Channel coding in ieee802 16e
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Channel Coding in IEEE802.16e. Student: Po-Sheng Wu Advisor: David W. Lin. Reference. IEEE Std 802.16a-2003, April 2003 IEEE Std 802.16-2004, October 2004 IEEE Std 802.16e™-2005 and IEEE Std 802.16™-2004/Cor1-2005 IEEE Std 802.16e/D9, June 2005. Outline. Overview RS code

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Channel Coding in IEEE802.16e

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Channel coding in ieee802 16e

Channel Coding in IEEE802.16e

Student: Po-Sheng Wu

Advisor: David W. Lin



  • IEEE Std 802.16a-2003, April 2003

  • IEEE Std 802.16-2004, October 2004

  • IEEE Std 802.16e™-2005 and IEEE Std 802.16™-2004/Cor1-2005

  • IEEE Std 802.16e/D9, June 2005



  • Overview

  • RS code

  • Convolution code

  • LDPC code

  • Future Work



Rs code

RS code

  • The RS code in 802.16a is derived from a systematic RS (N=255, K=239, T=8) code on GF(2^8)

Rs code1

RS code

Rs code2

RS code

  • 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

Rs code3

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.

Rs code4

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.

Shortened and punctured

Shortened and Punctured

Rs code5

RS code

Rs code6

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

Convolution code

Convolution code

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

Convolution code1

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 .

Convolution code2

Convolution code

  • Decoding: Viterbi algorithm

Convolution code3

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

Rs cc code

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.

Rs cc code1

RS-CC code

Ldpc code

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

Ldpc code1

LDPC code

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

Ldpc code2

LDPC code

  • Base model

Ldpc code3

LDPC code

  • if p(f,i,j) = -1

    • replace by z*z zero matrix


    • p(f,i,j) is the circular shift size

Ldpc code4

LDPC code

  • Encoding

    [u p1 p2]

Ldpc code5

LDPC code

  • Decoding

    • Tanner Graph

    • Sum Product Algorithm

Ldpc code6

LDPC code

  • Tanner Graph

Ldpc code7

LDPC code

  • Sum Product Algorithm

Ldpc code8

LDPC code

Ldpc code9

LDPC code

Future work

Future Work

  • Realize these algorithm in computer

  • Find some decoding algorithm to speed up

Channel coding in ieee802 16e

  • Thanks for your attention

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