Latency-Reliability Tradeoff in Short-Packet Communications - - PowerPoint PPT Presentation

Latency-Reliability Tradeoff in Short-Packet Communications

Giuseppe Durisi Chalmers, Sweden May 2016 joint work with J. ¨ Ostman, W. Yang, T. Koch, and Y. Polyanskiy

5G: beyond enhanced broadband 5G

higher data rates low latency high reliability massive number

• f devices

enhanced broadband massive MTC mission critical MTC

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Low-latency ultra-reliable MTC

LTE

• Long packets (500 bytes)
• PEP of 10−1 at 5 ms latency
• High reliability through

retransmissions 5G

• Short packets (10 bytes)
• 1 ms latency
• 10−5 − 10−9 PEP
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This talk

Understand the tradeoff between reliability, latency, and throughput

• How to deal with fading, how to use MIMO

The approach

• Rely on closed-form bounds and approximations

The main tool Finite-blocklength information theory

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A brief introduction to FBL IT

0.2 0.4 0.6 0.8 1

• max. coding rate

possible not possible rate → packet error probability Beginning of last century

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A brief introduction to FBL IT

0.2 0.4 0.6 0.8 1 blocklength rate → packet error probability 1948: Shannon, channel capacity

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A brief introduction to FBL IT

0.2 0.4 0.6 0.8 1 rate → packet error probability Vertical asymptotics ⇒ error exponent (Gallager,. . . )

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A brief introduction to FBL IT

0.2 0.4 0.6 0.8 1 rate → packet error probability Horizontal asymptotics ⇒ strong converse, fixed-error asymptotics (Wolfowitz, Strassen,. . . )

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A brief introduction to FBL IT

0.2 0.4 0.6 0.8 1 rate → packet error probability Today: tight bounds and accurate approximations (Hayashi, Polyanskiy, Poor and Verd´ u,. . . )

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AWGN channel, SNR = 0 dB, ǫ = 10−3

100 300 500 700 900 1100 1300 1500 1700 1900 0.1 0.2 0.3 0.4 0.5 capacity blocklength, n rate, R

Cawgn(ρ) = 1 2 log(1 + ρ)

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AWGN channel, SNR = 0 dB, ǫ = 10−3

100 300 500 700 900 1100 1300 1500 1700 1900 0.1 0.2 0.3 0.4 0.5 capacity meta-converse bound (PPV ’10) achievability bound (Shannon ’59) blocklength, n rate, R

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AWGN channel, SNR = 0 dB, ǫ = 10−3

100 300 500 700 900 1100 1300 1500 1700 1900 0.1 0.2 0.3 0.4 0.5 capacity meta-converse bound (PPV ’10) achievability bound (Shannon ’59) normal approximation blocklength, n rate, R

Cawgn(ρ) = 1 2 log(1 + ρ); Vawgn(ρ) = ρ(2 + ρ) 2(1 + ρ)2

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AWGN channel, SNR = 0 dB, ǫ = 10−3

100 300 500 700 900 1100 1300 1500 1700 1900 0.1 0.2 0.3 0.4 0.5 capacity meta-converse bound (PPV ’10) achievability bound (Shannon ’59) normal approximation blocklength, n rate, R

R∗(n, ǫ) ≈ Cawgn(ρ) −

• Vawgn(ρ)

n Q−1(ǫ) + 1 2 log n n

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Fundamental tool: binary hypothesis testing

• Binary hypothesis testing between PXnPY n | Xn and PXnQY n
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Fundamental tool: binary hypothesis testing

• Binary hypothesis testing between PXnPY n | Xn and PXnQY n
• Neyman-Pearson Beta function: β1−ǫ(PXnPY n | Xn, PXnQY n)
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Fundamental tool: binary hypothesis testing

• Binary hypothesis testing between PXnPY n | Xn and PXnQY n
• Neyman-Pearson Beta function: β1−ǫ(PXnPY n | Xn, PXnQY n)
• Performance of a (n, M, ǫ)-code [Vazquez-Vilar et al. 2015]

log M n = 1 n inf

QY n log

1 β1−ǫ(PXnPY n | Xn, PXnQY n)

• G. Durisi

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Fundamental tool: binary hypothesis testing

• Binary hypothesis testing between PXnPY n | Xn and PXnQY n
• Neyman-Pearson Beta function: β1−ǫ(PXnPY n | Xn, PXnQY n)
• Performance of a (n, M, ǫ)-code [Vazquez-Vilar et al. 2015]

log M n = 1 n inf

QY n log

1 β1−ǫ(PXnPY n | Xn, PXnQY n)

