Distributed Turbo Coding for Cooperative Wireless Networks

1
Distributed Turbo Coding for Cooperative Wireless
Networks
Yonghui Li University of Sydney
2
Outline

• Introduction
• Distributed Turbo Coding with Soft Information
  Relaying
• Performance Analysis
• Simulation Results
• Conclusions
• Open Problems

3
Introduction

• Why Cooperation in wireless networks?
• Increased coverage
• Reduced transmission power
• Cooperative diversity
• Cooperative coding gain
• Applications
• Cellular networks
• Wireless sensor networks
• Wireless Ad Hoc networks

Mobile Station (MS) 2
Base station (BS)
Mobile Station (MS) 1
4
2-Hop Relay Networks
2-hop relay network with a direct link
Two phases transmission I Source broadcasts
to relay and destination II Relay forwards to
the destination
5
Relaying Protocols

• Amplify and forward (AAF)
• Decode and forward (DAF)
• Detection and forward
• Compression and forward

6
Background

• Original concept
• Sendonaris, Erkip, and Aazhang, User cooperation
  diversity Part I system description, IEEE
  TransCom., pp. 19271938, Nov. 2003.
• --User cooperation diversityPart II
  implementation aspects and performance analysis,
  IEEE TransCom., pp. 19391948, Nov. 2003.
• Theoretical Framework
• Laneman Wornell, Distributed space-time-coded
  protocols for exploiting cooperative diversity in
  wireless networks, IEEE Trans. IT, pp.
  2415-2425, Oct. 2003.
• Laneman, Tse Wornell, Cooperative diversity in
  wireless networks efficient protocol and outage
  behavior, IEEE Trans. IT., pp. 3062-3080, Dec.
  2004.

7
Distributed Space time coding
User 1 data
Channel 1
User 2 data
Channel 2
Cooperation
Non cooperation

• Laneman Wornell, Distributed space-time-coded
  protocols for emploiting cooperative diversity in
  wireless networks, IEEE Trans IT, vol. 49, pp.
  2415-2425, Oct. 2003.
• Cooperative diversity!

8
Other Distributed ST Coding Schemes

• Distributed space time block codes (DSTBC)
• Dohler, et al., Performance analysis of
  distributed space-time block encoded sensor
  networks," IEEE Trans VT, Nov. 2006, pp.
  1776-1789.
• Distributed space time trellis codes (DSTTC)
• Li and Xia, A family of distributed
  space-time trellis codes with asynchronous
  cooperative diversity, IPSN 2005, April 2005,
  pp. 340 347.
• Chu Yuan, Performance Analysis and code
  design for distributed space-time trellis codes
  , 2007.
• A LDPC coded DSTBC scheme
• Dong, Xie Qiu Low-density parity-check
  coded distributed space-time cooperative System,
  VTC 2006-Spring, vol. 5, pp. 2383 2387.

9
Coded Cooperation
M. Janani, et al., Coded cooperation in wireless
communications space-time transmission and
iterative decoding, IEEE Trans. Signal
Processing, vol. 52, Feb. 2004, pp.362
371. Cooperative diversity and Coding gain !
10
Distributed Turbo Coding
Zhao Valenti, Distributed turbo coded
diversity for relay channel, Elec. Lett., pp.
786-787, May 2003.
Relay
source

• Block diagram of Parallel concatenated DTC

11
Destination Receiver

• The overall received signals at the destination
• Coded information bits transmitted from the
  source
• Parity symbol of the interleaved information
  bits transmitted from the relay.
• They form a distributed turbo code.

12
Distributed Turbo Coding

• Capacity Approaching
• Unrealistic assumption --- the error-free
  decoding at the relay.
• We refer to it as the Perfect DTC.

13
Outline

• Introduction
• Distributed Turbo Coding with Soft Information
  Relaying
• Performance Analysis
• Simulation Results
• Conclusions
• Open Problems

14
Our Contributions

• (1) Novelty Develop a practical DTC when
  imperfect decoding occurs at the relay.
• (2) Methodology Relay calculates and forwards
  the corresponding soft information
• (3) Challenge Develop a new coding scheme to
  calculate the parity soft estimates for the
  interleaved information

15
Transmitter of DTC-SIR
Information Symbols
Encoder Modulator
Destination
Relay
Calculation of Parity Soft Est. of interleaved
information
Calculation of the APP
Source
Block diagram of the proposed scheme
Information Codeword
Source
Soft Estimate of Interleaved Information
Relay
Time frame 1
Time frame 2
Transmission Scheduling
16
DTC-SIR

• First step Calculate APP for information bits
• Let ysr be the received signal sequence at the
  relay transmitted from the source.
• The relay first uses ysr to calculate the APP of
  bk, k1,, l, as follows
• 
  , w0, 1
• where m and m are a pair of states connected
  with bkw in the trellis, Ms is the number of
  states in the trellis, ak(m) and ßk(m) are the
  feed-forward and the feedback recursive
  variables, which can be calculated in a recursive
  format.

17
DTC-SIR

• 2nd step Calculate the APP of parity symbols
  for the interleaved source information
• Definitions
• 
  Interleaved version of the binary information
  stream B, where is the k-th symbol in .
• Vector of parity
  symbols of , where is the corresponding
  parity symbol of .
• 
  Set of the APPs of information bits
• 
  Set
  of APPs of interleaved information symbols

18
DTC-SIR

• , The APP of
  given PB, or equivalently, given .
  
