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 enhanced broadband higher data rates 5G low latency massive number high reliability of devices massive MTC mission critical MTC 2 / 25 G. Durisi
Low-latency ultra-reliable MTC LTE 5G • Long packets (500 bytes) • Short packets (10 bytes) • PEP of 10 − 1 at 5 ms latency • 1 ms latency • 10 − 5 − 10 − 9 PEP • High reliability through retransmissions 3 / 25 G. Durisi
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 4 / 25 G. Durisi
A brief introduction to FBL IT 1 packet error probability 0 . 8 max. coding rate possible 0 . 6 0 . 4 not possible 0 . 2 0 rate → Beginning of last century 5 / 25 G. Durisi
A brief introduction to FBL IT 1 packet error probability 0 . 8 0 . 6 0 . 4 blocklength 0 . 2 0 rate → 1948: Shannon, channel capacity 5 / 25 G. Durisi
A brief introduction to FBL IT 1 packet error probability 0 . 8 0 . 6 0 . 4 0 . 2 0 rate → Vertical asymptotics ⇒ error exponent (Gallager,. . . ) 5 / 25 G. Durisi
A brief introduction to FBL IT 1 packet error probability 0 . 8 0 . 6 0 . 4 0 . 2 0 rate → Horizontal asymptotics ⇒ strong converse, fixed-error asymptotics (Wolfowitz, Strassen,. . . ) 5 / 25 G. Durisi
A brief introduction to FBL IT 1 packet error probability 0 . 8 0 . 6 0 . 4 0 . 2 0 rate → Today: tight bounds and accurate approximations (Hayashi, Polyanskiy, Poor and Verd´ u,. . . ) 5 / 25 G. Durisi
AWGN channel, SNR = 0 dB, ǫ = 10 − 3 capacity 0.5 0.4 rate, R 0.3 0.2 0.1 100 300 500 700 900 1100 1300 1500 1700 1900 blocklength, n C awgn ( ρ ) = 1 2 log(1 + ρ ) 6 / 25 G. Durisi
AWGN channel, SNR = 0 dB, ǫ = 10 − 3 capacity 0.5 meta-converse bound (PPV ’10) 0.4 rate, R 0.3 achievability bound (Shannon ’59) 0.2 0.1 100 300 500 700 900 1100 1300 1500 1700 1900 blocklength, n 6 / 25 G. Durisi
AWGN channel, SNR = 0 dB, ǫ = 10 − 3 capacity 0.5 meta-converse bound (PPV ’10) 0.4 normal approximation rate, R 0.3 achievability bound (Shannon ’59) 0.2 0.1 100 300 500 700 900 1100 1300 1500 1700 1900 blocklength, n C awgn ( ρ ) = 1 V awgn ( ρ ) = ρ (2 + ρ ) 2 log(1 + ρ ) ; 2(1 + ρ ) 2 6 / 25 G. Durisi
AWGN channel, SNR = 0 dB, ǫ = 10 − 3 capacity 0.5 meta-converse bound (PPV ’10) 0.4 normal approximation rate, R 0.3 achievability bound (Shannon ’59) 0.2 0.1 100 300 500 700 900 1100 1300 1500 1700 1900 blocklength, n � V awgn ( ρ ) Q − 1 ( ǫ ) + 1 log n R ∗ ( n, ǫ ) ≈ C awgn ( ρ ) − n 2 n 6 / 25 G. Durisi
Fundamental tool: binary hypothesis testing • Binary hypothesis testing between P X n P Y n | X n and P X n Q Y n 7 / 25 G. Durisi
Fundamental tool: binary hypothesis testing • Binary hypothesis testing between P X n P Y n | X n and P X n Q Y n • Neyman-Pearson Beta function: β 1 − ǫ ( P X n P Y n | X n , P X n Q Y n ) 7 / 25 G. Durisi
Fundamental tool: binary hypothesis testing • Binary hypothesis testing between P X n P Y n | X n and P X n Q Y n • Neyman-Pearson Beta function: β 1 − ǫ ( P X n P Y n | X n , P X n Q Y n ) • Performance of a ( n, M, ǫ ) -code [ Vazquez-Vilar et al. 2015 ] log M = 1 1 n inf Q Y n log n β 1 − ǫ ( P X n P Y n | X n , P X n Q Y n ) 7 / 25 G. Durisi
Fundamental tool: binary hypothesis testing • Binary hypothesis testing between P X n P Y n | X n and P X n Q Y n • Neyman-Pearson Beta function: β 1 − ǫ ( P X n P Y n | X n , P X n Q Y n ) • Performance of a ( n, M, ǫ ) -code [ Vazquez-Vilar et al. 2015 ] log M = 1 1 n inf Q Y n log n β 1 − ǫ ( P X n P Y n | X n , P X n Q Y n ) • Metaconverse bound [ Polyanskiy et al., 2010 ] R ∗ ( n, ǫ ) ≤ 1 1 n sup log β 1 − ǫ ( P X n P Y n | X n , P X n Q Y n ) P Xn 7 / 25 G. Durisi
Fundamental tool: binary hypothesis testing • Binary hypothesis testing between P X n P Y n | X n and P X n Q Y n • Neyman-Pearson Beta function: β 1 − ǫ ( P X n P Y n | X n , P X n Q Y n ) • Performance of a ( n, M, ǫ ) -code [ Vazquez-Vilar et al. 2015 ] log M = 1 1 n inf Q Y n log n β 1 − ǫ ( P X n P Y n | X n , P X n Q Y n ) • Metaconverse bound [ Polyanskiy et al., 2010 ] R ∗ ( n, ǫ ) ≤ 1 1 n sup log β 1 − ǫ ( P X n P Y n | X n , P X n Q Y n ) P Xn • Achievability bounds of same form are available [latest one at ISIT’16] 7 / 25 G. Durisi
