, where recoding does not introduce significant linear dependence.…”

Performance and complexity of tunable sparse network coding with gradual growing tuning functions over wireless networks

“…In some cases, decoding complexity is not the only issue of RLNC solutions, since the overhead caused by the coding vector that needs to be embedded in each coded packet shall be also considered. Heide et al [14] analyzed the impact of different operational parameters (generation size, field size and density) over the RLNC overhead; their approach is similar to the one used in [6], combining a small number of packets (low density) in each transmission. Moreover, a more complex scheme where sparse codes and overlapping generations was exploited by by Sørensen et al in [15].…”