E303: Communication Systems

Professor A. Manikas Chair of Communications and Array Processing

Imperial College London

An Overview of Fundamentals: Principles of PCM

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 1 / 52 Table of Contents 1 Glossary 3 2 Introduction 4 3 PCM: Bandwidth & Bandwidth Expansion Factor 8 4 The Quantisation Process (output point-A2) 10 Uniform Quantisers 16 Comments on Uniform Quantiser 18 Non-Uniform Quantisers 21 max(SNR) Non-Uniform Quantisers 23 Companders (non-Uniform Quantisers) 26 Compression Rules (A and mu) The 6dB Law Differential Quantisers 34 Type-1 Type-2 (mse Diff Quant) Examples 5 Noise Effects in a Binary PCM 44 Threshold Effects in a Binary PCM 45 Threshold Point 46 Comments on Threshold Effects 47 6 CCITT Standards: Differential PCM (DPCM) 48 7 Problems of DPCM 49 8 Appendix-1: Alex Reeves - the "Father of PCM" 50 Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 2 / 52 Glossary Glossary CCITT = Comite Consultatif Internationale de Telegraphie et Telephonie This is an international committee based in Geneva, Switzerland, that recommends telecommunications standards, including the audio compression/decompression standards (codecs) and the famous V. standards for modem speed and compression (V.34 and so on). Although this organization changed its name to ITU-T (International Telecommunications Union-Telecommunication), the old French name lives on. Related standards: CCITT A-law, CCITT µ-law, codec, ITU-T, V. standards CCITT A-law = This is a CCITT-ratified audio encoding and compression technique supported by Windows and Web phones. Among other implementations, A-law was originally intended as a phone-communications standard. Related standards: CCITT µ-law, ITU-T. GSM = Groupe Speciale Mobile (Global System for Mobile Communications) This set of standards is widely used in Europe for cellular communications. The audio encoding subset of the GSM standard is best known to computer users because its data compression and decompression techniques are also being used for Web-phone communication and encoding WAV and AIFF files. Related standards: AIFF, codec, WAV

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 3 / 52 Introduction Introduction

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 4 / 52 Introduction

PCM = sampled quantised values of an analogue signal are transmitted via a sequence of codewords.

i.e. after sampling & quantisation, a Source Encoder is used to map the quantised levels (i.e. o/p of quantiser) to codewords of γ bits

i.e. quantised level codeword of γ bits 7→ and, then a digital modulator is used to transmit the bits, i.e. PCM system

There are three popular PCM source encoders (or, in other words, quantisation-levels Encoders).

I Binary Coded Decimal (BCD) source encoder I Folded BCD source encoder I Gray Code (GC) source encoder

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 5 / 52 Introduction

g(input) gq (output) 7→ samples gq : occurs at a rate Fs sec (N.B: Fs 2 Fg ) ≥ · Q = quantiser’slevels;

bits γ = log2(Q) level

N.B.:

codeword rate (point B) = quant. levels rate = sampling rate

γ bit codewords↑ levels↑ samples↑ − sec sec sec = Fs = 2Fg (1)

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 6 / 52 Introduction

bit rate: rb = γ Fs e.g. for Q = 16 levels then rb = 4 Fs ↑ bits↑ levels↑ γ level sec bits sec γ=4 γ=4 ↓ ↓ (e.g. transmitted sequ. = 101011001101 ...) z}|{ z}|{ γ=↑ 4 |{z} versions of PCM: I Differential PCM (DPCM),PCM with differential Quant. I Delta Modulation (DM): PCM with diff. quants having 2 levels i.e. +∆ or ∆ − are encoded↑ using a single binary digit I Note: DM DPCM ∈ I Others

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 7 / 52 PCM: Bandwidth & Bandwidth Expansion Factor PCM: Bandwidth & Bandwidth Expansion Factor

we transmit several bits for each quantiser’so/p level BPCM > Fg ⇒ B denotes the channel bandwidth where PCM F represents the message bandwidth  g Definition (PCM Bandwidth) baseband bandwidth:

channel symbol rate BPCM Hz (2) ≥ 2 bandpass bandwidth:

channel symbol rate BPCM 2 Hz (3) ≥ 2 ×

Note that, by default, the Lower bound of the ‘baseband’bandwidth is assumed and used in this course

