1. Introduction
1>Motivations for the use of PCM and digital transmission
This process of converting an analogue wave form such as that of telephone speech to a digital form inevitably involves an increase in bandwidth or in the frequency spectrum occupied in the medium being used and would appear at first to be a rather pointless complication of the process of conveying voice signals . The technical and economic advantages will be explained in following sections but a brief initial outline may help to put things in perspective. 2> The Quest for Time Division Multiplexing
For many years there have been attempts to realize the economic potentialities of time division of time division multiplexing (TDM) .It is by no means a new concept and was used in telegraphy before telegraphy came on the scene .The devices used were simply synchronized commutators where one at the sending end “sampled” each of a number of individual channels in sequence and transmitted the samples in sequence .The other devices at the receiving end received the samples and distributed them in the correct sequence to the corresponding individual channels. Obviously there was a problem of maintaining the commutators in synchronism. This problem remains but modern electronic methods have provided cheap and reliable ways of achieving the required result. Where, as in telegraphy, the information is digital, i.e. comprises a succession of units of information limited to a very few discrete values, e.g. the binary mark and space of telegraphy ,TDM is extremely simple and cheap.
It has long been known that an analogue wave form of limited bandwidth restricted to an upper frequency limited of f1 may be accurately conveyed by 2f1. If these samples are transmitted as narrow pulses, then the pluses corresponding to several channels may be sent consecutively in a regular cycle and it thus becomes feasible to apply TDM to analogue information.
This form of TDM has been used for transmission purpose and also for switching ,and various modulation techniques have been employed : for instance pulses amplitude ,pluses width and pulses position .In switching ,where the samples can be transmitted over wide band high ways, reasonable control of signal impairments can be achieved but on junction and truck routes the inevitable distortion of the pulses in amplitude and phase make it very difficult to control inter-channel interface or crosstalk without prohibitively costly equalizing .
It was partly in this quest for a more satisfactory answer to the TDM problem and partly to counter the high noise levels of earlier radio links that the late Alec Reeves over 30 years ago conceived the idea of PCM in which an analogue wave is sampled at regular intervals by narrow pluses and a numerical “description” of the amplitude of each sample is transmitted in place of the analogue wave form.
Although originally conceived against the background of noisy radio links， the first large scale commercial use of PCM has been on cable pairs .The
economic importance of increasing the capacity of the vast quantities of copper parts now installed on short-and medium-haul routes has long been recognized .The relatively poor crosstalk and noise characteristics of these pairs has proved a major obstacle to the introduction of multiplexing by traditional FDM methods .With PCM it has proved practicable as will be explained in the following sections ,to use two regular cable pairs to handle from 24 to 32 conversations. The contribution of PCM to the low quality radio link has not been ignored and not long ago the inventor was honoured in the USA in recognition of the use PCM to transmit Mariner IV’s TV pictures 200 000 000 miles back from Mars to our planet.
3> Noise Cancelling Aspects of Digital Transmission
The conversion of analogue information to a binary digital form of coding introduces a new range of opportunity and problems. The key to the attractions of digital transmission resides in the concept of regeneration. In classical analogue communication system the limiting factor in the establishing of a satisfactory connection between two remote users is the signal/noise ratio. Modern methods have established very satisfactory standards in regard to the limiting of attenuations of the signal, but no analogue amplifier can prevent the inevitable accumulation of noise. Each time the signal is amplified so also is the noise which has been added to it within the pass band involved.
The characteristic of digital transmission is that since has a restricted number of states (typically for binary data only two) then provided the acquired noise on any section does not exceed the level at which ambiguities (errors) will occur in recognizing which state was transmitted, the signal may be regenerated without error and noise is not accumulated. This is true in regard to all essential characteristic of the signal except for a residual form of noise known as phase or timing jitter, i.e. the varying displacement in time of the pulses from their ideal isochronous positions.
This ability of regeneration to avoid almost all noise accumulation results in the signal/noise ratio required on each section to reduce regeneration interpretation errors to a negligible quantity being much lower than an analogue system could tolerate on a complete connection. This means that the wider frequency spectrum requirements of the digital mode are more than counterbalanced (certainly on enclosed media) by the vastly improved noise and interference tolerance. This is an example of exchanging bandwidth for signal/noise ratio.
4> Time Switching and Multiplexing
A further aspect of the “ruggedness” of PCM is that the flexibility of TDM, particularly in regard to switching but also in such operation as through group patching and multiplex reorganization is greatly enhanced by the ability to store the transmitted information for very short periods in order to perform “slot changing.” This aspect will be analyzed in detail later. The point to be stressed here is both expensive and unreliable. Binary storage is on the other hand the foundation of all computer technology and is cheap, simple and reliable.
5>Application to Uses Other Than Telephony
The process of digitizing analogue information is not confined to voice signals but been extensively explored in regard to music, video, facsimile and other forms of intelligence. For some of these forms long distance transmission by analogue methods can present problems of phase equalization to a degree which does not apply to voice signals and in regard to them the digital mode has added attractions.
It may seem inconsistent to claim for PCM methods a relief from problems of phase equalization and at the same time admit concern about build-up of phase jitter in digital systems. The point is that phase errors in an analogue mode, like other forms of noise and distortion cannot be identified and eliminated. In the digital mode phase jitter is identifiable and can be reduced to whatever degree is needed.
