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View File - University of Engineering and Technology, Taxila

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the channel <strong>and</strong> reconstruct the source signal with an arbitrarily smallprobability <strong>of</strong> error ifHðX ÞT s> C cT cð6:3ÞThe parameter C c =T c is called the critical rate. When HðX Þ=T s ¼ C c =T c ,thesystem is said to be operating at the critical rate (at capacity). Fig. 5.8 (inChap. 5, Sec. 5.2) has demonstrated that operating a system at capacity isachievable only if the value <strong>of</strong> E b =N 0 is above the Shannon limit; that is,log e 2ð 1:6dBÞ. Recently, however, parallel-concatenated convolutional codeshave achieved a performance close to this theoretical limit [6] (more is said <strong>of</strong>the convolutional coding technique in Sec. 6.2.2). In general, the objective isto achieve maximum data transfer in a minimum b<strong>and</strong>width while maintainingan acceptable quality <strong>of</strong> transmission. To achieve this, an error-detecting codemust be devised. The most desirable solution is to use a forward errorcorrection (FEC) technique. Error detection coding is a technique foradding redundant (extra) bits to a data stream in such a way that an error inthe data stream can be detected [7].6.2 FORWARD ERROR CORRECTION CODINGTECHNIQUESForward error correction (FEC) techniques are widely used in control <strong>and</strong>telecommunication systems. FEC codes may be divided into two broad types:linear block codes <strong>and</strong> convolutional codes.6.2.1 Linear Block CodesIn linear block codes, the encoder splits up (or maps) the incoming data streaminto blocks <strong>of</strong> k digits <strong>and</strong> processes each block individually by addingredundancy (extra digits) as a parity check according to a predefined algorithm.The output <strong>of</strong> the encoder is a codeword with n digits, where n > k. Thecode rate is also given by (6.1).The general form <strong>of</strong> a linear block codeword isY ¼ GXð6:4ÞCopyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.

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