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 8 / 52 PCM: Bandwidth & Bandwidth Expansion Factor

Definition (Bandwidth Expansion Factor β) channel bandwidth β (4) , message bandwidth

N.B. for Binary PCM Channel Bandwidth: channel symbol rate B = PCM 2 bit rate γFs = = = γ F Hz 2 2 g ↑ log2 Q

BPCM = γFg (5) ⇒ Bandwidth Expansion Factor:

BPCM BPCM = γFg = γ β = γ (6) ⇒ Fg ⇒

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 9 / 52 The Quantisation Process (output point-A2) The Quantisation Process (output point-A2)

at point A2 : a signal discrete in amplitude and discrete in time.

The blocks up to the point A2, combined, can be considered as a discrete information source where a discrete message at its output is a “level” selected from the output levels of the quantiser.

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 10 / 52 The Quantisation Process (output point-A2) Definition The following mapping is called quantising

analogue samples finite set of levels 7→

where the symbol denotes a “map” 7→

N.B.: ADC

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 11 / 52 The Quantisation Process (output point-A2) quantiser parameters: Q : number of levels bi : input levels of the quantiser, with i = 0, 1, ... , Q   (b0 = lowest level): known as quantiser’s end-points   mi : outputs levels of the quantiser   (sampled values after quantisation) with i = 1, ... , Q; known as output-levels  rule: connects the input of the quantiser to m  i   RULE:

the sampled values g(kTs ) of an analogue signal g(t) are converted to one of Q allowable output-levels m1, m2, ... , mQ according to the rule:

g(kTs ) mi (or equivalently gq (kTs ) = mi ) 7→ iff bi 1 g(kTs ) bi with b0 = ∞, bQ = +∞ − ≤ ≤ − Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 12 / 52 The Quantisation Process (output point-A2) quantisation noise at each sample instance:

nq (kTs ) = gq (kTs ) gs (kTs ) (7) − 2 If the power of the quantisation noise is small, i.e. Pnq = nq (kTs ) = small, then the quantised signal (i.e. signal at the outputE of the quantiser)  is a good approximation of the original signal. quality of approximation may be improved by the careful choice of bi ’sand mi ’sand such as a measure of performance is optimised. e.g. measure of performance: Signal to quantisation Noise power Ratio (SNRq) signal power Pg SNRq = = quant. noise power Pnq

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 13 / 52 The Quantisation Process (output point-A2) N.B.: Types of Quantisation uniform non-uniform quantisers : uniform, or non-uniform  differential =  plus a differential circuit    Transfer Function: uniform quantiser non-uniform quantiser

for signals with CF = small for signals with CF = large

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 14 / 52 The Quantisation Process (output point-A2) The following figure illustrates the main characteristics of different types of quantisers

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 15 / 52 The Quantisation Process (output point-A2) Uniform Quantisers Uniform Quantisers N.B.: Uniform quantisers are appropriate for uncorrelated samples

let us change our notation: gq (kTs ) to gq and g(kTs ) to g the range of the continuous random variable g is divided into Q intervals of equal length ∆

(value of g) (midpoint of the quantising interval in which the value of g falls) 7→

bi 1 + bi or equivalently m = − for i = 1, 2, ... , Q (8) i 2

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 16 / 52 The Quantisation Process (output point-A2) Uniform Quantisers step size ∆: bQ b0 ∆ = − (9) Q rule:

bi = b0 + i ∆ rule: gq = mi iff bi 1 < g bi where bi 1 +b·i − ≤ mi = − (10)  2 for i = 1, 2, ... , Q

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 17 / 52 The Quantisation Process (output point-A2) Comments on Uniform Quantiser Comments on Uniform Quantiser

2 Since, in general, Q = large Pg Pg g ⇒ q ' ≡ E  Furthermore, large Q implies that Fidelity of quantiser = ↑

gq g '

Q = 8 16 are just suffi cient for good intelligibility of speech; − (but quantising noise can be easily heard at the background) voice telephony: minimum 128 levels; (i.e. SNRq 42dB) ' N.B.: 128 levels 7-bits to represent each level ⇒ transmission bandwidth = ⇒ ↑

