Chapter 2 Concatenated codes Ammar AbhHhdrohss Islamic University

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

Introduction n n Single level Concatenation usualy 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 (n 2, k 2) over GF(2 k 1) Inner Encoder (n 1, k 1) Channel Outer Decoder (n 2, k 2) Channel Coding Theory Inner Decoder (n 1, k 1) Slide 3

Single level Concatenation Codes n n 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 C 2. n The n 2 codewords of C 2 are encoded using C 1. n The information is transmitted one codeword of C 1 at time. n The resultant code (n 1 n 2, k 1 k 2) with minimum distance d 1 d 2; n where d 1, d 2 are the minimum distances for C 1, C 2, respectively. Channel Coding Theory Slide 4

k 2 n 2 - k 2 k 1 n 1 - k 1 Channel Coding Theory Slide 5

Channel Coding Theory Slide 6

Interleaving with concatenation codes Outer Encoder (n 2, k 2) over GF(2 k 1) Inner Encoder (n 1, k 1) Interleaver Channel Outer Decoder (n 2, k 2) Channel Coding Theory Inner Decoder (n 1, k 1) Deinterleav er Slide 7

Another example Channel Coding Theory Slide 8

Channel Coding Theory Slide 9