Cross-Layer Design of Rateless Random Network Codes for Delay Optimization

Abstract

We study joint network and channel code design to optimize delay performance. Here the delay is the transmission time of information packets from a source to sinks without considering queuing effects. In our systems, network codes (network layer) are on top of channel codes (physical layer) which are disturbed by noise. Network codes run in a rateless random method, and thus have erasure-correction capability. For the constraint of finite transmission time, transmission errors are inevitable in the physical layer. A detection error in the physical layer means an erasure of network codewords. For the analysis, we model the delay of each information generation in the network layer as independent, identically distributed random variables. The calculation approaches for delay measures are investigated for coded erasure networks. We show how to evaluate the rate and erasure probability of a set of channels belonging to one cut. We also show that the min-cut determines the decoding error probability in the sinks if the number of information packets is large. We observe that for a given amount of source information, larger packet length leads to fewer packets to be transmitted but higher physical-layer detection error probabilities. Further, longer transmission time (delay) in the physical-layer causes smaller detection error probability at the physical layer. Thus, both parameters have opposite impacts on the physical and network layer, considering delay. We should find the optimal values of them in a cross-layer approach. We then formulate the problems of optimizing delay performance, and discuss solutions for them.