Hybrid ARQ using Serial Concatenated Convolutional Codes over Fading Channels

1
Hybrid ARQ using Serial Concatenated
Convolutional Codes over Fading Channels

• Naveen Chandran
• Graduate Research Assistant
• Lane Dept. of Comp. Sci. Elect. Engg.
• West Virginia University
• Matthew C. Valenti (presenter)
• Assistant Professor
• Lane Dept. of Comp. Sci. Elect. Engg.
• West Virginia University
• mvalenti_at_wvu.edu

2
Overview

• FEC, ARQ, hybrid ARQ and retransmission
  strategies.
• Concatenated Convolutional Codes.
• Turbo codes
• Parallel (PCCC) vs. serial (SCCC) concatenations.
• Survey of hybrid ARQ techniques using turbo
  codes.
• Turbo Coding-ARQ System Model and process chart.
• Simulation parameters and assumptions.
• Throughput efficiency.
• Summary and future work.

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FEC and ARQ

• FEC Forward Error Correction
• Channel code used to only correct errors.
• ARQ Automatic Repeat Request
• Channel code used to detect errors.
• A feedback channel is present
• If no detected errors, an acknowledgement (ACK)
  is sent back to transmitter.
• If there are detected errors, a negative
  acknowledgement (NACK) is sent back.
• Retransmission if NACK or no ACK.
• Several retransmission strategies
• Stop and wait, go-back-N, selective repeat, etc.
• Selective repeat has better throughout
  performance than the others in the presence of
  propagation delays.
• However, throughput of stop and wait and
  selective repeat protocols are the same if no
  transmission delay is assumed.

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Hybrid FEC/ARQ

• Combines forward error correction with ARQ.
• Assumption Availability of a noise free feedback
  channel
• Uses an outer error detecting code in conjunction
  with an inner error correcting code
• The receiver first tries to correct as many
  errors as possible using the inner code.
• If there are any remaining errors, the outer code
  will (usually) detect them.
• Retransmission requested if the outer code
  detects an error.

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Retransmission Strategies

• Two generic types of hybrid FEC/ARQ.
• Type I hybrid ARQ
• Discard erroneous received code word.
• Retransmit until packet correctly received or
  until pre-set number of retransmissions is
  achieved.
• Small buffer size required but an inefficient
  scheme.
• Type II hybrid ARQ
• Store erroneous received code word.
• Optimally combine with retransmitted code word.
• Exploit incremental redundancy concept
• Effective Code rate is gradually lowered until
  packet is decoded correctly.
• System adapts to varying channel conditions.
• Larger buffer size required than Type-I but is a
  very efficient scheme.

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Turbo Codes

• Key features
• Concatenated Convolutional Codes.
• PCCC Parallel Concatenated Convolutional Codes.
• SCCC Serial Concatenated Convolutional Codes.
• Nonuniform interleaving.
• Recursive systematic encoding.
• RSC Recursive Systematic Convolutional Codes.
• For PCCC both encoders are RSC.
• For SCCC at least the inner encoder is RSC.
• Iterative decoding algorithm.
• MAP/APP based.
• Log-MAP In logarithmic domain.

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PCCCs

• Features of parallel concatenated convolutional
  codes (PCCCs)
• Both encoders are RSC.
• Performance close to capacity limit for BER down
  to about 10-5 or 10-6 (i.e. in the cliff region).
• BER flooring effect at high SNR.

Input
RSC Encoder 1
Systematic Output
Parity Output
RSC Encoder 2
Nonuniform Interleaver
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SCCCs

• Features of serially concatenated convolutional
  codes (SCCCs)
• Inner encoder must be recursive.
• Outer encoder can be recursive or nonrecursive.
• Performance not as good as PCCCs at low SNR.
• However, performance is better than PCCCs at
  high SNR because the BER floor is much lower.

Input
Output
Outer Encoder
Inner Encoder
Nonuniform Interleaver
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Turbo Codes and Hybrid ARQ

• Turbo codes have been applied to hybrid ARQ.
• Narayanan and Stüber
• Interleave the input to the turbo encoder with a
  different interleaving function for each
  retransmission.
• Use log-likelihood ratios from last transmission.
• Rowitch and Milstein.
• Rate-compatible punctured turbo (RCPT) codes.
• Buckley and Wicker
• Use cross-entropy instead of a CRC to detect
  errors.
• Error detection threshold adaptively determined
  with a neural network.
• All the above use PCCCs.
• Wu Valenti (ICC 2000) had PCCC/SCCC approach.