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 18 / 52 The Quantisation Process (output point-A2) Comments on Uniform Quantiser quantiser = UNIFORM if ( pdf of the input signal = UNIFORM then 2 2γ SNRq = Q = 2 (11)

Quantisation Noise Power Pnq : ∆2 quantisation Noise Power: P = (12) nq 12 rms value of Quant. Noise: ∆ rms value of Quant. Noise = fixed = = f g (13) √12 6 { }

∴ if g(t) = small for extended period of time

SNRq < the design value (14) ⇒

this phenomenon↑ is obvious if the signal waveform has a large CREST FACTOR Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 19 / 52 The Quantisation Process (output point-A2) Comments on Uniform Quantiser SNRq as a function of the Crest Factor

Remember: peak CREST FACTOR (15) ≡ rms By using variable spacing CREST FACTOR effects = ⇒ ↓

small spacing↑ near 0 and large| spacing{z at the extremes} I = this leads to NON-UNIFORM quantisers Prof. A. Manikas⇒ (Imperial College) E303: Principles of PCM v.19 20 / 52 The Quantisation Process (output point-A2) Non-Uniform Quantisers Non-Uniform Quantisers N.B.: Non-Uniform quantisers are (like unif. quants) appropriate for uncorrelated samples

step size = variable = ∆i

if pdf = uniform i/p 6 then non-uniform quants yield higher SNRq than uniform quants

rms value of nq is not constant but depends on the sampled value g(kTs ) of g(t)

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 21 / 52 The Quantisation Process (output point-A2) Non-Uniform Quantisers

rule: gq = mi iff bi 1 < g bi − ≤

where b0 = ∞, bQ = +∞ ∆i = bi bi 1 = variable − − − example:

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 22 / 52 The Quantisation Process (output point-A2) max(SNR) Non-Uniform Quantisers max(SNR) Non-Uniform Quantisers

bi , mi are chosen to maximize SNRq as follows: 2 I since Q = large Pgq Pg g SNRq = max if Pnq = min where ⇒ ' ≡ E ⇒ Q b  i 2 Pnq = ∑ (g mi ) pdfg dg (16) bi 1 − · · i=1 Z − I Therefore:

min Pnq (17) mi ,bi

dP nq = 0 dbj (17) dP (18) ⇐⇒  nq = 0  dmj 2 2 (bj mj ) pdfg (bj ) (bj mj+1) pdfg (bj ) = 0 for j = 1, 2, ... , Q 1 − bj · − − · − ⇒ 2 (g mj ) pdfg (g) dg = 0 for j = 1, 2, ... , Q ( − · bj 1 − · · − (19) Prof. A. Manikas (ImperialR College) E303: Principles of PCM v.19 23 / 52 In the second branch of Equation-19 the parameter mj can be seen as the statistical mean of the jth quantiser interval The Quantisation Process (output point-A2) max(SNR) Non-Uniform Quantisers Note:

the above set of equations (i.e. (19)) cannot be solved in closed form for a general pdf. Therefore for a specific pdf an appropriate method is given below in a step-form:

METHOD:

1. choose a m1 2. calculate bi ’s, mi ’s 3. check if mQ is the mean of the interval [bQ 1, bQ = ∞] if yes STOP − → else choose a new m1 and then goto step-2 →

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 24 / 52 The Quantisation Process (output point-A2) max(SNR) Non-Uniform Quantisers A SPECIAL CASE max(SNR) Non-Uniform Quantiser of a Gaussian Input Signal

if the input signal has a Gaussian amplitude pdf, that is pdfq = N(0, σg ) then it can be proved that:

2 1.96 Pnq = 2.2σg Q− (12)

not easy↑ to derive

In this case the Signal-to-quantisation Noise Ratio becomes:

2 Pgq σg 1.96 SNRq = = 2 1.96 = 0.45Q (13) Pnq 2.2σg Q −

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 25 / 52 The Quantisation Process (output point-A2) Companders (non-Uniform Quantisers) Companders (non-Uniform Quantisers) Their performance independent of CF SAMPLE UNIFORM SAMPLE Non-unif. Quant = + + COMPRESSION quantisER EXPANDER Compressor + Expander Compander ≡ 1 f f− g gc i.e. gc =f g : pdfg = uniform g 7→ { } c 7→ means↑ ”such that"

