Lecture 3: Selective repeat Hybrid ARQ

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Lecture 3 Selective repeat Hybrid ARQ

• References
• Samir Kallel, Efficient Hybrid ARQ Protocols
  with Adaptive
• Forward Error Correction, IEEE Trans.
  Commun., vol. 42,
• pp. 281-289, February/March/April 1994

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Outline

• Introduction to hybrid selective repeat ARQ
• Selective repeat type 1 hybrid ARQ
• Selective repeat type 2 hybrid ARQ
• Performance evaluation

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Selective repeat ARQ

• Unique features of selective repeat ARQ
• Out-of-sequence packets buffered at receiver side
• Finite buffer size buffer overflow
• Hybrid SR ARQ
• Do error correction
• Performance evaluation more difficult

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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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Basic Assumptions

• 1/2 convolutional code
• Coding rate ri(V-1)/(V-1hi)
• (V-1 information bits, hi redundancy
  bits)
• Buffer size qSb
• q positive integer
• Round trip delay Sb
• Physical overhead ?b
• Information packet size n (knpm) bits
• np bits for error detection
• m bits convolutional coding tail

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Type I SR 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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Transmission of Type 1 hybrid SR ARQ
Transmission of a packet ? of n(knpm) bits

• Level i, 0?iltq ? is encoded with the code of
  rate ri(V-1)/(V-1hi), hi?0, and transmitted in
  the channel.
• If error-free, finished
• Otherwise, discard the received sequence and move
  to level i1
• Level q at this point, the buffer is considered
  full. ? is transmitted using the code of rate
  rq(V-1)/(V-1hq), hq ? 0.
• If decoding successful, finish.
• Otherwise, discard the sequence and move to level
  q1
• Level i, igtq buffer overflow occurs, resulting
  in the loss of Sb bits which have to be
  retransmitted later. ? is transmitted using the
  code of rate rq(V-1)/(V-1hq), hq ? 0.
• If decoding successful, finish.
• Otherwise, discard the sequence and move to level
  i1

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Performance evaluation

• Transmission of a packet ? of n(knpm) bits
• Let ? ?b /n, and SSb/n
• Let Sj denote the event decoding success at level
  j of the ARQ protocol
• Let Fj denote the event of decoding failure at
  level j
• (r0, r1, , rt) denote the average number of
  bits that are transmitted per correctly decoded
  k-bit packet

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Performance evaluation (contd)

• We have

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Performance evaluation (contd)

• Given
• We have

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Performance evaluation

• Normalized throughput is

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Type 2 ARQ

• The k-bit information packet is encoded as an
  (n,k) block code for error detection
• run 1/2 repetition and punctured convolutional
  coding to choose h0, h1, h2, , hq for error
  correction so that we can have coding rate
• ri(V-1)/(v-1h0h1hi) which optimizes the
  performance
• Transmission of this packet includes m levels

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Transmission of type II SR ARQ

• Transmission of a packet ? of n(knpm) bits
• Level 0 ? is encoded with the code of rate
  r0(V-1)/(V-1h0), h0?0, and transmitted in the
  channel.
• If error-free, finished
• Otherwise, save the received sequence and move to
  level 1
• Level i, 1?iltq transmitter sends hi coded bits.
  At receiver side, a code word of rate
  ri(V-1)/(V-1h0h1hi), hi?1, is constructed
  and decoded.
• If error-free, finished
• Otherwise, save the received sequence and move to
  level i1
• Level q the receiver buffer is considered full.
  hq coded bits are sent. At receiver side, a code
  word of rate rq(V-1)/(V-1h0h1hq), hq?1, is
  constructed and decoded.
• If decoding successful, finish.
• Otherwise, discard the sequence and move to level
  q1Transmission of a packet ? of n(knpm) bits

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Transmission of type II SR ARQ (contd)

• Level j, jgtq buffer overflow occurs, resulting
  in the loss of Sb bits which have to be
  retransmitted later. hq coded bits are sent. At
  receiver side, a code word of rate
  rj(V-1)/(V-1h0h1(j-q1)hq) is constructed,
  and decoded.
• If decoding successful, finish.
• Otherwise, discard the sequence and move to level
  j1

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Performance evaluation

• Transmission of a packet ? of n(knpm) bits
• Let ? ?b /n, and SSb/n
• Let Sj denote the event decoding success at level
  j of the ARQ protocol
• Let Fj denote the event of decoding failure at
  level j
• (h0, h1, , ht) denote the average number of
  bits that are transmitted per correctly decoded
  k-bit packet

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Performance Evaluation

• We have

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Performance evaluation

• Normalized throughput is
• N500, S10, ?0.1, Gaussian channel, noiseless
  feedback

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Numerical results
SR type II
SR type I
SNR