An Overview of the Digital Modulation and Coding
...as providing some error-correction capability for the system. It does this by using a mapping from input sequence {Un} to the code sequence {Xn}, which inserts redundancy and which utilizes memory. Whereas in N modulator time slots, an uncoded system could transmit MN possible signals, the coded system will enforce constraints that allow a smaller number of coded signals. In this sense, each modulator symbol doesn’t carry as much information as it apparently could, and symbols are in some sense redundant. Memory is the other crucial aspect of good encoding schemes. In essence, a given message bit at the encoder input influences several, perhaps many, output symbols, hence waveform intervals. This provides a noise-averaging feature, which makes the decoder less vulnerable to the effects of noise, distortion, fading, and the like, occurring in one signaling interval. We will find that this is nothing more than an exploitation of the law of large numbers associated with a random channel mechanism. An additional role of the channel encoder, although one less commonly attributed to it, may be that of spectral shaping. The memory of the encoder can, if desired, produce an output symbol stream that ultimately shapes the power spectrum of the signal produced by the modulator. An example is the alternate mark inversion technique described previously; a very simple channel encoder remembers the polarity of the previous 1 symbol and uses the opposite upon receiving the next 1. the resultant spectrum has very small power spectral content near zero frequency. Another important example is in coding for magnetic recording channels, where encoding the binary magnetization signal to satisfy run-length constraints helps to increase the information density per unit area of the medium. We have seen that the combination of channel encoder and modulator provides a mapping from a bit stream to a signal waveform, which has aspects of redundancy and memory. In some applications, it is clear where these functions reside. For example, in the coding scheme used in the voyager mission to the outer planets, message bits were stream encoded, producing two coded symbols for every message bit, with a memory length of six information bits. Each coded symbol then simply phase switched the transmitted microwave signal. The memory and redundancy are clearly introduced by the encoder, and the modulator is a rather simple device. Now that we have characterized the function of the channel encoder and modulator, we might expect that the demodulator and channel decoder ought to be easily understood. Often, however, a quite improper conclusion about optimal detection is made, that the demodulator should make its best judgment of what the modulator input symbol was in a given interval and then pass this decision on to the decoder, which in turn uses the known encoder structure to make a best judgment of what encoder input message was sent. This will be called the error correcting code viewpoint. Good encoder/decoder combinations can indeed overcome scattered, or even bursty, errors produced in the demodulator decision process and dramatically improve system performance. The fact is, however, mach better performance is generally available if the demodulator resists the temptation to decide symbol by symbol, but instead passes to the decoder a seq...