There is an old Dara Singh movie, that Vish much loves, that we saw two or three times in L-7 at IIT Kanpur. In that movie Dara Singh's buxom Sweetie is captured in a sarson ka khet by a most evil dakoo. The Dakoo straps her down in an electric chair, then screws a pair of copper wires into the contact lugs, feeds the cable off a spool for one long mile or two, and sits there in the middle of a field fondling a big switch, waiting for Dara Singh to show up. 

    Dara Singh appears, spies the Dakoo, and charges at him on his white horse. At right that moment, the dakoo, his face illuminated with unrestrained glee, throws the switch, and electricity starts coursing down the Copper wire at an astonishing speed. The progress of many lethal amperes is made clearly and cleverly visible by the Director (also Dara Singh) by means of a blazing blue dot that zips down the wire towards the doomed beauty --- her ample flesh billowing cheerfully from between the leather straps that keep her confined. She is like a fresh tube of toothpaste: squeezed, but still uncapped. 

    Dara Singh's choices are clear. He can have either the Dakoo or the Sweetie. In half a nanosecond Dara Singh makes up his mind. That is the time it takes light to travel about 6 inches in free space. But in that time a current can move no more than 2 inches in Copper. On the other hand it takes a photon, born at 15 million degrees Kelvin in the core of the Sun, a million years to travel to the surface of the solar photosphere at the rather slowpoke rate of a mile per year. 

    So Dara Singh turns his horse around and starts after the blue dot in an exhilarating chase that sees Dara Singh ahead at times, and at times the blue shock of current. The word "shock", in the language of partial differential equations, applies to a situation where the solution to an equation shows a sudden upward surge, traveling forward in time. The electrical engineers in the audience experience a serious case of divided loyalties. Finally, after much drama and loud music, Dara Singh succeeds in snipping the wires with inches to spare. The blue dot falls harmlessly on the brown earth, sizzles briefly like an egg on a skillet, and goes out. The horse keels over and dies of exhaustion and tachycardia. And Dara Singh and Sweety (could it have been the tightly-dressed and loosely-pouting Mumtaz?) vent their feelings in a song. 

    This brings us to the serious business of the speed of web-access. While connected at 32 Kbps I spend half my time waiting for stuff to download over the pair of Copper lines that the telephone company has coming into my house. What we really need is a billion bits per second. Or at least a million. 

    This then is the question: Given a mile (say) of a pair of Copper wires, how many bps of data can be pumped through it?

    In every communication system the transmitter-end information is first coded, then used to modulate a carrier. The coding happens in two steps: source coding and channel coding. 

    The purpose of source coding is to reduce the bit rate of the data. Source coding is itself a two-step process made up of compression coding and compaction coding. 

    In compression coding we add some noise to data. This would be a terrible thing to do if we were transmitting financial data (for example). Even a few pennies here and there will throw the bean-counters into a tizzy. But for most video, image, and audio information we can add a lot of noise without causing serious damage. Of course, the noise has to be added in some intelligent way so as to minimize its perception by the ear or the eye. (Surely we see how intelligently compression noise has been added to the picture right above! We just can't see it, can we?) This is still an evolving art, even though standards like JPEG and MPEG have tried to freeze things in out of commercial necessity.

    For data that is too sensitive to noise, no compression is done.

    Where it can be employed, compression allows us to strike a desirable balance between bit-rate on one hand and perceptual quality on the other. Compression is undone at the receiver in a corresponding compression decoder. 

    Compaction coding, the second source coding step, introduces no noise. In other words, it is exactly invertible at the receiver. The trick is to use shorter code-words for symbols that occur frequently, like the letter and letter-combinations "e" and "th" in English, and to use longer code words for letters like "z" that are less frequent. Compaction is undone at the receiver in a corresponding compaction decoder. The JPEG-coded block diagram above employs compaction on top of compression.

    The compression coding step --- the dilution of data with noise --- makes compaction more effective. Compaction by itself will reduce the data rate, but when preceded by compression it reduces the data rate more.

    After the source coder comes the channel coder. The job of the channel coder is to package data for passage through the channel --- much as goods are crated before they are consigned to a ship's hold. The idea is to prevent any damage during shipment. No one minds if the crate takes a bit of a beating, so long as the stuff of real value inside is not damaged. 

