Nonbinary Coding: Towards a Unified Framework Across Multiple Layers

In addition to the invention of iterative decoded capacity-achieving channel coding schemes, namely, turbo codes in the early 1990’s and the rediscovery of low-density parity-check (LDPC) codes in the mid 1990’s, digital fountain codes and network coding are two recent breakthroughs in the coding community. They offer great promise for providing robust and efficient data transport through a large network, either wireless, wireline, or hybrid. Digital fountain codes are codes for channels with erasures (i.e., packet losses in a communication network), and operate in a forward manner without the need of a feedback channel. They have enabled a revolutionary way of non-flow-based data delivery over unreliable networks. Network coding is a paradigm shift in the coding community for both wireline and wireless networks. Instead of simply forwarding packets as in traditional routing, network coding allows an intermediate node to mix (code) the incoming packets to generate encoded outgoing packets. This has suggested many promising benefits for both wireline and wireless networks in terms of capacity and/or diversity gain. Coding in different layers has complementary strengths: channel coding is particularly suitable for combating fading and additive noise in wireless or wireline link, network coding transparently provides path diversity and local loss recovery, while application-layer coding is used to combat erasures (i.e., packet losses) inside a network. An illustration for the application of coding across the application, network, and link layers in a large network is shown in Figure 1 where erasure-correction coding (digital fountain codes) in the application layer is performed in an end-to-end manner between source and destination, intermediate (or relay) nodes use network coding, and channel coding is applied per link, possibly combined with high order modulation.