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Network coding offers new communications paradigm across multiple disciplines

The idea of network coding (NC, also known as netcode) is readily illustrated by the puzzle shown in Figure 1. Each arrow in the butterfly network is a channel for transmitting one bit of data. To receivers R1 and R2 the source intends to deliver a message represented by the two bits a and b. In straightforward fashion, bit a reaches node V and receiver R1 while bit b reaches V and R2. The dilemma concerns which bit node V should forward to node W upon receiving both data bits. If it forwards bit a, then receiver R1 will not get bit b. If it instead forwards b, R2 will not receive a. The solution is for node V to send out a bit indicating whether a and b are equal; for example, bit 0 when they are equal or otherwise bit 1. This new bit is called the binary sum or the exclusive OR between a and b in computer logic. When the new bit is forwarded from node W, it is used by receiver R1 to decode the value of b and by R2 for the value of a. While the dilemma confounds the conventional store-and-forward mechanism (i.e., copying), the solution suggests a fundamental concept that blends coding with data forwarding. Partial hints along these lines have appeared sporadically in the literature, including redundant array of independent disks (RAID), access to multi-channel LAN, and satellite networks. The concept was formalized as ‘network coding’ over a generic abstract network and its superiority to store-and-forward has been mathematically proven. Advantages can be quantified in terms of bit rate, latency, energy consumption, and other transmission variables. What types of communications networks can benefit from NC? One general scenario is broadcasting and data transmission in nature (such as wireless communication) including ad hoc and sensor networks. Another prospective use involves separate transmissions competing for a channel. To benefit from NC, the main effort must be to encode at intermediate nodes and to Figure 1. A message is represented by the two bits a and b. Which bit should node V send to node W in order for the message to reach both receivers R1 and R2?