Digital Signal Processing Reference
In-Depth Information
illustrated by the itu-t
10
v.2x modem recommendations [IT93]. Before ver-
sion v.32, error correction was not even considered in the phy layer of voice-
band modems. Error control was separated from the modem's analog front-end
and was defined in for example the v.42(bis) protocol recommendation. As a
consequence, the error control mechanism was entirely located in the data link
layer (dll)oftheosi model, completely unaware of the far more intriguing
activities that take place in the analog phy layer of the modem.
2.4
Coding for a narrowband, noisy channel
In the previous sections, the basic principles of error coding have passed the
critical eye of the reader.
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One minor detail was not considered during these
lively discussions, though. The error-correcting capabilities of coding are par-
tially based on redundancy, which means that the encoded data rate is higher
than the bit rate at the input of the encoder. If the capacity of the channel is
has not been pushed to its limits yet, the excess data throughput can be com-
pensated either by an increase of the symbol rate or by switching over to a
higher modulation depth. However, when the channel is going to be used near
the maximum theoretical capacity - which is almost always the goal in a wire-
less application - this implies that the rate of the encoded data stream will rise
above the Shannon capacity of the channel. If the channel is bandwidth-limited
and increasing the symbol rate is thus not an option, the only way to achieve
this is to pack more data bits in each symbol (i.e. increase the modulation
depth).
This method is used in the v.34 analog voiceband modems. The maximum
symbol rate used by these modems is 3,429 Hz which, in combination with
an average of 9
.
8 equivalent information bits per symbol, results in the well-
known 33.6 kbit/s throughput rate. The bit error rate achieved by this sys-
tem (P
e
<
1
/
10
5
) is fairly low, thanks to the use of a 4-d Trellis code variant
[For96, Wei87]. Inevitably, the redundancy on which tcm is based will al-
ways be translated in an increase of the data throughput. The only way to cope
with this larger throughput is to use a higher order modulation scheme. In the
v.34 standard, a maximum of 1,664 constellation points or the equivalent of
10
.
7 encoded bits per symbol is used. The raw data rate through the channel,
36
.
7 kbit/s, is thus 7
.
9% larger than the information capacity of the pstn line
(34 kbit/s). As expected, this leads to a higher error rate in the encoded data
stream. However, if the total energy per bit of information stays above the cod-
ing threshold of a particular coding algorithm, the net effect will be a decrease
of the bit error rate at the output of the decoder!
10
itu-t: itu Telecommunication Standardization Sector, better known as the former ccitt.
11
To the unfaithful reader who skipped a few pages for some obscure reason: don't try this again.
