ecting or correcting errors is found from the minimum distance between its codewords. The minimum codeword distance is found by calculating the distance between any two possible codewords generated by an encoder. It is denoted d and is used to find the maximum number of errors that the coding technique can detect or correct. For an error detection coding technique the largest number of errors that may occur without a possible false error detection is dmin -1. For an error correction coding technique the largest number of errors that may be corrected is less than or equal to 0.5 X (dmi-1). Common Error Control Codes As discussed in previous chapters, broadband telecommunications standards focus on delivery of data blocks from a content provider through a retailer network and different types of infra- structure such as wireless, optical fibre and satellite. The characteristics of different infrastruc- ture mean that processes leading to error occurrence are different. As a result the error control coding techniques used in different standards differ. The following sections describe the coding techniques widely used in these systems. Cyclic Redundancy Check Codes A popular error detection coding technique is the cyclic redundancy check (CRC) code. CRC codes are used in many standards including those of third and fourth generation of mobile communications systems (3G and 4G), fixed broadband standards based on digital subscriber line (DSL) and broadband satellite communications systems. CRC coding can work with var- iable input data sizes, which is in contrast to parity bit coding techniques. The principle behind CRC coding can be explained by the following division process. Assume data block '124354' is to be transmitted. Let us calculate the integer division 124354 241, where 241 is a prime number: 124354=515*241+239 The data '124354' is then appended by the remainder of the above division, namely '239', and the resulting data block '124354 239' is transmitted. The receiver examines the Broadband Telecommunications