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Lecture 3: Selective repeat Hybrid ARQ

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Title: Lecture 3: Selective repeat Hybrid ARQ


1
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

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

3
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

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

5
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

6
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

7
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

8
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

9
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

10
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

11
Performance evaluation (contd)
  • We have

12
Performance evaluation (contd)
  • Given
  • We have

13
Performance evaluation
  • Normalized throughput is

14
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

15
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

16
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

17
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

18
Performance Evaluation
  • We have

19
Performance evaluation
  • Normalized throughput is
  • N500, S10, ?0.1, Gaussian channel, noiseless
    feedback

20
Numerical results
SR type II
SR type I
SNR
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