Coding for Reliable Communication

The fundamental problem in information and communication theory is how to achieve reliable communication over channels that are originally unreliable in a sense that each individual transmission over the channel has the chance to be received incorrectly. The way to improve the reliability of the individual data bits is to use redundancy in a form of a forward error correction (FEC) code. This chapter begins by introducing the methods for error correction through some simple examples involving the binary symmetric channel. It explains how to select as few inputs as possible in order to guarantee high reliability for the transmission of a single input in the expanded channel. The chapter also discusses an important class of coding instruction, the linear block codes. In order to design a transmission mode with FEC coding and a specific modulation, we can apply a layered approach for the Gaussian channel, that is, the coding and modulation are designed separately.