No Symbol Left Behind a Link-Layer Protocol for Rateless Codes - - PowerPoint PPT Presentation

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No Symbol Left Behind a Link-Layer Protocol for Rateless Codes - - PowerPoint PPT Presentation

Oct 22, 2022 216 likes •626 views

No Symbol Left Behind a Link-Layer Protocol for Rateless Codes Peter Iannucci Jonathan Perry Hari Balakrishnan Devavrat Shah MIT Wednesday, August 29, 12 Preview of Key Ideas Wednesday, August 29, 12 Preview of Key Ideas 1.

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SLIDE 1

No Symbol Left Behind

a Link-Layer Protocol for Rateless Codes Peter Iannucci • Jonathan Perry Hari Balakrishnan • Devavrat Shah MIT

Wednesday, August 29, 12

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SLIDE 2

Preview of Key Ideas

Wednesday, August 29, 12

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SLIDE 3

Preview of Key Ideas

1 2 3 4

? ? ? ?

...

  • 1. Transmission Schedules & Rateless Codes

Wednesday, August 29, 12

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SLIDE 4

Preview of Key Ideas

1 2 3 4

? ? ? ?

...

  • 1. Transmission Schedules & Rateless Codes
  • 2. Backward Induction

Wednesday, August 29, 12

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SLIDE 5

Preview of Key Ideas

1 2 3 4

? ? ? ?

...

  • 1. Transmission Schedules & Rateless Codes
  • 2. Backward Induction

# of symbols P(decoded) 1

  • 3. The Decoding CDF

Wednesday, August 29, 12

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SLIDE 6

Automatic Repeat Request

Start payload

error?

NAK ACK

(ARQ)

Wednesday, August 29, 12

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SLIDE 7

Start

error?

NAK ACK

Hybrid ARQ

(HARQ)

redundancy

Wednesday, August 29, 12

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SLIDE 8

NAK

Type II HARQ

payload

error?

NAK

redundancy

Start

error?

ACK

Wednesday, August 29, 12

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SLIDE 9

NAK

Type II HARQ

payload

error?

NAK

redundancy

Start

error?

ACK

Wednesday, August 29, 12

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SLIDE 10

NAK

Type II HARQ

payload

error?

NAK

redundancy

Start

error?

ACK

Wednesday, August 29, 12

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SLIDE 11

NAK

Type II HARQ

payload

error?

NAK

redundancy

Start

error?

ACK

Wednesday, August 29, 12

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SLIDE 12

NAK

Type II HARQ

payload

error?

NAK

redundancy

Start

error?

ACK

Wednesday, August 29, 12

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SLIDE 13

NAK

Type II HARQ

payload

error?

NAK

redundancy

Start

error?

ACK

Wednesday, August 29, 12

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SLIDE 14

Transmission Schedule

payload redundancy

error? error?

Wednesday, August 29, 12

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SLIDE 15

Transmission Schedule

1

?

error?

?

error?

Feedback interval:

Wednesday, August 29, 12

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SLIDE 16

Transmission Schedule

1

?

error?

?

error?

Feedback interval:

(5, 5)

Wednesday, August 29, 12

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SLIDE 17

Rateless Codes

  • Prefix property (variable-length decoder)
  • Code is stronger when prefix is longer
  • Characterized by decoding CDF
  • (Potentially) also:
  • unlimited length
  • no need to pick constellation
  • tolerates arbitrary erasures

Wednesday, August 29, 12

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SLIDE 18

Rateless Codes

1 2 3 4 ... Feedback interval:

Aggressive

? ? ? ?

Wednesday, August 29, 12

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SLIDE 19

Rateless Codes

1 2 3 4 ... Feedback interval:

Aggressive

1 2 3 ... Feedback interval:

Moderate

? ? ?

1 2 ... Feedback interval:

Conservative

? ? ? ? ? ?

Wednesday, August 29, 12

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SLIDE 20

Backward Induction

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ... # symbols sent so far:

Strategy still unknown Strategy known Legend

Wednesday, August 29, 12

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SLIDE 21

Backward Induction

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ... # symbols sent so far:

Strategy still unknown Strategy known Legend

Wednesday, August 29, 12

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SLIDE 22

Backward Induction

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ... # symbols sent so far:

Strategy still unknown Strategy known Legend

Wednesday, August 29, 12

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SLIDE 23

Backward Induction

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ... # symbols sent so far:

Strategy still unknown Strategy known Legend

Wednesday, August 29, 12

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SLIDE 24

Backward Induction

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ... # symbols sent so far:

Strategy still unknown Strategy known Legend

Wednesday, August 29, 12

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SLIDE 25

Strategy still unknown Strategy known Legend

Backward Induction

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ... # symbols sent so far:

Wednesday, August 29, 12

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SLIDE 26

Strategy still unknown Strategy known Legend

Backward Induction

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ... # symbols sent so far:

Strategy to be found

Wednesday, August 29, 12

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SLIDE 27

Strategy still unknown Strategy known Legend

Backward Induction

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ... # symbols sent so far:

Strategy to be found Immediate cost to send so many symbols

Wednesday, August 29, 12

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SLIDE 28

Strategy still unknown Strategy known Legend

Backward Induction

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ... # symbols sent so far:

Strategy to be found Immediate cost to send so many symbols Cost of best fall-back plan (in event of NAK)

Wednesday, August 29, 12

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SLIDE 29

Strategy still unknown Strategy known Legend

Backward Induction

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ... # symbols sent so far:

Strategy to be found Immediate cost to send so many symbols Expected cost of fall-back

Wednesday, August 29, 12

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SLIDE 30

Strategy still unknown Strategy known Legend

Backward Induction

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ... # symbols sent so far:

Strategy to be found Immediate cost to send so many symbols Expected cost of fall-back

Wednesday, August 29, 12

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SLIDE 31

Strategy still unknown Strategy known Legend

Backward Induction

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ... # symbols sent so far:

Strategy to be found Immediate cost to send so many symbols Expected cost of fall-back

Wednesday, August 29, 12

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SLIDE 32

Induction: Base Case

  • Need to know strategy for all m > n

to find strategy for n.

  • How to bootstrap this infinite recursion?
  • Solution: modify the inputs to ensure that a

steady-state strategy exists

  • Full details in the paper

Wednesday, August 29, 12

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SLIDE 33

Summary of Results

  • Tested with Strider, spinal, raptor codes
  • Overhead ↓ 2.6–5.4x versus ARQ, HARQ
  • Throughput ↑ 26%
  • Throughput when inputs are only estimated

is just 1.57% less vs. fully known inputs

  • Estimation converges within 10-20 packets

Wednesday, August 29, 12

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SLIDE 34

Decoding CDFs

# of symbols P(decoded) 1

Wednesday, August 29, 12

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SLIDE 35

Decoding CDFs

# of symbols P(decoded) 1 High SNR Low SNR

Wednesday, August 29, 12

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SLIDE 36

Decoding CDFs

(empirical for spinal codes)

Wednesday, August 29, 12

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SLIDE 37

Decoding CDFs

(empirical for spinal codes)

Wednesday, August 29, 12

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SLIDE 38

Decoding CDFs

(empirical for raptor codes)

Wednesday, August 29, 12

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SLIDE 39

Key Ideas in RateMore

  • Even rateless codes need rate adaptation
  • More feedback = fewer wasted symbols
  • Induction picks # of symbols per feedback
  • Decoding CDF captures code and channel
  • Coordination helps amortize cost (paper)

Wednesday, August 29, 12

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SLIDE 40

Fading channel estimation

Wednesday, August 29, 12