PCM Basics

1. FUNDAMENTALS OF PCM

1.1 INTRODUCTION
This chapter is intended as an introduction to pulse code modulation (PCM), Time-Division multiplexing (TDM). Explanations have been limited to the most important principles and concepts. In order to keep this general survey brief and readily understandable circuitry is not dealt with in any great detail.
In the case of TDM the transmitted telephone signals are separated in a time period of 125 Micro second containing 32 time slot (see fig.1). One time slot in each of the consecutive period is allocated to each telephone signal.

1.2 PULSE AMPLITUDE SIGNAL:
It is sufficient to sample the waveform at regular intervals and to only transmit these samples (see fig.2). When a waveform is sampled, a train of short pulses is produced. The amplitude of each pulse represents the amplitude of the waveform at the specific sampling instants. This conversion is known as pulse amplitude modulation (PAM) .The envelope of the PAM signal reflects the original form of the curve (see fig.3.)
Relatively large intervals occur between each sample. These intervals can be used for transmitting other PAM signals, i.e. the samples of several different telephone signals can be transmitted one after the other in repeated cycles. When the pulses of several PAM signals are combined they form a PAM time-division multiplex signal (see fig. 4)

Periodic sampling of the analogue telephone signal “a”.
PAM signal consisting of he samples of analogue telephone signal “a”
PAM Time Division Multiplex signal consisting of samples taken from the three
analogue telephone signal “a , b , c” in repeated cycles.

2. SAMPLING THEOREM
The sampling theorem is used to determine the minimum rate at which an analogue signal can be sampled without information being lost when the original signal is recovered. The sampling frequency (f A) must be more than twice the highest frequency contained in the analogue signal (fS ):
fA > = 2fS

A sampling frequency (f A) of 8000Hz has been specified internationally for the frequency band (300 Hz to 3400 Hz) used in telephone systems, i.e. the telephone signal is sampled 8000 times per second. The interval between two consecutive samples from the same telephone signal (sampling interval = TA) is calculated as follows:

TA = 1/ fA = 1 / (8000 Hz) = 125 µs

shows how the telephone signal is fed via a low-pass filter to an electronic switch. The low-pass filter limits the frequency band to be transmitted; it suppresses frequencies higher than half the sampling frequency. The electronic switch -driven at the sampling frequency of 8000 Hz -takes samples from the telephone signal once every 125 µs. A pulse amplitude modulated signal is thus obtained at the output of the electronic switch.

Generation of PAM signals
3. QUANTIZING
The pulse amplitude modulated signals (PAM signal) still represents the telephone signal in analogue form. The first stage in the conversion to a digital signal is quantizing. The whole range of possible amplitude values is divided into quantizing intervals. The quantizing principle is shown in fig.6.
In order to simplify the explanation only 16 equal quantizing intervals are indicated. The quantizing intervals are numbered + 1 to + 8 in the positive range of the telephone signal and -1 to -8 in the negative range.

Uniform quantizing of the samples of an analogue telephone signal.
4. QUANTIZING DISTORTION
On the transmit side, therefore, several different analogue values fall within the same quantizing interval. On the receive side one signal value, corresponding-to the mid- point of the quantizing interval, is recovered for each quantizing interval. This causes small discrepancies to occur between the original telephone signal samples on the transmit side and the recovered values.

The discrepancy for each sample can be up to half a quantizing interval. The quantizing distortion which may arise on the receive side as a result of this manifests itself as noise superimposed on the useful signal. Quantizing distortion decreases as the number of quantizing intervals are increased. If the quantizing intervals are made sufficiently small the distortion will be minimal and the noise imperceptible.

If equally large quantizing intervals are used over the whole amplitude range, relatively large discrepancies will occur in the case of small signal amplitudes (uniform quantizing, see fig. 6). These discrepancies might be of the same order of magnitude as the input signals themselves and the signal -to- quantizing noise ratio would not be large enough. For this reason 256 unequal quantizing intervals are therefore used in the practice (non-uniform quantizing, see fig.7.)

- Small quantizing intervals for lower signal values.
- Larger quantizing intervals for higher signal values.

The ratio of the input signal to the possible discrepancy as a result of quantizing is therefore approximately the same for all input signal values.

