Marwan Hadri Azmi

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Design of LDPC codes for relay channels

• Presented by
• Marwan Hadri Azmi
• 1st year PhD candidate
• University of New South Wales

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• Outline of the presentation

• Relay channel model
• Capacity of relay channel
• Bound Evaluation for Relay Channel
• Decode and Forward (DF) Strategy
• LDPC code
• LDPC code in Relay Channel
• Result
• Conclusion and Future Work
• References

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Relay channel model

• Consider
• BAWGN relay channel
• BPSK modulation

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Relay channel model (cont.)
So, the received signal can be expressed as
With ? is a fixed and to be known attenuation
exponent (set ? 2)
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Capacity of relay channel
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Bound Evaluation for Relay Channel
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Bound Evaluation for Relay Channel (continue)
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Bound Evaluation for Relay Channel (continue)

• Based on the graph, there are 2 regimes
• When the relay is close to the source, there will
  be a maximizing ?, with 0 ?lt 0.5.
• When the relay is far from the source the maximum
  capacity will when ? 0.5. Since X and X1 is
  independent when ? 0.5, the RDF will be

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Bound Evaluation for Relay Channel (continue)
Bound for the BAWGN relay channel a 2 and SNR
0dB
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Bound Evaluation for Relay Channel (continue)

• CONCLUSION
• There are 2 regimes when the distance of relay
  varies from source to destination.
• When relay is close to source the sources and
  relays codeword will have some correlation. The
  correlation will be zero when relay is at a
  particular distance from the source and remain
  constant when it moves towards destination after
  that distance.
• RDF will be identical with the upper bound (relay
  capacity) when the relay is close to the source.
  RDF is less than the capacity when it moves
  towards the destination.

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Decode and Forward (DF) Strategy

• DF strategy was originally been proposed by Cover
  and El Gamal in 1979.
• DF strategy has 2 important elements Random
  binning and block Markov coding
• Random binning is done by partitioning W source
  possible message (2nR) into S bins (2nR1)
  determines by the relay possible message.
• Binning for LDPC code is done by the relay
  forwarding extra parity check bits to the
  destination to help destination decode sources
  message

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Decode and Forward (DF) Strategy (cont.)
X
X1
Y
Block Markov Coding in DF
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Decode and Forward (DF) Strategy (cont.)
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LDPC code

• The code can be represent using the parity check
  matrix, H

Tanner graph
Equation for variable and node degree distribution
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LDPC code in Relay Channel

• Binning using LDPC code
• Partition W into S is done by passing through the
  source codeword X into a hash function M, which
  is m x n matrix specified by its distribution of
  rate RM
• The codeword X is said to be if
  
• S will be syndrome of X for M hash
  function/matrix. S will be the input information
  for codeword X1.
• At destination, after received both information
  from source and relay, the codeword X should
  satisfy

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LDPC code in Relay Channel (cont.)
Encoding the LDPC code
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LDPC code in Relay Channel (cont.)
LDPC code Decoding
Tanner graph to decode Y at the destination
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LDPC code in Relay Channel (cont.)
Tanner graph to decode X at the destination after
S been decode from the previous graph
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Result
Result for LDPC with R 0.95, RM 0.46, R1
0.54 and d 0.446 with a 2 and n 214.
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Conclusion Future Work

• The sources and relays codes can be design
  separately since the set up of this work is at
  independent regimes (based on the information
  theory).
• Research on LDPC design in general at any
  distance (independent and dependent regimes) will
  be the extended work of this research.
• The work did not involved optimization of H
  matrix to achieve the capacity of decode and
  forward in relay channel.
• However, without optimizing the degree
  distribution, the LDPC perform within 0.65 dB
  from the theoretical limit.

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References

• Ezri, J. Gastpar, M. On the Performance of
  Independently Designed LDPC Codes for the Relay
  Channel , Information Theory, 2006 IEEE
  International Symposium on July 2006, Page(s)
  977 981.
• Thomas M. Cover, Abbas El Gamal, Capacity
  Theorems for the Relay Channel, IEEE
  Transactions on Information Theory, VOL. rr-25,
  NO. 5, SEFTEMBER 1979.
• Kramer, G. Gastpar, M. Gupta, P. Cooperative
  Strategies and Capacity Theorems for Relay
  Networks, Information Theory, IEEE Transactions
  on Volume 51,  Issue 9,  Sept. 2005 Page(s)3037
  - 3063

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Thank You