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 26 / 52 The Quantisation Process (output point-A2) Companders (non-Uniform Quantisers)

Popular companders: use log compression

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 27 / 52 The Quantisation Process (output point-A2) Companders (non-Uniform Quantisers) Two compression rules (A-law and µ-law) which are used in PSTN and provide a SNRq independent of signal statistics are given below:

µ-law (USA) A-law (Europe)

A 87.6 In practice ' µ 100  ' Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 28 / 52 The Quantisation Process (output point-A2) Companders (non-Uniform Quantisers) Compression-Rules (PCM systems)

Definitions (The µ and A laws)

µ-law A-law g A g g 1 g · max ln(1+µ ) 1+|ln(A)| gmax 0 g < A g = · gmax g g = · ≤ max c ln(1+| µ) | max c  1+ln(A g ) gmax 1 g  ·| | gmax < 1  1+ln(A) A ≤ gmax

  where

gc = compressor’soutput signal (i.e. input to uniform quantiser) g = compressor’sinput signal

gmax = maximum value of the signal g

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 29 / 52 The Quantisation Process (output point-A2) Companders (non-Uniform Quantisers) 6dB Law uniform quantisera:

SNRq = 4.77 + 6γ 20 log(CF) dB (20) − µ-law: SNRq = 4.77 + 6γ 20 log(ln(1 + µ)) dB (21) − A-law: SNRq = 4.77 + 6γ 20 log(1 + ln A) dB (22) − a peak Remember: CF = rms

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 30 / 52 The Quantisation Process (output point-A2) Companders (non-Uniform Quantisers) Figure illustrating the main characteristics of quantisers

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 31 / 52 The Quantisation Process (output point-A2) Companders (non-Uniform Quantisers) COMMENTS

uniform & non-uniform quantisers:

use them when samples are uncorrelated with each other (i.e. the sequence is quantised independently of the values of the preceding samples)

practical situation:

the sequence g(kTs ) consists of samples which are correlated with each other. In{ such a case} use differential quantiser.

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 32 / 52 The Quantisation Process (output point-A2) Companders (non-Uniform Quantisers)

Examples PSTN

8 Fs = 8kHz, Q = 2 (A = 87.6 or µ = 100), γ = 8 bits/level

i.e. bit rate: rb = Fs γ = 8k 8 = 64 kbits/sec × × Mobile-GSM

13 Fs = 8kHz, Q = 2 uniform γ = 13 bits/level, ⇒

i.e. bit rate: rb = Fs γ = 8k 13 = 104 kbits/sec × ×

which, with a differential circuit, is reduced to rb = 13 kbits/sec

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 33 / 52 The Quantisation Process (output point-A2) Differential Quantisers Differential Quantisers N.B.: Differential quantisers are appropriate for correlated samples namely they take into account the sample to sample correlation in the quantisation process;

Definition (Type-1 Diff Quant.) Transmitter (Tx) Receiver (Rx)

input current message  sample   

The weights w are estimated based on autocorr. function of the input The Tx & Rx predictors should be identical.

I Therefore, the Tx transmits also its weights to the Rx (i.e. weights w are transmitted together with the data)

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 34 / 52 The Quantisation Process (output point-A2) Differential Quantisers

In practice, the variable being quantised is not g(kTs ) but the variable d(kTs )

where d(kTs ) = g(kTs ) gˆ (kTs ) (14) − i.e.

Because d(kTs ) has small variations, to achieve a certain level of performance, fewer bits are required. This implies that DPCM can achieve PCM performance levels with lower bit rates. 6dB law: SNR = 4.77 + 6γ a in dB q (15) where 10dB < −a < 7.77dB − Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 35 / 52 The Quantisation Process (output point-A2) Differential Quantisers

Definition (Type-2: mse Diff. Quant) the largest error reduction occurs when the differential quantiser operates on the differences between g(kTs ) and the minimum mean square error (min-mse) estimator gˆ (kTs ) of g(kTs ) N.B.: mse = a better quantiser but it needs more hardware