Non-uniform quantizing is specified with the aid of characteristics. The CCITT recommends two such characteristics in G.711:

a) The 13- segment characteristic
(A-Law, e.g for the PCM 30 transmission system in Europe)
b) The 15 segment characteristic
(µ-Law, e.g. for the PCM24 transmission system in the USA)

Non-Uniform quantizing followed by encoding.

9. NON-UNIFORM QUANTIZING WITH A-LAW FOR THE
PCM 30 TRANSMISSION SYSTEM.

shows the “13 segment characteristic" (A-Law). It consists of seven segments in the positive range and seven in the negative range. The two segments bordering on zero are combined to form a single linear segment. This gives a characteristic with a total of 13 segments (hence the same “13 segment characteristic").

shows the positive section of the "13 segment characteristic" enlarged. The abscissa uses the value 1 as reference, this being the value assigned to the highest signal amplitude. The ordinate gives the numbers of the quantizing intervals (1 to 128) for positive signal amplitudes. The allocation of quantizing intervals to the Vin. signal amplitudes clearly demonstrates that higher signal amplitudes are quantized using a coarse scale and lower signal amplitudes using a fine scale. The Vin signal amplitudes are shown on the horizontal axis at the bottom of

Complete 13 segment Fig.9. Positive section of 13 segment characteristic
Characteristic (A-law) Characteristic (A-law) encoding, decoding.

5. ENCODING
The PCM signal to be transmitted is obtained by encoding the quantizing intervals. The electronic encoder allocates an 8-bit PCM word to each individual sample, this PCM word being associated with the determined quantizing interval (see fig. 7). The red arrows in fig. 9 show the PCM words for the individual signal amplitudes (samples). An 8-digit binary code is used for the 128 positive and 128 negative quantizing intervals (128+128) =256), the PCM words therefore have 8 bits. The first bit of all PCM words used for the positive quantizing intervals is a "1", the first bit of all PCM words used for the negative quantizing intervals is a "0". Bits no.2, 4 6 & 8 in every 8-bit PCM word are inverted for transmission as per CCITT Recommendations G.711 and G.732.

6. MULTIPLEXING
The 8-bit PCM words of a number of telephone signals can be transmitted consecutively in repeated cycles. A PCM word of one telephone signal is followed by the PCM words of all other telephone signals arranged in consecutive order. This creates a PCM time-division multiplex signal. The processes involved in multiplexing are carried out fully electronically. Fig. 10 shows the principle involved using four input signals sampled sequentially by switch A. Switch A moves from one input to the next, synchronous with the incoming PCM word train. The PCM time-division multiplex signal is then available at the output of switch A. The time interval within which a PCM word is transmitted is known as a time slot.

A bit train containing one PCM word from every of the input signals is known as pulse frame. In the example shown in Fig. 10, a pulse frame consists of 4 consecutive PCM words, one PCM word being from each of the input Signals S1 to S4. In the PCM 30 transmission system the pulse frame consists of 32 PCM words.

7. DIGITAL-TO-ANALOG CONVERSION (De-Multiplexing).
On the receive side the individual PCM signals are recovered from the Time Division Multiplex signal, i.e the 8-bit PCM words are distributed to the appropriate outputs. As with the multiplexing processes on the transmit side, the de-multiplexing processes are controlled fully electronically. Fig. 10 shows the principle involved using switch-B, synchronized with switch-A, distributes the PCM words to the 4 outputs.


8. Decoding
On the receive side a signal Vout is allocated to every 8-bit PCM word. It corresponds to the mid point of the particular quantizing interval. The characteristics for decoding is the same as that for non-uniform encoding on the transmit side. The Vout signal amplitudes are shown on the horizontal axis at the top of Fig. 9. The blue arrows in the diagram shows the Vout signal amplitudes which are allocated in the PCM words. The PCM words are decoded in the order in which they are received and converted a PAM signal. Finally the PAM signal is fed to a low pass filter, which reproduces the original analogue telephone signal.


Multiplexing & de-multiplexing principles.

9. SUMMARY OF FUNCTIONS:
- Transmit side.
a) Band-limiting of a telephone signal by means of a low-pass filter.
b) Sampling telephone signal. The resulting samples form a PAM signal.
c) Quantizing samples, i.e. the quantizing interval is determined for each sample.
d) Encoding samples, i.e. a binary PCM word is allocated to the determined quantizing interval. The telephone signal, which consists of 8-bit PCM words, is known as a PCM signal.
e) Multiplexing PCM signals, i.e. the PCM words in a telephone signals are interleaved with the PCM words from other telephone signals to form a PCM time-division multiplex signal.

