Comms

Sounds are broadcast by many animals. Some gibbons make sounds to hold their territory. Some birds make them to attract a mate. Some bats make them to locate prey. Some whales make them to find their way.

Some animals communicate to individuals or groups, like a partridge calling her young, geese talking to their partners, or bee-eaters talking among themselves.

In all these cases, the sound carries information and meaning. During this century, people have worked hard to discover the meanings of the audible and visual behaviour of many species of animals. Some people argue about whether any animals possess, or at least can understand, language and grammar.

Firstly, it can be used to denote what a message means to a sender and a recipient. For example, a bank statement ending with "£9876" carries a different meaning from one that says " - £123".

Secondly, it can be used in a more technical sense to denote the surprise value of a message. If someone says "Choose a letter which is after A and before J." - there will be 8 possibilities. The answer conveys information because it cannot be predicted. But if the request is "Choose a letter which is after A and before C.", the answer is predictable, and carries no information, except perhaps that the chooser has either understood an complied with the request, or, if the answer is not "B", has either misunderstood or disobeyed.

How can information be quantified? One way is to take all the outcomes and label them. In the first example the outcomes were B, C, D, E, F, G, H and I. A simple labelling scheme is to label the values 1, 2, 3, 4, etc. This is all very well, but what if there are 10000 outcomes? People solved this a long time ago, with a little help from the digit zero. When you get past 9 you start a tens value, so to write 10000 you don't need 10000 symbols - you only need five, chosen from a set of ten.

A simpler scheme is to use only two symbols, such as 1 and 2. To label eight values we could write 111, 112, 121, 122, 211, 212, 221 and 222. In practice it is far better to use 0 and 1, giving 000, 001, 010, 011, 100, 101, 110 and 111. With only these two symbols we can label any number of objects or values. Any pair of symbols would do, but the rules of computation would be the same. Since these include arithmetic, we might as well use numbers. In a computer or a communication system there are of course no numbers, only electric currents or light intensities. The hardware and software are programmed to use rules of logic that mean something to us, and of course the various parts of a system can recognize and use each others' outputs.

The lines below use the characters of a human language to represent a message. There are hundreds of different languages, each with its own characteristics. The examples show that a small proportion of errors need not reduce the intelligibility of a message to zero. This works because the printed word contains redundancy. The simple binary scheme does not - any error changes a character to another character, with little hope of detecting the error, let alone correcting it.

Characters in this string have been changed with a probability of  0 %.
Characters in this string have been changed with a probability of  1 %.
Characters in this string have been changed with a probability of  2 %.
Cearacters ingthis string have beon chmnged with a probability of  3 %.
Characters in this string have bken changed with a prrbability of  4 %.
Characters in thisostringphave been changed with a probability of  5 %.
Characters in this strqng zave bfen changed with a probabilltg of  6 %.
Charactersvin thiv string hrve been changed vith a probability of  7 %.
Charpctsrs in this string have ceen cvanged with a probability of  8 %.
Characters in this string havv been changed witf a probaaility of  9 %.
Characners in this stzing have beenwnhanged withra proqability of 10 %.
Chzractors ighthis string hive been ihanged with a prouability ot 11 %.
Ckaracters in ohis btringqhave beenmckanged with a probksilety of 12 %.
Chnriktkrs in this atring have qeen changed with a prabbbdlitr of 13 %.
Characterz insthis ktrins have been changod wrth alprobabilitnvof 14 %.
Characters in thjs strfoc hale bzen chafmej with a przbdbiliiy of 15 %.
Characters ik this string havenbeenjchanged wiwh a probabilioy of 16 %.
Cheracterr iaxlhis swringghave been lhanged wfthsa prosabiplty on 17 %.
Characters in thiststring havt been changed tith o probabieity of 18 %.
Chaqacters imstsis string have yecn ahanged wiyh n probajility of 19 %.
Chnracters inlthis string have xoentchanged with a psobaiility rf 20 %.

The numbers in the four digit columns have an extra digit called a parity. The digit ensures that in each column the data have all the party - they have either all an even number of digits or all an odd number. If one digit is changed by an error in transmission, the parity will be changed. This can be detected .although the error cannot be located within the word.

In the last column there are two extra digits. The idea is to use them for error correction. And in the last column the original encoding has been abandoned. The eight representations are designed to be as unlike each other as possible, so that an error in one digit does not make the word look like another legal value. Ideally it would be possible for the receiving system to guess the right answer when one digit is wrong. Can you discover the best set of eight five-digit codes?

