Lecture 2: Hybrid ARQ

1
Lecture 2 Hybrid ARQ

• References
• K. S. Chan, Li Ping and Sammy Chan, Adaptive
  Type II Hybrid
• ARQ Scheme using Zigzag Code, Electronics
  Letters, vol. 35,
• No. 24, November 1999
• Samir Kallel, Efficient Hybrid ARQ Protocols
  with Adaptive
• Forward Error Correction, IEEE Trans.
  Commun., vol. 42,
• pp. 281-289, February/March/April 1994
• Samir Kallel, Analysis of a Type II Hybrid ARQ
  Scheme with Code
• Combining, IEEE Trans. Commun., vol. 38, pp.
  1133-1137,
• August 1990

2
Outline

• Introduction to hybrid ARQ
• Type 1 hybrid ARQ
• Type 2 hybrid ARQ
• Performance evaluation

3
Pros and cons of traditional ARQ

• Advantages
• Simple
• High efficiency when channel is good
• High reliability
• Disadvantages
• Low throughput when channel is poor
• High delay

4
hybrid ARQ

• Both error detection and correction redundancies
  sent
• Receiver side
• Error detected, try to correct first
• Correction failed, retransmit
• Type subtypes
• Type 1 uncorrectable, discard
• Type 2
• Uncorrectable, save
• For the ith try received, combine with previous
  tries to do error correction

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Punctured and repetition convolutional code

• Original rate 1/2 convolutional codes
• (V-1)/V punctured convolutional code
• Deleting (V-2) bits from every 2(V-1) coded bits
  , according to the well-defined perforation
  pattern
• An example 7/8 code with m6, perforation
  pattern is

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Punctured and repetition convolutional code

• Low rate (V-1)/(2(v-1)k), k?1 repetition code
• obtained from rate 1/2 code by repeating k bits
  among every 2(V-1) coded bits
• The k bits that are repeated are determined by a
  well-selected repetition pattern
• An example 7/17 code

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Type 1 hybrid ARQ

• Basic idea vary the coding rate according to the
  channel conditions, the round trip delay, and
  buffer size
• Rates used ri(V-1)/(V-1i), i0,1,2, Chosen to
  maximize the throughput
• Each k-bit information packet, appended np parity
  bits for error detection and m known tail bits to
  memory of encoder.
• Nknpm bits encoded with the appropriate rate

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Type I hybrid ARQ

• Transmission of a packet ? of n(knpm) bits
• Level i, 0?iltt where t is a positive integer ?
  is encoded with the code of rate
  ri(V-1)/(V-1hi), hi?0, and transmitted in the
  channel. If error-free, finished. Otherwise, to
  level i1
• Level i, i ? t ? is transmitted using the code
  of rate rt(V-1)/(V-1ht), ht ? 0. If decoding
  successful, finish. Otherwise, to level i1

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Multi-dimensional zigzag code
d(1,1)
d(1,2)
d(1,3)
d(1,4)
d(1,5)
d(2,3)
p(1)
d(2,4)
d(2,5)
d(2,1)
d(2,2)
p(2)
d(3,2)
d(3,3)
d(3,4)
d(3,5)
d(3,1)
p(3)
p(I-1)
d(I,2)
d(I,3)
d(I,4)
d(I,1)
d(I,5)
p(I)
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An example of zigzag code
1
0
1
1
0
I5?5
p(1)1
1
0
1
0
0
p(2)1
1
1
0
1
0
p(3)0
T
1
1
P11010
1
1
p(4)1
1
0
1
0
1
p(5)0
1
11
Multi-dimensional zigzag code
J
J
J
D1
P1
D2
DN
PN
P2
I
(a)
I
I
J
D
I
(b)
P1
P2
PN
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Type 2 ARQ

• The k-bit information packet is encoded as an
  (n,k) block code for error detection.
• The n-bit block code-word is encoded as a
  N-dimensional concatenated zigzag code.
• Divide the N parity vectors into m groups group
  1 G1 includes P1 to Pm1 group 2 G2 includes
  Pm11 to Pm2
• Transmission of this packet includes m levels

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Type 2 ARQ

• Level 1 Initially, the n-bit information packet
  and parity vectors in group G1 is transmitted.
• Receiver m1-dimensional zigzag code. After the
  decoding, the receiver decodes the (n,k) block
  code.
• error-free, complete.
• Otherwise, move up to level 2.
• Level i, 1ltiltm1 transmitter sends all parity
  vectors in group Gi
• Receiver combined with the previously received
  sequences for the same data packet,
  m2-dimensional zigzag code. Decode it.
• successful, complete
• Otherwise, move up to level i1 for iltm or level
  1 for im

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An example

• Information packet 500-bit block code-word.
• Information matrix 10?50 9-dimensional
  concatenated zigzag code-word
• parity vectors P1 to P9 divided into 2 groups G1
  includes P1, P2, , P7 G2 includes P8, P9

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An example

• Level 1 10?50 information matrix and P1---P7 are
  transmitted to the receiver.
• Receiver 7-dimensional zigzag code-word. Decoded
  for the 10?50 matrix. Then decoded for error
  detection.
• If error-free, complete.
• Otherwise, move up to level 2.
• Level 2 Transmitting P8 and P9
• Receiver Combined with the sequences received at
  level 1 , a 9-dimensional concatenated zigzag
  code-word. Decoded.
• If it is error-free, complete.
• Otherwise, move back to level 1.

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Performance evaluation

• Packet ? is n(knpm) bits, round trip delay is
  Sb bits, and physical overhead is ??b bits
• Noiseless feedback channel
• For stop-and-wait, at least (n ??b Sb) bits
  needed to send a packet
• Unified throughput
• where is the average number of bits needed to
  correctly deliver a packet

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Performance evaluation

• For go-back-N ARQ
• At least (n ??b ) bits needed to send a packet
• Throughput is defined as
• where is the average number of bits needed to
  correctly deliver a packet
• N500 bits, ??b 50 bits, and Sb5000 bits
• Gaussian channel

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Numerical results Stop-and-wait
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Numerical results go-back-N