mbers of the same length as the channel codeword. In error control based on error detection and retransmission hard decision decoding, each real number in the sequence (automatic repeat request [ARQ]) can be more efficient is mapped to a channel code symbol before being than error correction alone (forward error correction processed by the channel decoder. When the real numbers [FEC]). We review the most important ARQ techniques are left unquantized or quantized to a number of levels that and discuss hybrid methods that combine ARQ and is greater than the size of the channel code alphabet, one Communications Engineering Desk Reference; ISBN: 9780123746481 Copyright © 2007 Elsevier Inc. All rights reserved CHAPTER 3.4 Channel protection fundamentals Source Source Encoder Channel Encoder Modulator Channel Destination Source Decoder Channel Decoder Demodulator Figure 3.4-1 Basic components of a digital communication system. 3.4.2 Shannon's source and 3.4.2.1 Source coding channel theorems A code C of size M over an alphabet B is a set of M words, possibly varying in length, made up of symbols from B. An information source is given by a sequence of random The words in C are called codewords. The length of variables Xn, each of which takes values in an alphabet A. a codeword C (i.e., the number of symbols in c) is We say that the source is discrete if the alphabet A is finite denoted c. When all the codewords in C have the same or countable. We say that the source is memoryless if the length k, we say that C is a block code of length k. random variables Xn are independent and identically dis- tributed. For simplicity, a discrete memoryless source Xn 3.4.2.1.1 Lossless source coding will be denoted by a random variable X whose probability To compress a discrete source Xn over alphabet A without distribution p(x) is the probability distribution common information loss, one can use a lossless encoding scheme to all the random variables Xn. (C,f), which consists of a code C (known as a source code) Definition 3.4.1 (Entro