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What did the Romans ever do for us? Packet switching...

And the railways, morse code. Sort of

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Going the extra mile?

Arqiva Aerial Mast site 36223 on Cleeve Hill

Will the last mile be radio in future?

In countries where traditional telephony was in extensive use, there is always a large infra structure of copper wire between exchanges and subscribers, the so called last mile. The replacement of all that wire would be a daunting and expensive task. However, the distances involved are usually quite short. The telephone wires to the subscriber were intended for speech frequencies and are not at all optimal for high bit-rate data.

Nevertheless using sophisticated systems such as trellis coding, the traditional analogue copper infra structure can be re-used for data, as is explained in the box section on the next page. In developing countries, the absence of the traditional telephone network has not been a great drawback. In many places the copper wire stage has been completely leap-frogged and the last mile subscriber link is via radio.

The feature that distinguishes IT networks from the traditional telephone network is not just that one is digital. Analogue phones must use circuit switching whereas IT uses packet switching. When a traditional dial-up phone call was made, a continuous exclusive analogue electrical circuit was created between the two parties by switches, relays and uniselectors that were controlled once by the dialling procedure. The entire information route was created by the network and is denied to other parties for the duration of the call.

Talking digital: ADSL and Trellis Coding

Analogue telephone wires, intended for speech, display impedance mismatches and develop standing waves when used at high frequencies, such that their frequency response and noise level are highly irregular. In ADSL, the modulation scheme divides the spectrum up into hundreds of channels, or bins, only 4kHz wide.

The lowest channels are not used, so that the traditional analogue speech still works normally. Some channels communicate from exchange to subscriber, a smaller number work the other way, making the system asymmetrical and putting the A in ADSL.

Each channel is independently measured for data integrity and if it contains a frequency that is suffering from standing waves or cancellation, then its data rate will have to be reduced, or it may be abandoned altogether, whereas other channels can run at top speed. The ADSL system adjusts itself individually to the characteristics of each line.

Unlike the processing in a computer, in which the data bits and the electrical signalling are both binary, modems send the binary data using non-binary signalling. Instead of sending bits having two states, they send symbols having multiple states instead. For example, if a symbol can have sixteen states, then one symbol can convey all combinations of four bits.

The symbol rate is limited by the available bandwidth, so by getting more bits into each symbol, the bit rate can be raised. Clearly, if there are sixteen states, the difference between them is more readily confused by noise, but as telephone lines were specified for analogue speech, their noise performance is over-specified for binary.

Trellis code

Here is set of four symbols, each one of which has sixteen states. One route through the trellis for a particular 16 bit pattern is shown. Trellis coding works by playing with the different combinations of routes

If the information rate to be sent is thought of as being like a pat of butter whose width is the bandwidth and whose height is the number of bits per symbol, then if you squeeze it in on one axis, it has to get bigger on the other. An analogue telephone line has limited bandwidth but good noise performance, so you squeeze the bandwidth and use multi-level signalling.

Imagine four symbols each having sixteen levels or states, such that each symbol specifies four bits for a total of sixteen bits. The diagram shows that the levels vertically and the symbols horizontally form a trellis. Carrying 16 bits, there are 65,536 different routes through the trellis, one of which is shown. However, if we used the same trellis structure, but only sent 14 bits, then only 16,384 different routes would be needed and the remainder would be invalid.

So if noise pushed the signal away from the correct level in one of the symbols, we would detect an invalid route through the trellis and therefore detect the error. If we were smart we might be able to figure out which valid route was the closest to the invalid one and thereby correct it. This means the apparent noise performance of our channel improved.

Although we lost a couple of bits in the process, Trellis coding doesn’t sacrifice any data capacity, because the improved noise immunity allows us to use more levels so we win more than we lose. Clearly there is some clever processing going on in an ADSL modem (have you noticed they get quite hot?) and it’s a fundamental enabling technology. Until that clever stuff could be implemented at low cost in LSI chips, broadband would stumble at the last mile.

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