Friday, October 20, 2017

ADSL2+ Sync Rate

If you have ever called up your ISP support team to complain, you may have heard them quote a number called SNR to describe the quality of your connection.

It's not quite as simple as a single number, though.

ADSL2+ uses multiple "channels" at once to transfer data between the ISP and your home modem. In the case of my ASUS modem, there are 512 channels: there is 2.208 MHz of available spectrum on the copper wire; these are split into equally spaced 4.3125 kHz wide channels.

However, not every channel (or bin) is created equally: there is almost certainly some electrical "noise" or congestion on the cables. Some bins are reserved for normal telephone connections, others for upstream and downstream communication with the server, with a few reserved as guards to keep sections separated.

I pay for a 4 Mb/s connection, so let's assume the ISP allows me 1672 bits' worth of downstream sync rate*. It is up to the modem and ISP to negotiate how to allocate the sync rate across the available bins. My modem surveys the ratio of signal to noise (SNR) across each bin in the downstream set of channels. A rule of thumb is that each bit requires about 3dB of SNR to reliably decode the signal without errors. Bins with higher SNR will therefore have higher bit capacity for bits.

My modem allows me to connect with SSH and look at three files, which are ordinarily used by the administrative web server interface to present me a way to easily change modem settings and view diagnostics:
  • /var/tmp/spectrum-bpc-ds
  • /var/tmp/spectrum-bpc-us
  • /var/tmp/spectrum-snr
Let's do some very simple mathematics with the data in these files that won't be too difficult to follow:

Data taken from the SNR file:
1672 bits to allocate
268 channels into which they must be allocated
10,523.27 dB (the sum of SNR across the available reception channels)

Assumptions:
3 dB/bit required to convert received signal without errors

1) 1672 bits * 3 dB/bit = 5016 dB SNR required to decode the signal

2) 10,523.27 dB - 5016 dB = 5507.27 dB unused SNR

3) 5507.27 dB / 268 channels = 20.54951 dB unused SNR per channel

4) Now, we iterate each of the 268 channels in turn. I'll demonstrate with the first channel, where the SNR was 24.21 dB.

a) 24.21 dB - 20.54951 dB = ~3.66 dB to be used for data reception

b) 3.66 dB / 3 dB/bit = ~1.22 bits

c) round 1.22 bits to a whole number: 1

It turns out that this simple algorithm gets us remarkably close to the numbers of bits per channel (BPC) in the other files, which are arrived at by the modem's own algorithms. The difference could even be accounted for by (lack of, or outdated) "bitswap", where bins are periodically re-checked for SNR and reallocated to make the best use of the spectrum as it evolves over time.


* Ignore - for now - that those numbers are not equivalent, they are effectively the same thing quoted for different units of time
 

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