Once Inter-Symbol Interference has been countered, the next hurdle is noise. Of particular importance is Quantisation noise, as this generally exceeds all the other sources. As was mentioned earlier, the quantisation error is a problem of Analogue to Digital Converters (ADC). In the downstream of the mixed analogue-digital channel, there is only one ADC left - that in the user's modem. The effect of this noise source has to be reduced.
In this case, both USR's and Lucent's methods are identical, partly because the problem is already half-solved. The quantisation error occurs when the ADC has to represent the continuous analogue signal with the nearest quantisation level. The simplest solution to this problem is to ensure that the received signal is always at a quantisation level when the ADC comes to sample it. Now, both the user's modem ADC and the exchange switch's DAC are 8 bit devices, so the former expects the same amplitudes as the latter generates. With some knowledge of the channel conditions, measured during the connection training sequence, it is possible to come close to the level criterion above. The quantisation noise can be greatly reduced, improving the signal to noise ratio.
Reducing the quantisation noise reveals the other noise sources. These are much harder to deal with, being of external origin and therefore outside the control of the modems. Unfortunately, the coding schemes chosen to reduce ISI and quantisation noise do not have good immunity to external noise. With 8 bits to a symbol, the distance between amplitude levels is very small - only a little noise is required to change the signal by one level and cause a bit error. This problem is exacerbated by the effect of companding, which groups the low-value quantisation levels very close together. The noise required to corrupt symbols using these low values is, therefore, further reduced.
Both products rely on error-correction, error-detection, and repeat-request systems much like those used in conventional modems. Error-correction aims to replace corrupted bits through a knowledge of the coding scheme and the channel characteristics. Error-detection is less ambitious: it aims to detect that bits have been corrupted, without being able to correct them. Many error algorithms are able to do both, detecting errors when their ability to correct has been exceeded. Finally, repeat-request is the system used when errors have been detected: the receiving modem asks for a re-transmission of the corrupted data.
For USR, the susceptibility to noise prompted a change in the coding scheme. Since companding adversely affects the low symbol values, they decided to use only the top 128 levels out of the possible 256. This is, effectively, forcing the most-significant bit to a "1", and using the remaining seven bits for data. The signal amplitude then never drops into the more vulnerable lower range. This change, naturally, limits the data transfer rate. Using a similar calculation to that used earlier for the Lucent coding scheme, the theoretical maximum data rate is
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