- Receive side.
a) De-multiplexing PCM time-division multiplex signal, i.e. the PCM words of the telephone signals are distributed to the individual lines.
b) Decoding PCM words in the PCM signal, i.e. a signal amplitude is allocated to each PCM word. The signal amplitude is equal to the midpoint value of the particular quantizing interval. A PAM signal is produced again.
c) Reproducing the original analogue telephone signal from the PAM signal with the aid of a low-pass filter.

The sequence in which the individual steps are carried out depends on the system used. It may differ from the sequence given here. The samples from several telephone signals could, e.g, be combined into a PAM time-division multiplex signal and then quantized and encoded in one common unit.


10. DIGITAL TRANSMISSION:
In digital transmission systems, analogue telephone signals are converted into digital form using pulse code modulation. Transmission systems PCM 30 are the basic systems used for this conversion. Higher-order digital transmission systems can be formed from these basic systems.

10.1 GENERAL FEATURES OF A PCM TRANSMISSION SYSTEM
- Speech Circuits
Separate channels are provided in the P.C.M. Transmission system for each direction of speech in a connection (subscriber A to subscriber B, subscriber B to subscriber A). Each pair of identically-numbered channel time slots in the pulse frames of the two transmission directions form one voice circuit.

- Synchronization of receive and transmit sections
P.C.M. transmission systems terminate at both ends in a digital multiplex unit. Each multiplex unit contains transmit and a receive section (see fig. 11). The transmit sections form the 8-bit PCM words to be transmitted, and the receive section converts the received PCM words back to analogue signals. In either speech direction the receive section must recover the analogue signals using the same timing signal as its associated transmit section. Thus the information received from the transmit section by the receive section contains not only the PCM signals but also the timing signal used to form them. In order to carry out these functions the transmit section is provided with a timing signal generator and the receive section with a timing signal detector which extracts the timing signal from the received PCM signal. The receive section is thus synchronized, i.e. it operates in step with the transmit section of the same speech direction.

Transmission of timing signals via a PCM transmission route.

Block diagram of a PCM transmission system.

- Line codes
The PCM signal generated by the transmit section consists of a succession of 8-bit PCM words in NRZ binary code (NRZ = non-return-to-zero). This digital signal cannot however be sent directly to line on account of its D.C component. The transmit section of the multiplex unit converts the PCM signal into a pseudoternary signal, e.g. an AMI signal (AMI =alternate mark inversion) with no dc component. An AMI signal contains long "0" bit sequences. PCM transmission routes often use a variant of the pseudoternary AMI code -the HDBJ code (HDBJ = third-order high-density-bipolar). This code limits the number of consecutive "0" bits to three and thus optimizes timing signal recovery in the regenerative repeaters.

- Line Terminating Unit
The line terminating unit forms the link between the digital multiplex unit and the transmission lines (see fig .12 ) In the transmit direction, for example, it injects the feeding current for the regenerative repeaters. On the receive side it regenerates the PCM signal and extends it to the receive section of the digital multiplex unit.

- Regenerative repeaters
Regenerative repeaters are installed on PCM transmission routes at intervals of roughly 2 to 5 km (see fig. 12). They regenerate the PCM signals in both directions, thus eliminating any distortion which may be caused by external interference and the transmission parameters of the lines.

11. PCM TRANSMISSION SYSTEMS
The transmission systems recommended by the CCITT and described below are the PCM 30 system, with 2048kbit/s (CCITT Recommendation G. 732), these combine 30 channels per transmission direction respectively to form a time-division multiplex signal. PCM 30 transmission systems are used throughout Europe and in many non-European countries. PCM 30 also known as "primary transmission systems" or basic systems. Their most important features are given in Table 1.

PCM 30 TRANSMISSION SYSTEM
The PCM30 transmission system (see also Table-l) enable 30 conversation to be transmitted

Table 1. Characteristics of the PCM-30
12. PCM-30 TRANSMISSION SYSTEM
The PCM-30 transmission system ( See also Table -1) enables 30 conversion to be transmitted simultaneously, e.g. via two balanced pairs of a VF cable.