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Turbo Coding-ARQ System Model

Channel Inter- leaver
Puncture Buffer
Turbo Encoder
BPSK Modul- ator
uk
yk
ak
Feedback for Type II Hybrid ARQ
ACK NACK


nk
Channel De-Inter- leaver
rk
Turbo Decoder
Error Detection
ûk
Channel Estimator
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Coding-ARQ process chart
Start with Maximum Code Rate
Transmit code bits not previously sent
PCCC / SCCC Error correction
Reduce code rate to next lower rate
NO
Detect Errors after correction
Errors Still?
YES
Lowest Rate?
YES
Go on to Next Data Frame
NO
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Simulation Parameters

• Input frame size N 1024.
• Channel types
• AWGN
• Fully-interleaved Rayleigh Fading
• Turbo Channel Code Parameters
• PCCC and SCCC
• Each comprised of two identical RSC codes.
• Constraint Length K 5.
• Generator Polynomials in octal
• Feedback 35.
• Feedforward 23.
• Encoders terminated with a 4 bit tail.
• Decoder uses max-log-MAP algorithm.

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Simulation Parameters contd.

• Puncturing
• Period 8.
• For PCCC, code rates range from 4/5 to 1/3.
• For SCCC
• Outer code rate 2/3 (Puncturing parity bits
  alternatively).
• Inner code rate ranges from 1 to 1/2.
• Overall code rate ranges from 2/3 to 1/3.
• Channel Interleaver
• Spread interleaver with S18.
• Interleaver Sizes
• PCCC 1024.
• SCCC 1544.

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Simulation Assumptions

• Perfect channel estimates.
• Perfect error detection after turbo decoding.
• Noise free feedback channel from receiver to
  transmitter for ACK/NACK.
• No transmission delays.
• Stop and wait performs just as well as selective
  repeat protocol.
• SCCC puncturing patterns not optimized.

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BER comparison PCCC in AWGN Channel (N1024)
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BER comparison PCCC in Fading Channel (N1024)
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BER comparison SCCC in AWGN Channel (N1024)
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BER comparison PCCC in Fading Channel (N1024)
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Throughput Efficiency

• Defined as expectation of the code rate as a
  function of frame error rate (FER) at a
  particular value of signal to noise ratio (Es /
  No).
• Mathematically defined as
• is a particular code rate and
  is the probability mass
• function of the rate.

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Throughput Efficiency contd.

• Probability that the system is transmitting at a
  particular rate is the product of
• Probability of frame errors at higher rates and
• Probability of success at current rate.
• Probability mass function is given by

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Throughput comparison
AWGN Channel
Fading Channel
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Discussion

• In each case, the throughput of PCCC is better
  than SCCC.
• Why?
• For hybrid-ARQ, its the location of the cliff
  that matters, not the height of the floor.
• Thus, hybrid ARQ is not able to exploit the
  benefits of SCCC.
• However, the puncturing patterns were not
  optimized for SCCC.
• Systems that combine PCCC/SCCC appear to be
  promising.

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Summary

• Conclusion
• Like PCCCs, SCCCs can be used as part of a type
  II hybrid FEC/ARQ scheme.
• SCCCs offer lower BER floors than PCCCs.
• But, this comes at the cost of the cliff
  occurring at higher SNR.
• Initial results show that since the cliff region
  is the predominant contributor towards throughput
  efficiency rather than the height of the BER
  floor, SCCCs have lower throughput efficiency
  than PCCCs.
• Future Work
• Optimize puncturing patterns for SCCC to reduce
  the gap between the throughput efficiencies of
  PCCC and SCCC.
• Exploit the fact that a PCCC code is a particular
  type of SCCC code.
• Promising results could be achieved by using
  hybrid PCCC/SCCC codes.

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Puncturing Patterns
Table 1 Octal puncturing patterns for PCCC based
systems with code polynomial g (35,23), frame
size N 1024 and puncturing period P 8.
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Puncturing Patterns
Table 2 Octal puncturing patterns for SCCC based
systems with code polynomial g (35,23), frame
size N 1024 and puncturing period P 8.