• Metaconverse bound [Polyanskiy et al., 2010]

R∗(n, ǫ) ≤ 1 n sup

PXn

log 1 β1−ǫ(PXnPY n | Xn, PXnQY n)

• G. Durisi

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Fundamental tool: binary hypothesis testing

• Binary hypothesis testing between PXnPY n | Xn and PXnQY n
• Neyman-Pearson Beta function: β1−ǫ(PXnPY n | Xn, PXnQY n)
• Performance of a (n, M, ǫ)-code [Vazquez-Vilar et al. 2015]

log M n = 1 n inf

QY n log

1 β1−ǫ(PXnPY n | Xn, PXnQY n)

• Metaconverse bound [Polyanskiy et al., 2010]

R∗(n, ǫ) ≤ 1 n sup

PXn

log 1 β1−ǫ(PXnPY n | Xn, PXnQY n)

• Achievability bounds of same form are available [latest one at

ISIT’16]

• G. Durisi

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Fundamental tool: binary hypothesis testing

• Binary hypothesis testing between PXnPY n | Xn and PXnQY n
• Neyman-Pearson Beta function: β1−ǫ(PXnPY n | Xn, PXnQY n)
• Performance of a (n, M, ǫ)-code [Vazquez-Vilar et al. 2015]

log M n = 1 n inf

QY n log

1 β1−ǫ(PXnPY n | Xn, PXnQY n)

• Metaconverse bound [Polyanskiy et al., 2010]

R∗(n, ǫ) ≤ 1 n sup

PXn

log 1 β1−ǫ(PXnPY n | Xn, PXnQY n)

• Achievability bounds of same form are available [latest one at

ISIT’16]

• Asymptotic analysis through Berry Esse´

en CLT

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Actual codes: bi-AWGN, ǫ = 10−3

102 103 104 105 0.6 0.7 0.8 0.9 1 Blocklength, n Normalized rate Turbo R=1/3 Turbo R=1/6 Turbo R=1/4 Voyager Galileo HGA Turbo R=1/2 Cassini/Pathfinder Galileo LGA BCH (Koetter-Vardy) BCH+OSD Polar+CRC R=1/2, L=32 Polar+CRC R=1/2, L=256 ME LDPC R=1/2, BP

• Y. Polyanskiy, “Channel coding: non-asymptotic fundamental limits,” Ph.D. dissertation,

Princeton University, Princeton, NJ, Nov. 2010.

• G. Durisi, T. Koch, and P. Popovski, “Towards massive, ultra-reliable, and low-latency

wireless communication with short packets,” Proc. IEEE, 2016

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A finite-blocklength problem in 5G

14 OFDM symbols 12 subcarriers

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A finite-blocklength problem in 5G

P P P P 14 OFDM symbols 12 subcarriers

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A finite-blocklength problem in 5G

P P P P 14 OFDM symbols 12 subcarriers

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A finite-blocklength problem in 5G

P P P P 14 OFDM symbols 12 subcarriers

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MIMO Rayleigh block-fading model

Encoder Decoder Fading Process

Hi Xi Yi Zi ∼ CN(0, N0)

• AWGN channel with fluctuating SNR

Yi = HiXi + Zi, i = 1, . . . , n

• Fading process unknown at TX and RX (no CSI)
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MIMO Rayleigh block-fading model

nc n = nc`, ` ∈ N

• nc: coherence interval
• ℓ: number of time-frequency diversity branches
• mt × mr MIMO channel
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Definition of (ℓ, nc, M, ǫ, ρ) code

decoder encoder

Xn J Y n ˆ J

+

W n

nc n = nc`, ` ∈ N

• Message J ∈ {1, 2, . . . , M}
• Encoder maps J to a codeword [X1, . . . , Xℓ]
• Power constraint: tr{XH

k Xk} = ncρ

• Decoder guesses J from [Y1, . . . , Yℓ]
• Maximum probability of error

max

1≤j≤M Pr{ ˆ

J = J | J = j} ≤ ǫ

• Rate: (log M)/(ncℓ)
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Maximum coding rate

decoder encoder

Xn J Y n ˆ J

+

W n

nc n = nc`, ` ∈ N

Maximum coding rate R∗(ℓ, nc, ǫ) = sup log M ncℓ : exists (ℓ, nc, M, ǫ, ρ)-code

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Our example: LTE evolution towards 5G

