Digital Signal Processing Reference
In-Depth Information
Clk
Fig. 9.12
Non-systematic
cyclic encoder
M
(
p
)
X
(
p
) =
M
(
p
)
G
(
p
)
1
2
3
+
+
If we divide
X
(
p
)by
G
(
p
) the quotient should be
M
(
p
). Encoder for (7, 4) may
be framed as follows: divide
p
3
M
(
p
)by
G
(
p
) to obtain
R
(
p
). If the received code
Y
(
p
)
=
รท
X
(
p
) then in the division
Y
(
p
)
G
(
p
) there should be no remainder. This
principle is employed in the decoder.
Figures
9.13
and
9.14
shows the block diagram of the encoder and the decoder,
called Meggitt decoder, based on the principle stated above. After 4 message bits
input, the 3 check bits are obtained.
Clk
M
(
p
)
+
1
2
3
+
C
3
, C
2
, C
1
M
4
, M
3
, M
2
, M
1
Fig. 9.13
Systematic cyclic encoder
9.5.3 Meggitt Decoder
In the Fig.
9.14
, the decoder circuit is shown for (7, 4) cyclic code with
G
(
p
)
=
p
3
p
2
1. All the 7 bits of the received vector Y are enter into the shift registers
and the same are stored into the buffer. After the 3rd bit the process of division starts
and after 7th bit, the syndrome is stored into the shift register. If the content of all
the cells are {000}, Y is taken as un-erroneous. In Meggitt decoder a typical pattern
of the syndrome {100} appears whenever the erroneous bit is shifted out of buffer.
This is used through a coincidence circuit to correct the erroneous circuit as shown
in the Fig.
9.14
.
+
+
9.6 BCH Code
BCH codes were invented in 1959 by Hocquenghem, and independently in 1960
by Bose and Ray-Chaudhuri [
6
]. The acronym
BCH
comprises the initials of these
inventors' names. This is a multilevel cyclic variable-length error-correcting code
used to correct multiple random error patterns. BCH codes may also be used with
Search WWH ::
Custom Search