    In channel coding, redundancy (packing data) is added to the signal data in a very controlled way. The added redundancy, while it kicks up the bit-rate, allows us to detect, even correct, at the receiver, any bits that are altered by channel noise. Those of us that have heard the latest hubbub about the so called turbo-codes that have recently been adopted by NASA for their deep-space probes, we know that this is still an exciting area of research. What the devil does "turbo" mean, by the way? And what is so terribly turbo about combining two convolutional coders? That I do not know. 

    I have always imagined, why I cannot say, that a turbo-charged engine is one in which the exhaust is reignited in oxidizer-rich surroundings in order to consume any partially-combusted fuel. But is that really so? Koi hai? It may be just a story that my brain cooked up in its spare time. It does that sometimes. [Someone told me later that a turbo engine uses the its exhaust to heat the incoming air, and that makes for a bigger bang in the combustion chamber.]

    Following source and channel coding the coded data is modulated. Till the time we hit a modulator, everything in the transmitter of a (modern) communication system is digital. The modulator maps the digital bit-stream into an analog signal because a physical channel cannot carry digital stuff. Sudden ups and downs give it a bad case of indigestion (because the Fourier transform of a pulse is a sinc function that decays only inversely with frequency). 

    Typically, a modulator chops up an incoming bit-stream into short bit-length words. To each word it assigns what I call an atom (not a standard term in the business), where an atom is defined as a little analog squiggle. Then the modulator strings these atoms together like beads on a string, adding them together where they (unlike regular beads) overlap. And out comes a modulated waveform. The receiver demodulates the received signal and tries to recover the transmitted words as best as it can. 

    I am myself, by dint of training and habit, mostly a source-code man. But I'm increasingly fascinated by the modulation problem. I think there is room for improvement there. So, even though the words "stochastic", "stationary", and "ergodic" give me the heebie-jeebies, I am bravely beginning to dabble in modulation. I'll let you know when I invent something. But don't hold your breath! 

    The modulated signal is injected into a channel. Channel here being a sophisticated term for Copper pair, or coax, or free space. 

    Whenever a charged particle is accelerated it spits out photons, preferentially in a direction perpendicular to the accelerating vector. Their numbers dropping as the cosine squared of the angle of elevation from the perpendicular plane. Equivalently (in classical language --- since most of us are such old coots) the accelerating charge creates a non-zero doh-E-by-doh-tee term in the third of Maxwell's equations. Which in turn creates a variable magnetic field, therefore a non-zero doh-H-by-doh-tee term in the fourth equation, which in turn creates a variable electric field, and so on. And so the photons propagate to every corner of the universe. And so a solar flare is able to wreck havoc in communication circuits down here on earth. And so an antenna is able to radiate information because a driving circuit in a cell-phone shakes electrons up and down its length. 

    When a photon collides with a charged particle, and if it is consumed on collision, it imparts the acceleration of its parent-charge to the absorbing-charge. We can see a star a billion light-years from us because the photons it sent out accelerate charges in our retinas or in the dish of a radio-telescope. The absorbing charge, when accelerated, becomes itself a secondary radiator and spits out the photon it had lately absorbed --- scattering it, as people say. Why is the sky blue? Because atmospheric molecules scatter more red photons than blue. 

    Coupling through radiated photons, the signal in one telephony pair causes radio-interference in another pair, and we must take care to not to make any one signal too hot lest it kill the signals in adjacent pairs. "Dekhiye aap ekdum phone rakh deejiye. Line choDD deejiye saheb. Sunte nahi kya! ... Saala! Doosri party se baat ho rahi hai."

    Residential telephone wiring in new homes in US now sometimes uses cable shielded against RF (radio-frequency) interference from washing machines and garage-door openers, etc. This makes it better-suited for data traffic. A metal foil around the Copper pair is used to absorb and scatter incident radiation. But the cost of such shielding for every pair in the huge local-loop cables that carry thousands of Copper pairs (between the home and the Central Office) will be prohibitive. Those will remain unshielded. 

    So incident RF is one way for a channel to inject noise into the signal. There are others. Like the thermal motion of electrons determined by the Boltzmann constant and the ambient temperature. Amplifier noise. And the very serious phase distortion and amplitude distortion described below. 

