Channel Coding in IEEE802.16e

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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 (N255, K239, T8) code on GF(28)

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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 h0

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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(26) 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 Euclids (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 codeword can be
  expressed as the null space of H, Hx0
• 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 zz zero matrix
• else
• p(f,i,j) is the circular shift size

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LDPC code

• Encoding
• u p1 p2

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LDPC code

• Decoding
• Tanner Graph
• Sum Product Algorithm

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LDPC code

• Tanner 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