Digital Communications

9Error Control Coding

A communication system should provide information transmission in a cost‐effective way, at a rate, level of reliability and quality that are acceptable to a user. The key parameters available to the system designer are transmitted signal power, channel bandwidth and the receiver noise, which determine the energy per bit to noise PSD ratio E_b/N₀ required to achieve a given error probability. E_b/N₀ uniquely determines the bit error probability for a particular modulation system. Practical considerations, for example, signal attenuation, fading, shadowing, distortion and multi‐user interference, usually limit the level of the E_b/N₀. Accordingly, for a modulation scheme of interest, it may not be possible to achieve acceptable bit error probability performance at the desired data rate. For a fixed value of the E_b/N₀, error‐control coding is one of the available options for improving the reliability of data transmission, that is, with less bit errors. Error control coding may be exercised mainly as source coding that aims to remove the redundancy in the signal to be transmitted and to minimize the transmission rate with minimum loss in its information content; and channel coding that aims to minimize the number of errors in the data delivered to the user due to signal attenuation, fading, shadowing, noise and distortion due to channel. In this chapter, we will consider only channel coding.

9.1 Introduction to Channel Coding

Figure 9.1 shows the block diagram ...