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 36 / 52 The Quantisation Process (output point-A2) Differential Quantisers

i.e. T gˆ (kTs ) = w g˜

where

T g˜ = [g˜ ((k 1)Ts ), g˜ ((k 2)Ts ), ... , g˜ ((k L)Ts )] − T − − ( w = [w1, w2, ... , wL]

rule:

2 choose w to minimize (g(kTs ) gˆ (kTs )) ... for the Tx E − 2 choose w to minimize (dq (kTs ) + gˆ (kTs )) ... for the Rx  E  

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 37 / 52 The Quantisation Process (output point-A2) Differential Quantisers Differential Quantisers: Examples Example (Power of d(kTs)) Consider:

At point B: The power of d(kTs ) can be found as follows:

2 2 σd = d E 2 2 = g (kTs ) + g ((k 1)Ts ) 2 g(kTs )g((k 1)Ts ) E  E − − E { − } =σ2 =σ2 2 Rgg (Ts )  g  g · | {z } ⇓ | {z } | {z } 2 2 2 Rgg (Ts ) σd = 2 σg 2 Rgg (Ts ) = 2 σg (1 2 ) (23) · − · · · − σg

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 38 / 52 The Quantisation Process (output point-A2) Differential Quantisers

Example (diff. circuit: signals)

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 39 / 52 The Quantisation Process (output point-A2) Differential Quantisers

disadvantages : unrecoverable degradation is introduced by the quantisation process.

I (Designer’stask is to keep this to a subjective acceptable level)

2 σg = Rgg (0)

Rgg (τ) 2 : is known as the normalized autocorrelation function σg

DPCM with the same No of bits/sample generally gives better → results than PCM with the same number of bits.

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 40 / 52 The Quantisation Process (output point-A2) Differential Quantisers

Example (mse DPCM)

assume a 4-level quantiser: I/P O/P +5 input +255 +7 0 ≤ input ≤ +4 +1 4≤ input≤ 1 1 −255≤ input≤ − 5 −7 − ≤ ≤ − −

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 41 / 52 The Quantisation Process (output point-A2) Differential Quantisers

Example (cont.)

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 42 / 52 The Quantisation Process (output point-A2) Differential Quantisers Example (cont.)

From the last two figures we can see that small variation to the i/p signal (25V 26V) ⇐⇒ large variations to⇓ o/p waveforms Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 43 / 52 Noise Effects in a Binary PCM Noise Effects in a Binary PCM It can be proved that the Signal-to-Noise Ratio at the output of a binary PCM system, which employs a BCD encoder/decoder and operates in the presence of noise, is given by the following expression SNRout at point A of the CS-Block-Diagram on page-4 2 2γ g0(t) 2 SNR = = (24) out E2 2 2γ n0(t) + nq0(t) 1 + 4 pe 2 E { } E { } · · where

pe = f(type of digital modulator)

pe = T (1 ρ) EUE − · q  e.g. if the digital modulator is a PSK-mod. then

pe = T √2 EUE · Prof. A. Manikas (Imperial College) E303: Principlesn of PCM o v.19 44 / 52 Noise Effects in a Binary PCM Threshold Effects in a Binary PCM Threshold Effects in a Binary PCM

22γ We have seen that: SNRout = 2γ 1+4 pe 2 · ·

Let us examine the following two cases: SNRin = high and SNRin = low

i) SNR in = HIGH ii) SNR in = LOW

SNRin = high pe = small SNRin = low pe = large ⇒ ⇒ 2γ 1 + 4 pe 2 1 ⇒ · · ' 2γ 2γ 2γ SNRout = 2 1 + 4 pe 2 4 pe 2 ⇒ ⇒ · · ' · ·

SNR 6γ dB SNR 1 out out 4 pe ⇒ ' ⇒ ' ·

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 45 / 52 Noise Effects in a Binary PCM Threshold Point Threshold Point Definition (Threshold point)

Threshold point is arbitrarily defined as the SNRin at which the SNRout, i.e.

22γ SNR = out 2γ 1 + 4 pe 2 · · falls 1dB below the maximum SNRout (i.e. 1dB below the value 22γ).

Proof. By using the above definition it can be shown (. . . for you. . . ) that the threshold point occurs when

1 pe = 16 22γ (25) · where γ is the number of bits per quant. level.

