1.  Ammar Abh-Hhdrohss Islamic University -Gaza 1 Chapter 2 Concatenated codes

2. Slide 2 Channel Coding Theory 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.

3. Slide 3 Channel Coding Theory Single level Concatenation Codes Outer Encoder (n2, k2) over GF(2 k1 ) Inner Encoder (n1, k1) Channel Inner Decoder (n1, k1) Outer Decoder (n2, k2)

4. Slide 4 Channel Coding Theory Single level Concatenation Codes Reed-Solomon is used usually as the outer code. First, the k 1 k 2 binary information digits are divided into k 2 bytes of k 1 information digits each. These k 2 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 (n 1 n 2, k 1 k 2 ) with minimum distance d 1 d 2 ; where d1,d2 are the minimum distances for C1, C2, respectively.

5. Slide 5 Channel Coding Theory k1k1 n 1 - k 1 k2k2 n 2 - k 2

6. Slide 6 Channel Coding Theory

7. Slide 7 Channel Coding Theory Interleaving with concatenation codes Outer Encoder (n2, k2) over GF(2 k1 ) Interleaver Inner Encoder (n1, k1) Channel Inner Decoder (n1, k1) Deinterleav er Outer Decoder (n2, k2)

8. Slide 8 Channel Coding Theory Another example

9. Slide 9 Channel Coding Theory