Fundamental Limits of Caching Urs Niesen Jointly with Mohammad - - PowerPoint PPT Presentation

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Fundamental Limits of Caching Urs Niesen Jointly with Mohammad - - PowerPoint PPT Presentation

Jan 16, 2024 299 likes •1.25k views

Fundamental Limits of Caching Urs Niesen Jointly with Mohammad Maddah-Ali Bell Labs, Alcatel-Lucent Video on Demand Video on demand is getting increasingly popular: Netflix streaming service Amazon Instant Video Hulu Verizon / Comcast on

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Fundamental Limits of Caching

Urs Niesen Jointly with Mohammad Maddah-Ali

Bell Labs, Alcatel-Lucent

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Video on Demand

Video on demand is getting increasingly popular: Netflix streaming service Amazon Instant Video Hulu Verizon / Comcast on Demand . . .

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Video on Demand

Video on demand is getting increasingly popular: Netflix streaming service Amazon Instant Video Hulu Verizon / Comcast on Demand . . . ⇒ Places significant stress on service provider’s networks

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Video on Demand

Video on demand is getting increasingly popular: Netflix streaming service Amazon Instant Video Hulu Verizon / Comcast on Demand . . . ⇒ Places significant stress on service provider’s networks ⇒ Caching (prefetching) can be used to mitigate this stress

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Caching (Prefetching)

20 40 60 80 100 6 12 18 24 time of day normalized demand

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Caching (Prefetching)

20 40 60 80 100 6 12 18 24 time of day normalized demand

High temporal traffic variability

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Caching (Prefetching)

20 40 60 80 100 6 12 18 24 time of day normalized demand

High temporal traffic variability Caching can help smooth traffic

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The Role of Caching

Conventional beliefs about caching:

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The Role of Caching

Conventional beliefs about caching: Caches useful to deliver content locally

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The Role of Caching

Conventional beliefs about caching: Caches useful to deliver content locally Local cache size matters

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The Role of Caching

Conventional beliefs about caching: Caches useful to deliver content locally Local cache size matters Statistically identical users ⇒ identical cache content

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The Role of Caching

Conventional beliefs about caching: Caches useful to deliver content locally Local cache size matters Statistically identical users ⇒ identical cache content Insights from this work:

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The Role of Caching

Conventional beliefs about caching: Caches useful to deliver content locally Local cache size matters Statistically identical users ⇒ identical cache content Insights from this work: The main gain in caching is global

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The Role of Caching

Conventional beliefs about caching: Caches useful to deliver content locally Local cache size matters Statistically identical users ⇒ identical cache content Insights from this work: The main gain in caching is global Global cache size matters

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The Role of Caching

Conventional beliefs about caching: Caches useful to deliver content locally Local cache size matters Statistically identical users ⇒ identical cache content Insights from this work: The main gain in caching is global Global cache size matters Statistically identical users ⇒ different cache content

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Problem Setting

K users caches server shared link

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Problem Setting

K users caches server N files, N ≥ K for simplicity shared link

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Problem Setting

K users caches size M server N files shared link

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Problem Setting

K users caches size M server N files shared link Placement: cache arbitrary function of files (linear, nonlinear, . . . )

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Problem Setting

K users caches size M server N files shared link Delivery:

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Problem Setting

K users caches size M server N files shared link Delivery: - requests are revealed to server

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Problem Setting

K users caches size M server N files shared link Delivery: - requests are revealed to server

  • server sends arbitrary function of files
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Problem Setting

K users caches size M server N files shared link Delivery: - requests are revealed to server

  • server sends arbitrary function of files
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Problem Setting

K users caches size M server N files shared link Question: smallest worst-case rate R(M) needed in delivery phase?

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Conventional Caching Scheme

N files, K users, cache size M

M N

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Conventional Caching Scheme

N files, K users, cache size M

M N

M N

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Conventional Caching Scheme

N files, K users, cache size M

M N

M N

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Conventional Caching Scheme

N files, K users, cache size M

M N

M N

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Conventional Caching Scheme

N files, K users, cache size M

M N

M N

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Conventional Caching Scheme

N files, K users, cache size M

M N

M N

Performance of conventional scheme: R(M) = K · (1 − M/N)

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Conventional Caching Scheme

N files, K users, cache size M

M N

M N

Performance of conventional scheme: R(M) = K · (1 − M/N) Caches provide content locally ⇒ local cache size matters Identical cache content at users

