Digital Signal Processing Reference
In-Depth Information
of the encoder.
6
At the receiving end of the transmission chain, the decoder
despreads
the information embedded in a sequence of multiple data bits to a
single information bit. The despreading effect of the decoder on the received
bit stream is sometimes compared with the
energy despreading correlation
in
a matched filter.
This spreading of information is probably the most important function of the
encoding/decoding process. During transmission, noise accumulates on the
transmitted symbols which leads to incorrect decisions of the symbol demap-
per. The recomposition of a single unencoded bit from a sequence of received
data bits is a constructive process from an energy viewpoint, independent from
the error coding strategy in use. On the other hand, the noise energy of a single
bit error is spread out over multiple unencoded bits which are still embedded
somewhere in the coded sequence, so that a single error partially affects the
information of several information bits at the same time (Figure 2.2).
1
0
0
1
information bits
0
data bits / data symbols
1
0
0
0
0
1
1
1
1
0
1
0
0
4
1
1
0
0
1
1
0
1
4
3
6
5
2
1
1
1
1
2
0
0
0
1
1
5
0
1
1
1
1
0
3
0
1
0
1
TX
0
0
6
0
0
0
Channel
noise / interference / ISI
Decoder
error free in ideal
coding scheme if
E
bit
/N
0
> -1.59dB
RX
1
0
demapping error,
symbol error
0
1
0
1
0
0
0
0
1
1
1
1
0
1
0
0
4
1
1
0
0
1
10
2
5
6
?
4
1
1
1
1
1
2
0
0
0
1
1
0
5
1
1
0
(virtual) noise density N
0
??
0
0
1
0
0
0
6
0
Figure 2.2.
Error coding spreads the information associated to a certain input bit over multi-
ple data symbols. If data is corrupted during transmission, the original informa-
tion can be recovered thanks to redundant information in other symbols.
6
A convolutional encoder can be expressed using a set of fir filters [Rod95, Ros76].