• packet length:

168 symbols

• 14 OFDM symbols, 12

tones per symbol

• PEP ǫ = 10−5
• SNR ρ = 6 dB
• 2 × 2 MIMO

168 84 42 24 12 8 6 4 coherence interval nc (log scale) 1 2 4 7 14 21 28 42 0.5 1 1.5 2 2.5 3

= ⇒

spacing tones apart in frequency spacing OFDM symbols apart in time time-frequency diversity branches ℓ (log scale) bit/channel use

nc n = nc`, ` ∈ N

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Our example: LTE evolution towards 5G

• packet length:

168 symbols

• 14 OFDM symbols, 12

tones per symbol

• PEP ǫ = 10−5
• SNR ρ = 6 dB
• 2 × 2 MIMO

168 84 42 24 12 8 6 4 coherence interval nc (log scale) 1 2 4 7 14 21 28 42 0.5 1 1.5 2 2.5 3

= ⇒

spacing tones apart in frequency spacing OFDM symbols apart in time time-frequency diversity branches ℓ (log scale) bit/channel use

nc n = nc`, ` ∈ N

• A. Lozano and N. Jindal, “Transmit diversity vs. spatial multiplexing in modern MIMO

systems,” IEEE Trans. Wireless Commun., vol. 9, no. 1, pp. 186–197, Sep. 2010.

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Asymptotic IT: outage capacity

nc n = nc`, ` ∈ N

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Asymptotic IT: outage capacity

nc n = nc`, ` ∈ N

lim

nc→∞R∗(ℓ, nc, ǫ) = Cout,ǫ

= sup {R : inf Pout(R) ≤ ǫ} Pout(R) = Pr ℓ

• k=1

log det(Imr + HH

k QkHk) ≤ ℓR

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Asymptotic IT: outage capacity

nc n = nc`, ` ∈ N

lim

nc→∞R∗(ℓ, nc, ǫ) = Cout,ǫ

= sup {R : inf Pout(R) ≤ ǫ} Pout(R) = Pr ℓ

• k=1

log det(Imr + HH

k QkHk) ≤ ℓR

• Same as when CSI is available at RX; CSI acquisition cost is lost
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Asymptotic IT: outage capacity

nc n = nc`, ` ∈ N

lim

nc→∞R∗(ℓ, nc, ǫ) = Cout,ǫ

= sup {R : inf Pout(R) ≤ ǫ} Pout(R) = Pr ℓ

• k=1

log det(Imr + HH

k QkHk) ≤ ℓR

• Same as when CSI is available at RX; CSI acquisition cost is lost
• Fast convergence [Yang, Durisi, Koch, Polyanskiy, ‘14]

R∗(ℓ, nc, ǫ) = Cout,ǫ + O log nc nc

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Asymptotic IT: outage capacity

nc n = nc`, ` ∈ N

lim

nc→∞R∗(ℓ, nc, ǫ) = Cout,ǫ

= sup {R : inf Pout(R) ≤ ǫ} Pout(R) = Pr ℓ

• k=1

log det(Imr + HH

k QkHk) ≤ ℓR

• Same as when CSI is available at RX; CSI acquisition cost is lost
• Fast convergence [Yang, Durisi, Koch, Polyanskiy, ‘14]

R∗(n, ǫ) = Cawgn −

• Vawgn

n Q−1(ǫ) + O log n n

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Asymptotic IT: outage capacity

nc n = nc`, ` ∈ N

lim

nc→∞R∗(ℓ, nc, ǫ) = Cout,ǫ

= sup {R : inf Pout(R) ≤ ǫ} Pout(R) = Pr ℓ

• k=1

log det(Imr + HH

k QkHk) ≤ ℓR

• Same as when CSI is available at RX; CSI acquisition cost is lost
• Fast convergence [Yang, Durisi, Koch, Polyanskiy, ‘14]

R∗(ℓ, nc, ǫ) = Cout,ǫ + O log nc nc

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Outage capacity

168 84 42 24 12 8 6 4 coherence interval nc (log scale) 1 2 4 7 14 21 28 42 0.5 1 1.5 2 2.5 3 Cout,ǫ time-frequency diversity branches ℓ (log scale) bit/channel use

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Asymptotic IT: ergodic capacity

nc n = nc`, ` ∈ N

lim

ℓ→∞R∗(ℓ, nc, ǫ) = Cerg

= 1 ncℓ sup I(X; Y)