Fundamental to communication is the concept of bandwidth, being one of the variables which determines the rate at which information can be sent.

Many of the sounds made by living things are produced for communication. Some sounds, of course, are only by-products, such as the sound of a flying swan, or the rustling of leaves in the wind. For a sound to convey information it must have structure . A continuous burst of sound conveys little information - the amplitude, duration, phase and frequency are the only variables. By modulating a wave in some way, the information content can be greatly increased. An early example of this was the amplitude modulation of radio waves using Morse code to chop the wave into little pieces according to a simple code. The Morse code increased the data rate by using shorter codes for the most frequently used letters , and longer codes for the least used ones. This scheme was designed to match English usage. It might not be so good in other languages. Most codes use the same length for all characters.

How much information can be packed into a signal? The bandwidth is the obvious factor. Another important factor is the amount of noise in the channel, expressed as a signal-to-noise ratio, S/N. We could imagine that running the transmitter flat-out could correspond to a number, such as 256, and that lower power levels could correspond to smaller numbers. But if the amount of noise corresponds to one unit, this scheme will not work, because adjacent values will be confused. Worse still, because noise fluctuates, the damage will sometimes be worse than the average .

In fact, many communication systems use extra data values to construct an error-correction system. The cost of the extra information is more than outweighed by the overall gain in data-rate. In fact, the design of a system has to balance channel bandwidth, S/N ratio, and acceptable error-rate, in determining the achieved data-rate. Most systems are digital, and the quantity of information is measured in bits, which are data which can take only two possible values. But many transmission systems are essentially of analogue type, modulated by the digital data.

The next three pictures illustrate the effect of signal-to-noise ratio on digitizing reliability..

The first picture symbolically represents a system in which the amplitude range is divided into eight levels. By transmitting signals quantized to these levels, digital data can be sent. The second picture hints at one of the reasons why this may not be a good idea. Noise on the signal has the potential to switch a value into the wrong level. The third picture shows this happening. Even with the noise level of the second picture occasional noise pulses could cause trouble.

This is one reason why computers have usually used binary hardware. Another reason is the difficulty of making devices with the required accuracy. Binary systems are also very efficient in storage capacity.

The next sets of pictures illustrate damped sines of about 160 Hz and about 640 Hz. Frequencies in the region of the second set are sometimes used in public places to gain attention before announcements. Each picture shows a pulse that is half as long as the previous one, though the frequency remains the same. The pictures show the oscillations in time and the frequency spectra in Hz, except the last one, which is on a different scale.. The shorter pulses occupy a wider bandwidth. If the pulse is short enough it is not heard as a musical tone but as a boom or a click. Although the last pulse includes s few complete cycles, they die away so rapidly that the perceived frequency is not very definite. This is hardly surprising, as the second cycle is only about a third as big as the first.

Click on these pictures to hear the sounds. Then choose 'Open file from its current location'..

You can try this by gently striking a suitable saucepan, wok, metal plate, or anything else which will ring . By changing the position and tightness of our grip you can generate a wide range of pulses. One reason that the pulses die away is that the object is losing energy to the sound wave. The grips that make short pulses are absorbing the energy into the hand. From the examples we see that the transition from musical tone to click depends on the number of cycles, not on the duration or the frequency.

This behaviour has practical uses. To test a piece of china or porcelain before purchase, give it a light tap with a pencil. If it is cracked, you will hear a dull click instead of a clear tone, even if the crack is invisible under the glaze. In older times, people in a train station often saw a man walking along the train, hitting each wheel with a hammer. He was listening for signs of cracked wheels.

The pulse in the second case is preceded by a faint tone. This happens because the recording is a small section from a stream of pulses at 1 second intervals, and this recording was timed badly. Although the tail of the pulse looks small on the graph, the ear has a logarithmic response, and can hear faint sounds. If the response of the ear were linear we would be continually be startled by loud sounds and straining to hear faint ones. A passing vehicle, for example, would create a very sharp pulse of perceived sound.

The logarithmic response is expressed in Bels, usually in the form of decibels, dB. The ear hears a change from 1 unit of power to 10 units of power as very similar to the change as from 10 units to 100 units. So as fra as hearing is concerned, going from a 1 watt amplifier to a 10 watt one is equivalent to going from a 10 watt one to a 100 watt one. The dB represents a fairly small change in power, which is fairly easily detected. As the decibel is a relative unit, some derived units are used for absolute measurements. For example, 10 dBm means 10 dB more power than 1 milliwatt, that is, 10 mW.

