Linear Network Codes: A Unified Framework for Source, Channel, and Network Coding

This report is a summary of the issue of separation and code design for network data transmission environments, as discussed in the paper by Effros et al. [1]. It is often considered that the failure of source-channel separation in network environments is a crucial obstacle in applying information theoretic tools in networks. However, with a consistent framework for digital networks, the source-channel separation turns out to be more robust than existing counterexamples may suggest. More interestingly, the separation of source and channel code design does not necessarily simplify the design of communication systems for digital networks; rather such decomposition of a problem into modular tasks may increase complexity as the decomposition imposes unnecessary conditions. The network coding literature assumes independent data bits and lossless links, hence endorses a philosophy where source and channel coding are separated from network coding or routing. However, there are simple examples showing neither separate source-network coding nor separate channel-network coding techniques guarantee optimal performance. We further argue that the major challenge in design of network systems is the lack of separation of large networks into canonical elements such as simple multiple access or broadcast networks, rather than the lack of source-channel separation in networks.