Fundamental tool: binary hypothesis testing • Binary hypothesis testing between P X n P Y n | X n and P X n Q Y n • Neyman-Pearson Beta function: β 1 − ǫ ( P X n P Y n | X n , P X n Q Y n ) • Performance of a ( n, M, ǫ ) -code [ Vazquez-Vilar et al. 2015 ] log M = 1 1 n inf Q Y n log n β 1 − ǫ ( P X n P Y n | X n , P X n Q Y n ) • Metaconverse bound [ Polyanskiy et al., 2010 ] R ∗ ( n, ǫ ) ≤ 1 1 n sup log β 1 − ǫ ( P X n P Y n | X n , P X n Q Y n ) P Xn • Achievability bounds of same form are available [latest one at ISIT’16] • Asymptotic analysis through Berry Esse´ en CLT 7 / 25 G. Durisi
Actual codes: bi-AWGN, ǫ = 10 − 3 1 Turbo R=1/3 Turbo R=1/6 Turbo R=1/4 0 . 9 Voyager Normalized rate Galileo HGA Turbo R=1/2 0 . 8 Cassini/Pathfinder Galileo LGA BCH (Koetter-Vardy) BCH+OSD 0 . 7 Polar+CRC R=1/2, L=32 Polar+CRC R=1/2, L=256 ME LDPC R=1/2, BP 0 . 6 10 2 10 3 10 4 10 5 Blocklength, n 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 8 / 25 G. Durisi
A finite-blocklength problem in 5G 12 subcarriers 14 OFDM symbols 9 / 25 G. Durisi
A finite-blocklength problem in 5G P P 12 subcarriers P P 14 OFDM symbols 9 / 25 G. Durisi
A finite-blocklength problem in 5G P P 12 subcarriers P P 14 OFDM symbols 9 / 25 G. Durisi
A finite-blocklength problem in 5G P P 12 subcarriers P P 14 OFDM symbols 9 / 25 G. Durisi
MIMO Rayleigh block-fading model Fading Process H i X i Y i Encoder Decoder Z i ∼ CN (0 , N 0 ) • AWGN channel with fluctuating SNR Y i = H i X i + Z i , i = 1 , . . . , n • Fading process unknown at TX and RX (no CSI) 10 / 25 G. Durisi
MIMO Rayleigh block-fading model n c n = n c `, ` ∈ N • n c : coherence interval • ℓ : number of time-frequency diversity branches • m t × m r MIMO channel 11 / 25 G. Durisi
Definition of ( ℓ, n c , M, ǫ, ρ ) code n c W n ˆ J X n Y n J + encoder decoder n = n c `, ` ∈ N • Message J ∈ { 1 , 2 , . . . , M } • Encoder maps J to a codeword [ X 1 , . . . , X ℓ ] • Power constraint: tr { X H k X k } = n c ρ • Decoder guesses J from [ Y 1 , . . . , Y ℓ ] • Maximum probability of error 1 ≤ j ≤ M Pr { ˆ J � = J | J = j } ≤ ǫ max • Rate: (log M ) / ( n c ℓ ) 12 / 25 G. Durisi
Maximum coding rate n c W n ˆ J J X n Y n + encoder decoder n = n c `, ` ∈ N Maximum coding rate � log M � R ∗ ( ℓ, n c , ǫ ) = sup : exists ( ℓ, n c , M, ǫ, ρ ) -code n c ℓ 13 / 25 G. Durisi
Our example: LTE evolution towards 5G • packet length: coherence interval n c (log scale) 168 84 42 24 12 8 6 4 168 symbols 3 • 14 OFDM symbols, 12 bit/channel use 2 . 5 2 spacing tones apart in frequency tones per symbol = ⇒ 1 . 5 spacing OFDM symbols apart in time 1 • PEP ǫ = 10 − 5 0 . 5 0 • SNR ρ = 6 dB 1 2 4 7 14 21 28 42 time-frequency diversity branches ℓ (log scale) • 2 × 2 MIMO n c n = n c `, ` ∈ N 14 / 25 G. Durisi
Our example: LTE evolution towards 5G • packet length: coherence interval n c (log scale) 168 84 42 24 12 8 6 4 168 symbols 3 • 14 OFDM symbols, 12 bit/channel use 2 . 5 2 spacing tones apart in frequency tones per symbol = ⇒ 1 . 5 spacing OFDM symbols apart in time 1 • PEP ǫ = 10 − 5 0 . 5 0 • SNR ρ = 6 dB 1 2 4 7 14 21 28 42 time-frequency diversity branches ℓ (log scale) • 2 × 2 MIMO n c n = n c `, ` ∈ 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. 14 / 25 G. Durisi
Asymptotic IT: outage capacity n c n = n c `, ` ∈ N 15 / 25 G. Durisi
Asymptotic IT: outage capacity n c →∞ R ∗ ( ℓ, n c , ǫ ) = C out ,ǫ lim n c = sup { R : inf P out ( R ) ≤ ǫ } n = n c `, ` ∈ N � ℓ � � log det( I m r + H H P out ( R ) = Pr k Q k H k ) ≤ ℓR k =1 15 / 25 G. Durisi
Asymptotic IT: outage capacity n c →∞ R ∗ ( ℓ, n c , ǫ ) = C out ,ǫ lim n c = sup { R : inf P out ( R ) ≤ ǫ } n = n c `, ` ∈ N � ℓ � � log det( I m r + H H P out ( R ) = Pr k Q k H k ) ≤ ℓR k =1 • Same as when CSI is available at RX; CSI acquisition cost is lost 15 / 25 G. Durisi
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