12.1 1Pulse frames. (see Fig.13)
8000 samples per second are transmitted as 8-bit PCM words in both directions for each of the 30 speech circuits. This means that, within a period of 125us (= reciprocal of 8kHz), 30 PCM words, each with 8 bits, are transmitted consecutively in each direction. In addition to these 30 PCM words a further 2x8 bits are also transmitted: 8 bits for signalling and 8 bits which contain alternately a bunched frame alignment signal and a service word. The 30 PCM words together with the other 2x8 bits form a pulse frame. Pulse frames are transmitted directly one after the other.

Pulse frame structure in a PCM-30 transmission system.

12.2 Bunched Frame alignment signal
The receive sections determine the timing of the pulse frames with the aid of the incoming bunched frame alignment signals, so that the bits can be allocated to the individual speech circuits in the correct sequence.
The bunched frame alignment signal and the service word are transmitted alternately in channel 0. Bit 1 in channel 0. Bit 1 in channel 0 is reserved for international use. The bunched frame alignment signal contained in bits 2 to 8 channel time slot 0 has always the same pattern (0011011).

Bit number
1
2
3
4
5
6
7
8


Binary value
X
0
0
1
1
0
1
1


Bunched frame alignment signal in channel time slot 0 of a pulse frame
Bit 1 = x reserved for international use
Bit 2 to 8 bunched frame alignment signal

Service word (see fig. 15)
Service words carry service signals. Bit 3 of the service signals an urgent alarm. "0" means "no alarm"; "1" signals one of the following conditions:
Power failure (if signal still possible)
Codec failure
Failure of incoming 2048kbit/s signal
Failure of frame alignment
Bunched frame alignment signal error rate > lx10-3
Bits 4 to 8 of the service word are reserved for national use.


Bit number
1
2
3
4
5
6
7
8


Binary value
X
1
A
Y
Y
Y
Y
Y


Service word in channel time slot 0 of pulse frame
Bit 1 = x reserved for international use
Bit 2 = 1 prevents faulty identification of bunched frame alignment signal
Bit 3 = A reserved for signalling urgent international alarms
Bit 4 to 8 = Y bunched frame alignment signal

12.3 Signalling
Signalling (e.g. answer, clear back and dial signals) is provided for in channel 16 ("Out-slot") .A distinction is made between:
Channel -associated signalling for 30 speech circuits and
Signalling via a common channel with 64 Kbit/s
In the case of channel-associated signalling channel 16 is subdivided so that particular bits are available for each of the 30 telephone channels (see Table-2). For this reason, 16 pulse frames are combined to form a multi-frame. A bunched multi-frame alignment signal in channel time slot 16 of pulse frame 0 is transmitted at the start of the multi-frame. The bit pattern of this bunched multi- frame alignment signal is "0000".
The channel time slots 16 in a multi-frame are each divided into two groups of 4 bits (a, b, c, d). One of these 4-bit groups in the multi-frame is allocated to each of the 30 telephone channels for signalling. The signalling bit rate per telephone channel is then 2 Kbit/s.
If channel 16 (= 64 Kbit/s) is not to be used for channel associated signalling it can be used for transmitting other digital signals, e. g. for common channel signalling (CCITT No.6, No.7) or for data transmission.

Pulse Frame Nos.
Bits in channel time slot 16
a b c d a b c d
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
0 0 0 0
Telephone Channel 1
Telephone Channel 2
Telephone Channel 3
Telephone Channel 4
Telephone Channel 5
Telephone Channel 6
Telephone Channel 7
Telephone Channel 8
Telephone Channel 9
Telephone Channel 10
Telephone Channel 11
Telephone Channel 12
Telephone Channel 13
Telephone Channel 14
Telephone Channel 15
x y x x
Telephone Channel 16
Telephone Channel 17
Telephone Channel 18
Telephone Channel 19
Telephone Channel 20
Telephone Channel 21
Telephone Channel 22
Telephone Channel 23
Telephone Channel 24
Telephone Channel 25
Telephone Channel 26
Telephone Channel 27
Telephone Channel 28
Telephone Channel 29
Telephone Channel 30

Table 2 Allocation of the bits in the channel time slot 16 of PCM 30 multi-frame to the telephone channels for channel associated signalling.
0000 = Bunched multi-frame signal
X = Reserve bit.
Y = Bit for signalling failure of multi-frame alignment.

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