On code parameters and coding vector representation for practical RLNC

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 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.