1 Channel Coding in IEEE802.16e Student: Po-Sheng Wu Advisor: David W. Lin

2 Reference IEEE Std a-2003, April 2003 IEEE Std , October 2004 IEEE Std e™-2005 and IEEE Std ™-2004/Cor IEEE Std e/D9, June 2005

3 Outline Overview RS code Convolution code LDPC code Future Work

4 Overview

5 RS code The RS code in a is derived from a systematic RS (N=255, K=239, T=8) code on GF(2^8)

6 RS code

7 This code then is shortened and punctured to enable variable block size and variable error- correction capability. Shorten ： (n, k) → (n-l, k-l) Punctured ： (n, k) → (n-l, k) In general, the generator polynomial in IEEE802.16a h=0

8 RS code They are shortened to K’ data bytes and punctured to permit T’ bytes to be corrected. When a block is shortened to K’, the first 239- K’ bytes of the encoder input shall be zero When a codeword is punctured to permit T’ bytes to be corrected, only the first 2T’ of the total 16 parity bytes shall be employed.

9 RS code When shortened and punctured to (48,36,6) the first 203(239-36) information bytes are assigned 0. And only the first 12(2*6) bytes of R(X) will be employed in the codeword.

10 Shortened and Punctured

11 RS code

12 RS code Decoding : The Euclid’s (Berlekamp) algorithm is a common decoding algorithm for RS code. Four step: -compute the syndrome value -compute the error location polynomial -compute the error location -compute the error value

13 Convolution code Each RS code is encoded by a binary convolution encoder, which has native rate of ½, a constraint length equal to 7.

14 Convolution code “1” means a transmitted bit and “0” denotes a removed bit, note that the has been changed from that of the native convolution code with rate ½.

15 Convolution code Decoding: Viterbi algorithm

16 Convolution code The convolution code in IEEE802.16a need to be terminated in a block, and thus become a block code. Three method to achieve this termination  Direct truncation  Zero tail  Tail biting

17 RS-CC code Outer code: RS code Inner code: convolution code Input data streams are divided into RS blocks, then each RS block is encode by a tail-biting convolution code. Between the convolution coder and modulator is a bit interleaver.

18 RS-CC code

19 LDPC code low density parity checks matrix LDPC codes also linear codes. The codeword can be expressed as the null space of H, Hx=0 Low density enables efficient decoding  Better decoding performance to Turbo code  Close to the Shannon limit at long block length

20 LDPC code n is the length of the code, m is the number of parity check bit

21 LDPC code Base model

22 LDPC code if p(f,i,j) = -1  replace by z*z zero matrix else  p(f,i,j) is the circular shift size

23 LDPC code Encoding [u p1 p2]

24 LDPC code Decoding  Tanner Graph  Sum Product Algorithm

25 LDPC code Tanner Graph Tanner Graph

26 LDPC code Sum Product Algorithm

27 LDPC code

28 LDPC code

29 Future Work Realize these algorithm in computer Find some decoding algorithm to speed up

30  Thanks for your attention