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Conventional Caching Scheme

N = 2 files, K = 2 users

2 2 M R conventional scheme

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Conventional Caching Scheme

N = 4 files, K = 4 users

4 4 M R conventional scheme

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Conventional Caching Scheme

N = 8 files, K = 8 users

8 8 M R conventional scheme

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Conventional Caching Scheme

N = 16 files, K = 16 users

16 16 M R conventional scheme

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Conventional Caching Scheme

N = 32 files, K = 32 users

32 32 M R conventional scheme

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Conventional Caching Scheme

N = 64 files, K = 64 users

64 64 M R conventional scheme

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Conventional Caching Scheme

N = 128 files, K = 128 users

128 128 M R conventional scheme

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Conventional Caching Scheme

N = 256 files, K = 256 users

256 256 M R conventional scheme

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Conventional Caching Scheme

N = 512 files, K = 512 users

512 512 M R conventional scheme

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Proposed Caching Scheme

N files, K users, cache size M

Design guidelines advocated in this work: The main gain in caching is global Global cache size matters Different cache content at users

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Proposed Caching Scheme

N files, K users, cache size M

Design guidelines advocated in this work: The main gain in caching is global Global cache size matters Different cache content at users Performance of proposed scheme: R(M) = K · (1 − M/N) · 1 1 + KM/N

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Proposed Caching Scheme

N = 2 files, K = 2 users

2 2 M R conventional scheme proposed scheme

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Proposed Caching Scheme

N = 4 files, K = 4 users

4 4 M R conventional scheme proposed scheme

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Proposed Caching Scheme

N = 8 files, K = 8 users

8 8 M R conventional scheme proposed scheme

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Proposed Caching Scheme

N = 16 files, K = 16 users

16 16 M R conventional scheme proposed scheme

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Proposed Caching Scheme

N = 32 files, K = 32 users

32 32 M R conventional scheme proposed scheme

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Proposed Caching Scheme

N = 64 files, K = 64 users

64 64 M R conventional scheme proposed scheme

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Proposed Caching Scheme

N = 128 files, K = 128 users

128 128 M R conventional scheme proposed scheme

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Proposed Caching Scheme

N = 256 files, K = 256 users

256 256 M R conventional scheme proposed scheme

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Proposed Caching Scheme

N = 512 files, K = 512 users

512 512 M R conventional scheme proposed scheme

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Recall: Conventional Scheme

N = 2 files, K = 2 users, cache size M = 1

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Recall: Conventional Scheme

N = 2 files, K = 2 users, cache size M = 1

B A

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Recall: Conventional Scheme

N = 2 files, K = 2 users, cache size M = 1

B1, B2 A1, A2

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Recall: Conventional Scheme

N = 2 files, K = 2 users, cache size M = 1

A1, B1 A1, B1 B1, B2 A1, A2

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Recall: Conventional Scheme

N = 2 files, K = 2 users, cache size M = 1

A1, B1 A1, B1 B1, B2 A1, A2

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Recall: Conventional Scheme

N = 2 files, K = 2 users, cache size M = 1

A1, B1 A1, B1 B1, B2 A1, A2 A2

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Recall: Conventional Scheme

N = 2 files, K = 2 users, cache size M = 1

A A1, B1 A A1, B1 B1, B2 A1, A2 A2

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Recall: Conventional Scheme

N = 2 files, K = 2 users, cache size M = 1

A A1, B1 A A1, B1 B1, B2 A1, A2 A2 ⇒ Identical cache content at users ⇒ Gain from delivering content locally

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Recall: Conventional Scheme

N = 2 files, K = 2 users, cache size M = 1

A1, B1 A1, B1 B1, B2 A1, A2

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Recall: Conventional Scheme

N = 2 files, K = 2 users, cache size M = 1

A1, B1 A1, B1 B1, B2 A1, A2 A2, B2

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Recall: Conventional Scheme

N = 2 files, K = 2 users, cache size M = 1

A A1, B1 B A1, B1 B1, B2 A1, A2 A2, B2

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Recall: Conventional Scheme

N = 2 files, K = 2 users, cache size M = 1

A A1, B1 B A1, B1 B1, B2 A1, A2 A2, B2 ⇒ Multicast only possible for users with same demand

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Recall: Conventional Scheme

N = 2 files, K = 2 users, cache size M = 1 1 2 1 2 M R conventional scheme proposed scheme

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Proposed Scheme

N = 2 files, K = 2 users, cache size M = 1

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Proposed Scheme

N = 2 files, K = 2 users, cache size M = 1

B A

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Proposed Scheme

N = 2 files, K = 2 users, cache size M = 1

B1, B2 A1, A2

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Proposed Scheme

N = 2 files, K = 2 users, cache size M = 1

A1, B1 A2, B2 B1, B2 A1, A2

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Proposed Scheme

N = 2 files, K = 2 users, cache size M = 1

A1, B1 A2, B2 B1, B2 A1, A2

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Proposed Scheme

N = 2 files, K = 2 users, cache size M = 1

A1, B1 A2, B2 B1, B2 A1, A2 A2 B1

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Proposed Scheme

N = 2 files, K = 2 users, cache size M = 1

A1, B1 A2, B2 B1, B2 A1, A2 A2 B1

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Proposed Scheme

N = 2 files, K = 2 users, cache size M = 1

A1, B1 A2, B2 B1, B2 A1, A2 A2 ⊕ B1

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Proposed Scheme

N = 2 files, K = 2 users, cache size M = 1

A A1, B1 B A2, B2 B1, B2 A1, A2 A2 ⊕ B1

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Proposed Scheme

N = 2 files, K = 2 users, cache size M = 1

A A1, B1 B A2, B2 B1, B2 A1, A2 A2 ⊕ B1 ⇒ Different cache content at users ⇒ Multicast to 2 users with different demands

