Coding allows bit errors introduced by transmission of a modulated signal through a wireless channel to be either detected or corrected by a decoder in the receiver. Coding can be considered as the embedding of signal constellation points in a higher-dimensional signaling space than is needed for communications. By going to a higher-dimensional space, the distance between points can be increased, which provides for better error correction and detection.

In this chapter we describe codes designed for additive white Gaussian noise channels and for fading channels. Codes designed for AWGN channels typically do not work well on fading channels because they cannot correct for long error bursts that occur in deep fading. Codes for fading channels are mainly based on using an AWGN channel code combined with interleaving, but the criterion for the code design changes to provide fading diversity. Other coding techniques to combat performance degradation due to fading include unequal error protection codes and joint source and channel coding.

We first provide an overview of code design in both fading and AWGN, along with basic design parameters such as minimum distance, coding gain, bandwidth expansion, and diversity order. Sections 8.2 and 8.3 provide a basic overview of block and convolutional code designs for AWGN channels. Although these designs are not directly applicable to fading channels, codes for fading channels and other codes used in wireless systems (e.g., spreading codes in CDMA) require background in these fundamental techniques.