On the design of low complexity decoding (LCD) network codes

Network coding has recently attracted significant attention as its new paradigm promises to benefit various areas of communication and networks. The benefits come at a cost since encoding operations are required at intermediate nodes, and decoding operations are required at destination nodes. In some applications, the receive ends (the destinations) cannot, or may not want to, perform complex decoding operations. Hence, it is desirable to design network codes that can be decoded with a minimal complexity. We propose a design algorithm that results in network codes with a lower decoding complexity. This is achieved by minimizing the number of operations at the sinks to recover data sent by the source. Ideally, the sinks just receive “native” packets (packets that are in their original form) and hence only require perhaps some “shuffling” (permutation) operations. To achieve maximum throughput, in general, the ideal case does not happen too often. Hence there is a need to find low complexity decoding (LCD) network codes. We make use of a concept known as information decomposition to classify different information flows on all the links in a network. A greedy search algorithm examines the information flows on the links to the sinks and assigns global coding vectors in such a way that the resultant network code is a LCD network code, in other words, fewer operations, compared to other network codes, are required to recover data transmitted by the source. We define a complexity measure for the decoding operations and investigate the performance of LCD codes and compare the decoding complexity of LCD codes with that of network codes obtained by the conventional polynomial time algorithm. We demonstrate, by using 500 random networks with 50 nodes, that the average decoding complexity of our network codes is about 20 folds lower than that of the conventional network codes. The experiment also demonstrates that the number of “native” packets arriving at the sinks in our LCD network codes is significantly higher than that in a conventional network code. The network codes found may be useful in some special applications such as data transmission in a sensor network.