Cryptography Reference
In-Depth Information
(1)
r
i
(1)
(2)
r
i
,
r
i
d
i
d
i
1
Mux
D
D
D
d
d
i
2
i
3
(2)
r
i
Figure 5.2 - Example of an encoder for non-systematic convolutional codes.
of convolutional codes. They give us the opportunity to compare the properties
of these three families. The decoding algorithms most commonly used in cur-
rent systems are presented in Section 5.4. Finally, Section 5.5 tackles the main
tail-biting
and
puncturing
techniques.
d
i
d
i
,
r
i
r
i
Mux
(1)
s
i
d
i
D
D
D
(0)
(2)
s
i
s
i
s
(3)
Figure 5.3 - Example of a encoder for recursive systematic convolutional codes.
5.2
Representations of convolutional codes
This chapter makes no claim to tackle the topic of convolutional codes exhaus-
tively. Non-binary or non-linear codes are not treated, nor are encoders with
several registers. Only the most commonly used codes, in particular for the
construction of turbocodes, are introduced. The reader wishing to go further
into the topic can, for example, refer to [5.11].
5.2.1 Generic representation of a convolutional encoder
Figure 5.4 gives a suciently general model for us to represent all the convo-
lutional codes studied in this chapter. At each instant
i
, it receives a vector
d
i
of
m
bits at its input. The code thus generated is a binary code. However,