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Proposed Scheme

N = 2 files, K = 2 users, cache size M = 1

A A1, B1 A A2, B2 B1, B2 A1, A2 A2⊕A1 A A1, B1 B A2, B2 B1, B2 A1, A2 A2⊕B1 B A1, B1 A A2, B2 B1, B2 A1, A2 B2⊕A1 B A1, B1 B A2, B2 B1, B2 A1, A2 B2⊕B1

⇒ Works for all possible user requests ⇒ Simultaneous multicasting gain

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Proposed Scheme

N = 2 files, K = 2 users, cache size M = 1 1 2 1 2 M R conventional scheme proposed scheme

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Proposed Scheme

N files, K users, cache size M

Scheme can be generalized to arbitrary:

Number of files N Number of users K Cache size M

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Proposed Scheme

N files, K users, cache size M

Scheme can be generalized to arbitrary:

Number of files N Number of users K Cache size M

Enables multicast to KM/N + 1 users with different demands

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Comparison of the Two Schemes

N files, K users, cache size M

Conventional scheme: R(M) = K · (1 − M/N) Proposed scheme: R(M) = K · (1 − M/N) ·

1 1+KM/N

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Comparison of the Two Schemes

N files, K users, cache size M

Conventional scheme: R(M) = K · (1 − M/N) Proposed scheme: R(M) = K · (1 − M/N) ·

1 1+KM/N

Rate without caching K

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Comparison of the Two Schemes

N files, K users, cache size M

Conventional scheme: R(M) = K · (1 − M/N) Proposed scheme: R(M) = K · (1 − M/N) ·

1 1+KM/N

Rate without caching K Local caching gain 1 − M/N

Significant when local cache size M is of order N

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Comparison of the Two Schemes

N files, K users, cache size M

Conventional scheme: R(M) = K · (1 − M/N) Proposed scheme: R(M) = K · (1 − M/N) ·

1 1+KM/N

Rate without caching K Local caching gain 1 − M/N

Significant when local cache size M is of order N

Global caching gain

1 1+KM/N

Significant when global cache size KM is of order N

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Comparison of the Two Schemes

N files, K users, cache size M

Conventional scheme: R(M) = K · (1 − M/N) Proposed scheme: R(M) = K · (1 − M/N) ·

1 1+KM/N

Rate without caching K Local caching gain 1 − M/N

Significant when local cache size M is of order N

Global caching gain

1 1+KM/N

Significant when global cache size KM is of order N

⇒ Global gain can be Θ(K) smaller than local gain

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Can We Do Better?

Theorem The proposed scheme is optimal to within a constant factor in rate.

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Can We Do Better?

Theorem The proposed scheme is optimal to within a constant factor in rate. ⇒ Information-theoretic bound

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Can We Do Better?

Theorem The proposed scheme is optimal to within a constant factor in rate. ⇒ Information-theoretic bound ⇒ Constant is independent of problem parameters N, K, M

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Can We Do Better?

Theorem The proposed scheme is optimal to within a constant factor in rate. ⇒ Information-theoretic bound ⇒ Constant is independent of problem parameters N, K, M ⇒ No other significant gain besides local and global

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Conclusions

A New Approach to Caching

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Conclusions

A New Approach to Caching

The main gain in caching is global

⇒ Multicast to users with different demands

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Conclusions

A New Approach to Caching

The main gain in caching is global

⇒ Multicast to users with different demands

Global cache size matters

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Conclusions

A New Approach to Caching

The main gain in caching is global

⇒ Multicast to users with different demands

Global cache size matters Statistically identical users ⇒ different cache content

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Conclusions

A New Approach to Caching

The main gain in caching is global

⇒ Multicast to users with different demands

Global cache size matters Statistically identical users ⇒ different cache content Significant improvement over conventional caching schemes

⇒ Reduction in rate up to order of number of users

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Conclusions

A New Approach to Caching

The main gain in caching is global

⇒ Multicast to users with different demands

Global cache size matters Statistically identical users ⇒ different cache content Significant improvement over conventional caching schemes

⇒ Reduction in rate up to order of number of users

Papers available on arXiv

⇒ Maddah-Ali, Niesen: “Fundamental Limits of Caching” ⇒ Maddah-Ali, Niesen: “Decentralized Caching Attains Order-Optimal Memory-Rate Tradeoff” ⇒ Niesen, Maddah-Ali: “Coded Caching with Nonuniform Demands”