• It holds for all 0 < ǫ < 1 (strong converse)
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Asymptotic IT: ergodic capacity

nc n = nc`, ` ∈ N

lim

ℓ→∞R∗(ℓ, nc, ǫ) = Cerg

= 1 ncℓ sup I(X; Y)

• It holds for all 0 < ǫ < 1 (strong converse)
• At high SNR [Zheng & Tse, ‘02; Yang et al., ‘12]

Cerg(ρ) = m∗ (1 − m∗/nc) log ρ + c + o(1) where m∗ = min{mt, mr, ⌊nc/2⌋}

• Tight bounds available [Alfano et al., ‘14, Devassy et al., ‘15]
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Ergodic capacity

168 84 42 24 12 8 6 4 coherence interval nc (log scale) 1 2 4 7 14 21 28 42 0.5 1 1.5 2 2.5 3 Cerg (USTM lb) m∗

t = 1

time-frequency diversity branches ℓ (log scale) bit/channel use

Unitary space-time modulation (USTM) ⇒ isotropically distributed input with orthogonal columns

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Asymptotic approximations on R∗(ℓ, nc, ǫ)

168 84 42 24 12 8 6 4 coherence interval nc (log scale) 1 2 4 7 14 21 28 42 0.5 1 1.5 2 2.5 3 Cout,ǫ Cerg (USTM lb) m∗

t = 1

time-frequency diversity branches ℓ (log scale) bit/channel use

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FBL to unveil the nonasymptotic truth

• Metaconverse bound
• Dependence testing

achievability bound

• Appropriate choice of input

distribution and auxiliary channel (USTM!)

100 300 500 700 900 1100 1300 1500 1700 1900 0.1 0.2 0.3 0.4 0.5 capacity converse bound achievability bound ≈ normal approximation blocklength, n rate, R

• G. Durisi, T. Koch, J. ¨

Ostman, Y. Polyanskiy, and W. Yang, “Short-packet communica- tions over multiple-antenna Rayleigh-fading channels,” IEEE Trans. Commun., 2016

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Nonasymptotic bounds on R∗(ℓ, nc, ǫ)

168 84 42 24 12 8 6 4 coherence interval nc (log scale) 1 2 4 7 14 21 28 42 0.5 1 1.5 2 2.5 3 ℓ∗ mt = 1 Cout,ǫ Cerg (USTM lb) time-frequency diversity branches ℓ (log scale) bit/channel use MC upper bound DT lower bound R∗(nc, l, ǫ)

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Diversity or multiplexing? 2 × 2 MIMO, ǫ = 10−5

168 84 42 24 12 8 6 4 coherence interval nc (log scale) 1 2 4 7 14 21 28 42 0.5 1 1.5 2 2.5 3 Alamouti Cout,ǫ Cerg (USTM lb) time-frequency diversity branches ℓ (log scale) bit/channel use MC upper bound DT lower bound R∗(nc, l, ǫ)

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Diversity or multiplexing? 4 × 4 MIMO, ǫ = 10−5

168 84 56 42 24 12 8 coherence interval nc (log scale) 1 2 3 4 7 14 21 1 2 3 4 5 6 FSTD Cout,ǫ Cerg (USTM lb) time-frequency diversity branches ℓ (log scale) bit/channel use MC upper bound DT lower bound R∗(nc, ℓ, ǫ, ρ)

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Conclusions

• FBL IT: elegant theory, tight bounds, engineering insights
• Optimal design of mission-critical MTC must rely on FBL IT
• Extensions: CSIT and power control, minimum energy per bit
• Open issues:
• Higher reliability? Shorter packet size? Normal approximation?
• User acquisition, packet detection overhead?
• (Decision/stop) feedback?
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SPECTRE: short packet communication toolbox

• Collection of numerical routines in

finite-blocklength information theory

• Available freely on GitHub

github.com/yp-mit/spectre

• Contributors: A. Collins, G. Durisi, J.

¨ Ostman, V. Kostina, Y. Polyanskiy, I. Tal, W. Yang

• Want to contribute? Contact us!

102 103 104 105 0.6 0.7 0.8 0.9 1 Blocklength, n Normalized rate Turbo R=1/3 Turbo R=1/6 Turbo R=1/4 Voyager Galileo HGA Turbo R=1/2 Cassini/Pathfinder Galileo LGA BCH (Koetter-Vardy) BCH+OSD Polar+CRC R=1/2, L=32 Polar+CRC R=1/2, L=256 ME LDPC R=1/2, BP

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