Digital Signal Processing Reference
In-Depth Information
Joint coding and modulation
In Section 2.4, the general idea of modulation-aware error coding was further
explored using the example of the 33
.
6 kbit/s analog voiceband v.34 modem
system. The v.34 modem standard employs
Trellis coded modulation
(tcm),
which was invented by Gottfried Ungerboeck in 1982 [Ung82]. Tcm is a
modulation-aware channel coding technique for bandwidth-limited channels.
In the tcm scheme, information bits are pushed through the channel at the
maximum theoretical throughput rate. At first sight, it might seem impossible
to attach redundant information to the transmitted symbol stream, because the
channel is already used at the maximum symbol rate. However, Ungerboeck
managed to solve this problem by increasing the modulation depth of the sys-
tem to below the noise floor of the channel. Doing this way, the increased data
rate of the transmitter allows to attach redundant information to the transmit-
ted symbol stream, while the rate of effective (unencoded) information does
not surpass the theoretical capacity of the channel. Two important ideas were
contained in Ungerboeck's way of doing. First, by modulating the signal with
an accuracy which is below the noise floor of the channel, the discretizing ef-
fects of the symbol-to-bit demapper (and the dac/adc) are ruled out of the
picture, while only the noise floor of the channel itself remains responsible
for the signal-to-noise ratio of the received symbol stream. Secondly, modu-
lating below the noise floor of the channel does not increase the error rate of
the system, because only the minimum Euclidean distance between sequences
(which is set by the noise floor of the channel) is important to the decoder in
the receiver.
The advantage of the Trellis coding process is that a sequence of information
bits is mapped onto a sequence of symbols at the output of the receiver, while
the information that is contained in a single incoming bit is spread over a se-
quence of multiple symbols at the output of the system. The net result is that a
single error in the received symbol stream affects multiple information bits at
the same time, which means that the channel noise is effectively smoothened
over multiple information bits. For as long as the bit energy over thermal noise
density stays above a certain level (E
b
/N
0
>
1
.
59 dB), error-free communica-
tion should be possible. The longer the sequence over which the information
of a single unencoded bit is spread, the better noise energy can be levelled over
multiple bits and the bigger the chances of survival are for the error correction
mechanism. However, it should be intuitively clear that the larger the set of
possible sequences is, the more difficult it becomes for the error decoder in the
receiver to find the sequence with the highest probability of being transmitted.
Which, of course, will be reflected in the power consumption profile of the
system.
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