There is, finally, a rapidly growing demand for transmission of data and for higher speed telegraphy. Here the network is dealing with information in the required binary form and the basic attractions of a digital network are self evident. 6> Move to Comprehensive Digital Networks
The earlier section of what follow deal with the application of digital transmission to voice signals and other analogue information. Later there is examination of the greatly increased attraction in regard both to performance and to cost of complete networks with all transmission and switching operating in the digital mode so that analogue/digital conversion and its inverse occur only at terminals and all intervening operations are performed on the digital form of the information. This concept is more far-reaching in its consequence than might at first be supposed. It means that the peculiar characteristics of variant types of information and the special problems associated with them can be confined to the terminal conversion areas. The central transmission network operations remain basically the same for all types of information, except of course for the variations in digital rate needed. The flexibility of TDM allows these variations to be accommodated cheaply and simply and even admits of reorganization of the patterns of usage as terminal conversion techniques change or new modes of usage arise. The only significant reservation in this connection is the possibility that different types of information will present different demands in regard to error rate and phase jitter. As will be indicated later even these problems admit of some degree of adsorption into the terminal conversion areas.
These factors add up to some very considerable advantages for this mode of communication and account for the rapid advances in technology and scale of application over the last decade or so.
2. Theoretical Considerations of PCM
1> Introduction
Any practical communication system must be a compromise between the requirements for high quality and low cost. The frequency spectrum will be limited by the bandwidth which can be made available and there must be varying
degrees of cumulative distortion and noise. PCM cannot eliminate the transmission degradations but it does reduce and simplify them by confining them essentially to considerations of digital error rate and timing or phase jitter. This state of affairs is attained by acceptance of certain impairments introduced at the terminal analogue/digital and digital /analogue conversion processes. It is necessary to start by an examination of these impairments and the steps which have to be taken to hold them to a subjectively satisfactory level. It must be emphasized that the subjective aspects are very important and vary from one type of information to another, for instance as between speech and television. This section examines the problem mainly in relation to speech.
It is impossible in one short section to treat the theory in any depth. For more detailed examination the reader should such volumes as Cattermole’s. What will be attempted here is to indicate the nature of the issues involved and the ways in which an acceptable code of practice is being established. 2> Essential Elements of Terminal conversion
The essential elements involved in the terminal process are: sampling, quantizing, companding and coding. The last is inescapably involved with desired characteristics of digital transmission which will be dealt with further in subsequent sections. Some reference is needed here, however it also involved with the practical implementation of quantizing and companding.
Most of that which follows is relevant to the basic process of digitizing a signal voice channel and the need for this will probably arise. It should be remembered, however, that nearly all system in use to data are multiplex systems and these processes of sampling, quantizing and coding and their receiving counterparts are conducted sequentially by a common unit serving a number of voice channels. This sequential operation unit is then the essential basic of the multiplexing process. (1) Sampling
PCM represents in many ways the culmination of a long search for effective methods of employing time division multiplexing in the handing of analogue information. The basic of all such approaches is the idea of periodic sampling and PCM shares with all the earlier attempts the inherent limitations.
The first limitation is the relationship of the bandwidth or more accurately the upper limit of the spectrum to the sampling rate. The theory that a wave form limited to an upper frequency f may be completely conveyed by sampling at a rate of 2f is obviously as it stands theoretical idealism. It pre-supposes infinitely short sampling periods, a signal of infinite duration and perfect filters. The first of these issues is relatively unimportant and the distortion due to a sampling period of finite but practically feasible duration, for example 2 or 3% of the sampling rate, is quite negligible.
The other considerations are of practical importance. A signal such as speech is in its essential nature a succession of short duration periods of transmitted power with little or no sustained repetition, and filters are necessarily imperfect, especially if they are to be simple and cheap.
Determination of a practical compromiser for a sampling rate to handle voice signals over the 300~3400HZ spectrum now firmly established for telephony involves, therefore, some examination of the limitations of practicable methods of sampling and counterpart of demodulating and filtering, together with some consideration of subjective issues concerning the tolerance of voice communication to particular classes of distortion.
A value of 8000 samples per second has received world-wide agreement and is now one of the solidly established parameters. (2) Quantizing
The next problem to be examined is that of the distortion arising from the fundamental requirement of PCM that samples transmitted cannot be continuously variable but must be chosen from a finite set, the number of which is a function of the length of the binary number we are prepared to assign for the transmission of each sample. (3) Companding
One of the major problems of practical PCM is the very wide range of power levels to be handled. The range within the speech of one speaker is some 25 dB and if to this is added differences between loud and quiet talkers and the attenuation of established connections before a PCM link is encountered we are faced with a need to handle a range of some 60dB. If the lowest level to be handled just exceeds one step and peak clipping is reasonably limited then this 60dB on a uniform step basis would involve about ±1000 levels. (4) Coding
Coding, that is the expression of a quantized sample magnitude in terms of a binary number for transmission over the channel, may be executed in many ways. The main categories may be described as: Parallel coding Sequential coding Counting.
In briefly describing these coding methods certain restraints on the choice of code which may be imposed by some line system will be ignored and we will assume freedom to transmit any binary number.
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