• We develop the following recursive equations to
  calculate this probability,

S0 S1 S2 S3
S0 S1 S2 S3
19
DTC-SIR
S0 S1 S2 S3
S0 S1 S2 S3
20
Soft Estimate Calculation

• 3rd step Calculation of the parity soft symbol
  estimate for the interleaved source information
• For BPSK modulation, we assume 0, 1 are mapped
  into 1 and -1, separately. Then the soft estimate
  of , can be calculated as follows,
• 
  , k1,,l

21
Modeling of Soft Information

• Conventional modeling

the exact transmitted symbol.
an equivalent noise.
If and are independent, then the
average power of is
.
However, it can be noted , and
.
This means that and are not independent.
22
Modeling of Soft Information

• New model of soft information
• where is an equivalent noise with
  mean
• and variance
• The signals transmitted from the relay can
  then be written as

23
Soft Information Relaying

• a normalization factor calculated from
  the transmitted power constraint at the relay
• where P2 is the transmitted power limit at
  the relay.
• The destination received signal forwarded
  from the relay at time k, denoted by yrd,k, can
  be written as
• 
  equivalent noise with zero mean and variance of

24
Iterative Receiver
Information sequence
Received from Source
Turbo code sequence
Parity Soft Estimate of Interleaved Information
Received from Relay
Time frame 2
Time frame 1
Receiving Scheduling
Iterative receiver
25
Outline

• Introduction
• Distributed Turbo Coding with Soft Information
  Relaying
• Performance Analysis
• Simulation Results
• Conclusions
• Open Problems

26
Performance Analysis

• Definitions
• Average destination SNR for
  the signals transmitted from the source
• Average destination SNR for
  the signals transmitted from the relay
• Average received SNR at the
  relay.
• Psd the received power at the destination
  transmitted from the source
• Prd the received power at the destination
  transmitted from the relay
• Psr the received power at the relay transmitted
  from the source

27
BER Upper Bound

• The BER upper bound for DTC-SIR
• The BER upper bound for perfect DTC is
  given by

28
Performance Loss of DTC-SIR

• The performance loss of the DTC-SIR compared to
  the perfect DTC at the same SNR, denoted by
  BERloss, can be approximated as
• Observations
• Increasing Rdfree can reduce SNRloss. Hence use
  of a robust coding scheme can reduce the gap
  between the DTC-SIR and the perfect DTC
• Decreasing can also reduce
  SNRloss.

29
Outline

• Introduction
• System Model
• Distributed Turbo Coding with Soft Information
  Relaying
• Performance Analysis
• Simulation Results
• Conclusions
• Open Problems

30
Simulation Conditions

• BPSK modulation.
• Frame size 130 symbols
• 4-state recursive systematic convolutional code
  (RSC) with the code rate of ½ as the turbo
  component code
• Code generator matrix and its
  dfree is 5.
• The BER loss of the DTC-SIR compared to the
  perfect DTC
• For simplicity, we also assume Prd and Psd are
  the same. Therefore is equal to .

31
Scenario I

• Comparison of the perfect DTC and the DTC-SIR for
  various
• In this case, we investigate the
  performance of the DTC when the channel quality
  from the source to the relay is fixed and that
  from the source to the destination and the one
  from the relay to the destination are varied.

32
Simulation Results
BER performance comparison at rs-r10dB.
33
BER performance comparison at rs-r15dB.
34
BER performance comparison at rs-r25dB.
35
Analytical and Simulation Results

• Comparison between the analytical performance
  loss and simulation results.
• The calculated bounds are only tight for the
  higher because of some approximations. .

36
Throughput Comparison

• Throughput comparison of two schemes
• Assumption ARQ protocol is performed for the
  DTC-ARQ in the link from the source to the relay.
  The maximum number of retransmission is set as 3.

37
Scenario II

• 2. Comparison of the perfect DTC and the DTC-SIR
  for various SNR gaps between and .
• 
  SNR gap between and .
• We assume that the signal energy decays
  exponentially at the order of k with distance
  between two nodes. Then we have
• Power amplification factor
• Geometrical distribution factor
• We evaluate the performance the DTC-SIR for
  various SNR gaps to investigate the effect of
  power amplification factor and the network
  geometrical distribution on system performance
  and throughput

38
Simulation Results

• Performance comparison for various SNR_Gap0dB

39

• Performance comparison for various SNR_Gap4dB

40
Analytical and Simulation Results

• Comparison between the analytical and simulation
  results

41
Throughput

• Throughput comparison

42
Discussions

• DTC-SIR can approach the perfect DTC as SNR_Gap
  increases.
  
• It is determined by the power amplification
  factor and the geometrical distribution factor .
• In order to increase the SNR_Gap, we should
• (1) Decrease dsr/drd. This can be achieved by
  placing the relay closer to the source than to
  the destination
• (2) Increase Ps/Prd. This can be achieved by
  making the transmit power from the source larger
  than that from the relay.

43
Outline

• Introduction
• System Model
• Distributed Turbo Coding with Soft Information
  Relaying
• Performance Analysis
• Simulation Results
• Conclusions
• Open Problems

44
Conclusions

• We present a new cooperative coding scheme ----
  DTC--SIR.
• In DTC-SIR, the relay delivers the corresponding
  soft information of the codeword to the
  destination.
• In order to make the performance of the DTC-SIR
  approach the the perfect DTC,
• - The relay should be placed as closer to the
  source as possible
• - and/or make the ratio of source and relay
  transmit power as larger as possible

45
Open problems

• Distributed coding for multi-hop networks
• Distributed LDPC codes
• Distributed space time codes
• MIMO relay networks

46
Questions ?