Sometimes figures in dB are quoted for the noise generated by airliners, cars, pneumatic drills, etc These are meaningless without the comparison power, and without a knowledge of the distance. On the other hand, if dB figures are given for two different aircraft, and we know that they were obtained under identical conditions and definitions, then they can be compared, even if their absolute value is meaningless.

Decibels must be used only for measuring power ratios. Sometimes people measure voltage ratios in dB, saying that a factor of 10 in voltage is 20 dB. This is correct only if they are comparing voltages at the same place in a system. But if an amplifier has an input impedance of 10 kilohms and drives an 8 ohm speaker, it is best to stick to volts and not mention dB. On the other hand, it is often useful to quote the power gain of RF amplifiers in dB.

By a handy coincidence, the logarithm₁₀ of 2 is about 3.01. So people sometimes refer to a factor of two in power as 3 dB, often when specifying a bandwidth. Again, dB must only be used when the impedances match, or when we have really measured the actual power.

The sounds made when digital data are sent on a telephone line are incomprehensible to us. Here is a simple example of a method of sending data. The first picture is a link to a larger picture. The second is a link to the sound.

The telephone line is an analogue channel with a bandwidth from about 300 Hz to about 3400 Hz. The problem is to pack as much information as possible into this band without generating errors. This method uses the amplitude and phases of the signal to represent the digital values.

As the first picture shows, the amplitude of the sine can take four different values. The small sections are a third as large as the big sections. By using these two amplitudes upside down, two more values are created. The wav file provides the sound of these data. A second channel is created in the same way, but with a phase shift compared with the first one. The two sets of four values can be combined in sixteen different ways. A rate of 9.6 kilobauds can be obtained on a telephone line. The transmitting and receiving systems have to be designed carefully in order to achieve the maximum data-rate with an acceptable error rate. Many other ingenious encoding schemes have been invented.

The second picture shows the amplitudes of the upper trace and the lower trace plotted as an X-Y graph. Each of the sixteen vectors corresponds to a different digital value. For accurate communication of the data, the bright patches at the ends of the vectors must not approach each other. The third picture shows a 16QAM constellation diagram, which includes only the peaks of the signals . It is at these instants that the receiver must decide which level the signal is at. The fourth picture shows that the difficulties of S/N ratio need not prevent multi-level systems being built. In the 128QAM system, there are twelve levels in each signal, creating 144 potential signal codes. Only 128 are needed, so the four at each corner are not used.

One of the problems in designing a communication system is the fluctuation in demand. Making a system which would never make anyone wait for a connection would be extremely expensive, and would have a lot of unused capacity most of the time. So the designers have to create a suitable compromise, and they have to maximize the efficiency of the system they create. The first picture below shows the result of a simple calculation using pseudo-random numbers. The assumptions were - 1000 subscribers - all using the system equally - no peak periods. Time was divided into equal periods. In each period, the probability of a non-engaged subscriber starting a call was assumed to be 1 %. For each one already using the system, the probability of ending the call in a given period was 10 %.

The chart area runs from 0 to 31 horizontally. The graph peaks at nine subscribers, and is essentially dead by about twenty. In reality, the variation of system usage with time would complicate the design.

The mobile telephone networks are divided into cells with towers. Each tower has a bandwidth allocation, chosen to minimize interference with its neighbours. The bandwidth could be divided into frequency bands, to be allocated as people start calls. This is frequency division multiple access. One problem is that while people are travelling, they can go into areas where their channel is weak. They may even lose the call. A variation of this is time division multiple access, in which several calls can share a frequency. The channel is divided into short time-slots, so that the calls use the channel in rotation. The samples from a given set of time-slots are joined up to form a smooth signal.

Code division multiple access, CDMA, allows every call to use the whole frequency bandwidth. If a particular frequency band should fade, the rest of the bandwidth can keep the calls going. To separate the calls, each new call is allocated a digital code. Each digitized sample of conversation is superposed on the code before transmission. All the call signals are added together before transmission from a tower. The receivers have to disentangle the signals before routing them to their recipients. One advantage of the system is that the transmitted signals are so messy. It is impossible for an unauthorized person to obtain the information from the signals. A disadvantage is that each signal is immersed in all the others, giving a very poor S/N ratio, which the system must cope with. To make sure that all the signals have a more or less equal S/N ratio, the strength of each transmission must be such that it has equal strength at the receiver. These and other factors make CDMA a complicated system to implement.



Click on these pictures for an enlargement. They may show artefacts caused by graphical aliasing.