tion of redundancy to the the return of a positive or negative acknowledgement (ACK or transmitted digit stream in such a way that errors introduced in the NAK) to the sender on receipt of a data block, a system known as channel can be detected, and in certain circumstances corrected, in stop-and-wait ARQ. In go-back-N ARQ, receipt of a NAK by the the receiver. It is therefore a form of channel coding, so called transmitter makes it retransmit the erroneous codeword and the N-1 because it compensates for imperfections in the channel; the other following ones, where N is chosen so that the time taken to send N form of channel coding is transmission (or line coding), which has codewords is less than the round trip delay from transmitter to different objectives such as spectrum shaping of the transmitted receiver and back again. This obviates the need for a buffer at the signal. ECC is used to lower the probability of error from the input receiver. In selective repeat ARQ, only the codewords for which to the output of the communication system. The added redundancy NAKs have been returned are re-transmitted. Performance analysis means, however, that extra digits have to be transmitted over the (Lin, 1983) shows that this is the most efficient system, although it channel, so that either the channel transmission rate must be in- requires an adequate buffer in the receiver. creased, or the rate of transmission of digits from input to output must be reduced. 14.2.3 Arithmetic for ECC The controlled addition of redundancy in ECC contrasts with source coding (data compression) in which redundancy is removed from the source signal. For a signal (such as speech) with a high In a digital communication system, each transmitted digit is selected degree of intrinsic redundancy it would in principle be possible to from a finite set of M values and is described as an M-ary digit. For perform some error detection and correction at the receiver without example, binary digits (bits) have one of two values, which may be adding further