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 46 / 52 Noise Effects in a Binary PCM Comments on Threshold Effects Comments on Threshold Effects

Comments

The onset of threshold in PCM will result in a sudden in the output noise power. ↑ Psignal = SNRin = SNRout reaches 6γ dB and becomes independent of Psignal ↑ ⇒ ↑ ⇒ above threshold: increasing signal power no further improvement in SNRout ∴ ⇒ The limiting value of SNRout depends only on the number of bits γ per quantisation levels Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 47 / 52 CCITT Standards: Differential PCM (DPCM) CCITT Standards: Differential PCM (DPCM)

Definition (DPCM) DPCM , PCM which employs a differential quantiser

i.e. DPCM reduces the correlation that often exists between successive PCM samples

kbits kbits The CCITT standards 32 sec DPCM The CCITT standards 64 sec DPCM speech signal - Fg = 3.2kHz audio signal - Fg = 7kHz ksamples ksamples Fs = 8 sec Fs = 16 sec bits bits Q = 16 levels (i.e. γ = 4 level ) Q = 16 levels (i.e. γ = 4 level )

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 48 / 52 Problems of DPCM Problems of DPCM:

1 slope overload noise: occurs when outer quantisation level is too small for large input transitions and has to be used repeatedly

2 “Oscillation” or granular noise: occurs when the smallest Q-level is not zero. Then, for constant input, the coder output oscillates with amplitude equal to the smallest Q-level.

3 “Edge Busyness” noise: occurs when repetitive edge waveform is contaminated by noise which causes it to be coded by different sequences of Q-levels.

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 49 / 52 Appendix-1: Alex Reeves - the "Father of PCM"

&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 50 / 52 Appendix-1: Alex Reeves - the "Father of PCM" Appendix-1: Alex Reeves - the "Father of PCM" The Reeves Lectures celebrate the life and work of an Imperial Collegegraduate who was one of the world’sgreatest - but least conventional - scientists and engineers. Born a year after the death of Queen Victoria, he devised the technology on which our ’information age’depends. A committed pacifist, he developed a navigation system that altered the course - and perhaps the outcome - of WWII. A prolific and practical DEEE: Introduction of the 1st ALex-Reeves Lecture in inventor, he routinely experimented with the paranormal. 2006 Alec Harley Reeves was born on 2nd March 1902 at Redhill, "The Department of Electrical & Electronic Engineering hosts Surrey. He went to Reigate Grammar School and in 1918 won an annual lecture event directed to topics of wide interest and a Governors’Scholarship to the City and Guilds Engineering importance to engineers and the community. The new lecture College - later part of Imperial College. He received its ACGI series commemorates Alec Reeves, an alumnus of Imperial (equivalent to a BSc) in 1921 and then came to Imperial to College London. do postgraduate research. As well as important theoretical Reeves is widely regarded as ’thefather of the digital age’in work on radio, he invented a cathode ray tube radio direction that he was the inventor of Pulse Code Modulation, one of finder. the platforms which underpins today’spervasive digital In 1923, Reeves joined the communications firm International technology, and also undertook important work on radar and Western Electric. Working initially at New Southgate, North radio navigation in wartime Britain. Read more about Alec London, with the distinguished French engineer Maurice Reeves below. Deloraine, he helped create the first high-frequency radio The 2006 Alec Reeves Lectures, will be given by David telephone link across the Atlantic. Robertson and Tony Sale. David, a well known communicator When in 1925 IWE was taken over by International Telephone on science and technology, will be talking about the life and and Telegraph, Reeves moved to its Paris laboratory where, in work of Reeves himself. Tony has long been associated with 1937, he made his greatest contribution to engineering the historical and technical aspects of the vital wartime history. Pulse Code Modulation made possible the digital code-breaking activities, mainly undertaken at Bletchley Park, transmission of speech and our modern multimedia age. and will be talking about the events leading up to the re-build Though PCM was not used commercially until the later of the Colossus computer. invention of the transistor, Bell Labs applied it for the 14.30 Alec Reeves: designer of the digital age - David complex and cumbersome radio system on which Churchill and Roosevelt talked in total secrecy for much of WWII. Robertson - Room 408 "

Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 51 / 52 Appendix-1: Alex Reeves - the "Father of PCM" The Germans invaded France in 1940 and Alec Reeves escaped to Spain - reaching England on a coal boat without his possessions. Initially reluctant to do war work, he saw the moral necessity of defeating Hitler and joined the Royal Aircraft Establishment at Farnborough. Under the powerful Head of Scientific Intelligence, R V Jones, he played a key role in the Alec Reeves: designer of the digital age, by David Robertson ’battleof the beams’- helping detect and destroy the radio navigation Abstract: In 1937, a British electrical engineer solved a problem - and laid systems with which the Nazis inflicted deadly damage on cities like the foundations for the modern world. The engineer was Alec Reeves who London and Coventry. was working at the Paris laboratories of the American multinational ITT. Britain’scounter-attack was initially hampered by poor navigation and The ’problem’was how to reduce noise on long-distance radio telephone Reeves now joined the Telecommunications Research Establishment (TRE) circuits. Since Alexander Graham Bell had invented the telephone in 1876 to help our bombers find and hit their target. His solution was Oboe - the , speech and music were sent by what he called a ’voiceshaped current’- most accurate navigational device until the age of the satellite. one that varied continuously in line with the original sound. It worked well After WWII, Reeves returned to ITT’sUK laboratory STL where he but had a key weakness. Radio and cable systems - especially long ones - sought ways to increase the capacity and reliability of communications needed amplifiers to boost the signal at intermediate points. But when you systems, helped develop early electronic switching systems and was a amplified the signal, you automatically boosted the snap crackle and pop. pioneer of semiconductor devices - including the ’positive gap’germanium Reeves’answer was as simple as it was radical. Instead of sending an diode. He was also among the first to appreciate the potential of light as a ’analogue’or copy of the original sound, he proposed it be sampled at carrier, inspiring the STL team under Charles Kao and George Hockham regular intervals. The values of the samples would be turned into numbers that invented optical fibres. and these numbers transmitted as streams of unequivocal on-off pulses. Reeves spent his final years as a freelance ’boffi n’- spotting trends or His technique, was called Pulse Code Modulation. It eliminated unwanted proposing avenues of research for younger engineers to investigate. He was noise and is the basis of all modern telecoms networks. But there is much also a ’fatherfigure’in communications and electronics - predicting more to Reeves’legacy, for without PCM we’dhave no CDs, DVDs or universal mobile telephony, portable phone numbers, satellite navigation CD-ROMS; no digital radio and television; no digital landline or mobile and the Internet. And he saw how communications could change lifestyles, telephony; no broadband networks; no email, e-commerce or World Wide noting that ’thetransport of intelligence and information is ... much more Web. sensible than the much slower and more expensive moving about of human In World War 2, Reeves faced another challenge: how to ensure pilots bodies’. could find their targets, especially at night and in poor weather. His Alec Reeves died of bowel cancer on 13 October 1971. He had received answer? A ’blindbombing’system called Oboe so accurate that a bomb most - if perhaps not all - of the honours he could have expected as a dropped from 30,000 feet could land within 50 yards of its target. major scientist and inventor: an OBE and a CBE; the top medal from Later Reeves inspired the invention of that other key ingredient of our America’sFranklin Institute; awards from professional bodies like the IEE; ’information age’- optical fibres that transmit huge volumes of information honorary degrees - and a stamp in recognition of PCM. over tiny threads of glass. Alec Reeves is virtually unknown to the public at large. One reason may be the way he got his ideas. He was passionately If Alec Reeves is less well known than contemporaries of similar stature involved with spiritualism and believed he was inspired by daily ’dialogue’ such as Claude Shannon and Alan Turing, this may reflect his with great scientists from the past such as Michael Faraday. unconventional methods. Many creative people believe ideas are ’out These and other aspects of the life of a rare and controversial genius will there’,waiting to be grasped. Reeves took the phrase literally, sharing be explored by David Robertson in ’AlecReeves: Designer of the digital with his father - the distinguished geographer Edward Reeves - a lifelong age’ interest in the paranormal. Like Thomas Edison, Oliver Lodge and John Logie Baird, he thought he could communicate with the dead. He even claimed his work was ’guided’by the great 19th century experimentalist Michael Faraday. Prof. A. Manikas (Imperial College) E303: Principles of PCM v.19 52 / 52