An ARQ Technique Using Related Parallel and Serial Concatenated Convolutional Codes

1
An ARQ Technique Using Related Parallel and
Serial Concatenated Convolutional Codes

• Yufei Wu
• formerly with
• Mobile and Portable Radio Research Group
• Virginia Tech
• now with
• Motorola
• Schaumburg IL
• Matthew C. Valenti (presenter)
• Dept. of Comp. Sci. Elect. Eng.
• West Virginia University

2
Overview

• FEC, ARQ, and hybrid ARQ
• Concatenated Convolutional Codes
• Turbo codes
• Parallel (PCCC) vs. serial (SCCC) concatenations.
• Brief survey of hybrid ARQ techniques using turbo
  codes.
• Relationships between PCCC and SCCCs
• How to encode a PCCC using a SCCC encoder.
• A new hybrid ARQ technique that uses related SCCC
  and PCCCs.

3
FEC and ARQ

• FEC
• Forward Error Correction.
• Channel code used to 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.

4
Hybrid ARQ

• Hybrid ARQ 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.
• Combining strategies
• Type I hybrid ARQ
• Discard previously received code word.
• Type II hybrid ARQ
• Keep previously received code word.
• Combine with received retransmitted code word.
• Variations Code combining and diversity
  combining.

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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.
• BER flooring effect at high SNR.

Systematic Output
Input
RSC Encoder 1
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 Stuber
• 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.
• None propose using SCCCs.

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A General Purpose Encoder

• It is possible to generate related PCCC and
  SCCCs using a single encoder.
• Outputs constitute a SCCC.
• Outputs constitute a PCCC.

RSC Encoder 1
RSC Encoder 2
interleavers
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Equivalent SCCC Encoder

• We may express the general encoder as a SCCC
  encoder.
• ?eq is an equivalent interleaver.
• RSC 1s systematic output must be mapped to the
  first half of the input into RSC 2.
• RSC 1s parity output must be mapped to the last
  half of the input into RSC 2.

RSC Encoder 1
RSC Encoder 2
equivalent interleaver
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Equivalent PCCC Encoder

• If is not transmitted, then the encoder can
  be expressed as a PCCC encoder

RSC Encoder 1
RSC Encoder 2
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New Hybrid ARQ Technique

• Encode data with error detection code.
• Then encode with the generalized encoder.
• Transmit the PCCC information
• Store in a buffer
• Decode received PCCC code word.
• Check decoded PCCC code word for errors.
• If no errors, then stop.
• Otherwise, send NACK to the transmitter.
• Transmit
• Combine received with received to
  create a received SCCC code word. Decode.
• Check decoded SCCC code word for errors.
• If no errors then stop.
• Otherwise discard information and go back to (1).

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Simulation Parameters

• 16 bit error detecting CRC code.
• 1,024 bit input into FEC encoder.
• Includes the 16 parity bits.
• S-random or spread interleaver design.
• Both RSC 1 and RSC 2 are identical constraint
  length 4 RSC encoders (rate ½).
• Both encoders are terminated with a 3-bit tail.
• Decoder uses 10 iterations of log-MAP.
• AWGN channel and BPSK/QPSK modulation.
• Compared with
• Conventional PCCC code
• Type-I hybrid ARQ PCCC with maximum of 1
  retransmission.

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BER Comparison
0
10
PS-ARQ
PC-ARQ
-1
10
PC-FEC
-2
10
BER
-3
10
-4
10
-5
10
-6
10
-5
-4.5
-4
E
/N
(dB)
s
0
15
FER Comparison
0
10
-1
10
-2
10
FER
-3
10
-4
10
PS-ARQ
PC-ARQ
PC-FEC
-5
10
-5
-4.5
-4
E
/N
(dB)
s
0
16
Throughput Efficiency
0.35
0.3
0.25
0.2
Throughput Efficiency
0.15
0.1
PS-ARQ
0.05
PC-ARQ
PC-FEC
0
-5
-4.5
-4
E
/N
(dB)
s
0
17
Complexity Load
4
10
PS-ARQ
PC-ARQ
PC-FEC
3
10
Complexity Load
2
10
1
10
0
10
-5
-4.5
-4
E
/N
(dB)
s
0
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Summary

• Conclusion
• An SCCC encoder can be used to encode a PCCC.
• This result was used to develop a new hybrid ARQ
  strategy.
• The proposed technique offers superior
  performance over ARQ techniques derived solely
  from PCCCs.
• Future work
• Comparison with other ARQ techniques.
• Narayanan and Stuber
• Rowitch and Milstein
• Use of other encoders and puncturing schemes.
• Determine what to do if there are residual errors.