Binary Codes, Graphs, and Trellises

In this chapter we focus on the structure and description of binary convolutional codes and their encoders. Both algebraic and graph-based methods are used to develop a generic description of the codes. It is shown that both recursive and feedforward encoders can be used to generate the same convolutional code. The distinctions between various encoders for a given code are discussed, and an emphasis is placed on the properties of recursive, systematic convolutional encoders. It is shown that such descriptive and analytic techniques can also be applied to block codes through the BCJR trellis construction technique.

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