Chapter 2
Concatenated codes
bA rammA h-Hhdrohss Islamic
University -Gaza
1
Introduction




Single level Concatenation usualy done by using done by using
non-binary outer code and binary simple inner code.
This reduce complexity and increase reliability of the code.
Multilevel concatenation can achieve very powerful codes with
very simple inner and outer codes.
The decoding is done in multiple stages which reduce the overall
complexity.
Channel Coding Theory
Slide 2
Single level Concatenation Codes
Outer
Encoder
(n2, k2)
over
GF(2k1)
Outer
Decoder
(n2, k2)
Channel Coding Theory
Inner
Encoder
(n1, k1)
Channel
Inner
Decoder
(n1, k1)
Slide 3
Single level Concatenation Codes


Reed-Solomon is used usually as the outer code.
First, the k1k2 binary information digits are divided into k2 bytes
of k1 information digits each. These k2 bytes are encoded using
C2.

The n2 codewords of C2 are encoded using C1.

The information is transmitted one codeword of C1 at time.

The resultant code (n1n2, k1k2) with minimum distance d1d2;

where d1,d2 are the minimum distances for C1, C2, respectively.
Channel Coding Theory
Slide 4
k2
n2 - k2
k1
n1 - k1
Channel Coding Theory
Slide 5
Channel Coding Theory
Slide 6
Interleaving with concatenation codes
Outer
Encoder
(n2, k2)
over
GF(2k1)
Inner
Encoder
Interleaver
(n1, k1)
Channel
Outer
Decoder
(n2, k2)
Channel Coding Theory
Inner
Decoder
Deinterleav
er
(n1, k1)
Slide 7
Another example
Channel Coding Theory
Slide 8
Channel Coding Theory
Slide 9