    Every information-bearing signal contains many different frequencies. A signal with one single frequency can carry 0 bps at best. Every component frequency propagates at a different speed through a channel. (We see a rainbow because red light travels faster through water or glass than does blue light.) This effect the electrical engineers call phase distortion. Physicists call it dispersion. Dispersion or phase-distortion is just one of the many hurdles that Mother Nature places in our way as we strive for better download speed. 

    Because of phase distortion the frequencies that go in all together at the transmitting end, come out quite out of synch at the receiving end. 

    Then there is amplitude distortion: Different frequencies are differently attenuated during their passage through the channel. 

    If we put a sharp looking square pulse in at one end of a Copper pair, what comes out at the other end is a parody. A squiggly and sorry mess that looks nothing like what we saw going in. It looks like someone poured water on the pulse and jumped up and down on it with heavy boots. That is the work of phase and amplitude distortion. 

    Here is how to fix the problem: Take the Copper pair, measure its phase and amplitude distortion at various frequencies. At one end of the wires add a dubba with some electronics. Let this dubba contain a little circuit called a filter that adds more delay to those frequencies that are delayed too little by the channel, and less delay to those that are delayed too much. Let the dubba do this in such a way that all the frequencies end up being delayed by the same amount. In other words, equalize the delay. If we can build such a filter, the channel and the filter together are said to yield a linear phase response which is the holy-grail of channel engineering. Also let this filter boost those frequencies more that are more attenuated by the channel, and boost those less that are less attenuated, such that the channel and the filter together yield a flat amplitude response. 

    This remedy for phase and amplitude distortion is called equalization, and every modem (= modulator + demodulator) contains an equalization filter. 

    Then there is echo noise. Every place where a channel changes character (characteristic impedence the engineers call it) there is a reflection and a refraction. Just as light will reflect and some refract as it passes from air into water, so a signal will reflect and refract where a telephone tradesperson has hooked up a 24 gauge pair with a 26 gauge pair. Or where the phone company has spliced in a dangling stub, called a "bridged tap" in the business, not knowing in advance whether a pair will deliver service at point A or B or C. And all these anomalies cause energy to run up and down the line, muddying the signal. 

    The telephone plant was designed for voice, and when people stick an analog data-modem in at their home, that modem injects a signal within the narrow band from 0 to 4 KHz. At data speeds of 32 Kbps, the modems are already packing an astonishing 8 bps per Hertz of available bandwidth, even as they must keep their energy budget in check for fear of killing adjacent signals. 

    But a copper pair can carry signals at frequencies higher than 4 KHz. At higher frequencies, it is true, that the local-loop, the stretch of wires from the Central Office (CO) to the home, becomes an increasingly better radiator, leaking energy into space. (The FCC should perhaps start regulating emission from telephone loops.) Still some energy can be coupled to the receiver all the way to 2 or 3 MHz, even across a couple of miles. 

    The 4 KHz limitation is historically due to the nature of the switches that the telephone companies have in place at their Central Offices (COs). So here comes the Digital Subscriber Loop (DSL) that will begin to replace the present analog subscriber loop --- unless it is overtaken by wireless local loops. 

    The DSL puts a box of electronics at each end of the local loop. One at the CO, and one at the home. This is unlike conventional analog modems where there is just one modem at the customer end.

In a DSL the high-speed data will be stripped at the CO end, and fed to a packet switch (a.k.a. ATM = Asynchronous Transfer Mode switch) designed for aggregated trunked data-rates as high as 100 Mbps or 1 Gbps or 1 Tbps = 1,000 Gbps. The voice information could still go over a voice switch. But that too, in time, will travel ATM. 

    Moreover, when we put electronics at both end of the local loop it becomes possible to better measure channel noise and distortion, and to better counter it. So we can improve the ratio of signal to noise. 

    Here in the US every LEC (Local Exchange Carrier = local phone company) is now in trial-mode with DSL. People are so tired of low-speed data connections, that there is an immense unmet demand for DSL. The race is on from New York to California. Could someone tell me whether DSL fever has got to India? Bangalore, Mumbai, Delhi, Chennai? Is private capital in play? Or is India going to hang its hat on wireless local loop? It is quite possible that the latter choice may make better economic sense in India.