TABLE OF CONTENTS Channel codes are vital in fully exploiting the potential capabilities of spread-spectrum communication systems. Although direct-sequence systems greatly suppress interference, practical systems require channel codes to deal with the residual interference and channel impairments such as fading. Frequency-hopping systems are designed to avoid interference, but the hopping into an unfavorable spectral region usually requires a channel code to maintain adequate performance. In this chapter, some of the fundamental results of coding theory [1], [2], [3], [4] are reviewed and then used to derive the corresponding receiver computations and the error probabilities of the decoded information bits.
A channel code for forward error control or error correction is a set of codewords that are used to improve communication reliability. An ( n, k) block code uses a codeword of n code symbols to represent k information symbols. Each symbol is selected from an alphabet of q symbols, and there are q k codewords. If q = 2 m, then an ( n, k) code of q- ary symbols is equivalent to an ( mn, mk) binary code. A block encoder can be implemented by using logic elements or memory to map a k-symbol information word into an n-symbol codeword. After the waveform representing a codeword is received and demodulated, the decoder uses the demodulator output to determine the information symbols corresponding to the codeword. If the demodulator produces a sequence of discrete...
