1 channel coding in ieee802.16e student: po-sheng wu advisor: david w. lin

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Channel Coding in IEEE802.16e

Student: Po-Sheng Wu

Advisor: David W. Lin

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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

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Outline

Overview RS code Convolution code LDPC code Future Work

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Overview

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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)

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RS code

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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

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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.

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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.

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Shortened and Punctured

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RS code

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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

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Convolution code

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

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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 .

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Convolution code

Decoding: Viterbi algorithm

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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

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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.

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RS-CC code

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LDPC code

low density parity checks matrix LDPC codes also linear codes. The codewor

d 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

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LDPC code

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

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LDPC code

Base model

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LDPC code

if p(f,i,j) = -1 replace by z*z zero matrix

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

f

0

( , ), p(i,j) 0

, , p(i,j)z, p(i,j)>0

p i j

p f i j

z

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LDPC code

Encoding

[u p1 p2]

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LDPC code

Decoding Tanner GraphTanner Graph Sum Product Algorithm

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LDPC code

Tanner GraphTanner Graph

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LDPC code

Sum Product Algorithm

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LDPC code

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LDPC code

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Future Work

Realize these algorithm in computer Find some decoding algorithm to speed up

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Thanks for your attention