Online Coded Caching
Mohammad Ali Maddah-Ali
Bell Labs, Alcatel-Lucent, USA
joint work with
Ramtin Pedarsani
UC-Berkeley
Urs Niesen
Bell Labs
Video on Demand
• Video on Demand
– Netflix
– Amazon
– Hulu
– Verizon/Comcast
–…
Places significant stress on service providers’ networks.
Caching can be used to mitigate this stress.
Least Recently Used (LRU)
Server
• LRU caching gain: deliver
content locally (local gain)
LRU File
• LRU is approximately optimum
Cache
for single cache [Sleator, Tarjan, 85]
• LRU is widely used in industry
User
• Cache every uncached requested file
• Cache is full: Evict the Least Recently Used (LRU).
Beyond Local Gain
Maddah-Ali, Nisien, Fundamental Limits of Caching. 2012
A1
A2
B1
B2
• Local Gain = 0.5
• Global (coding) Gain = 0.5
A2
A2⊕B1
B1
• As number of cashes increases
A1
B1
A2
B2
• Local gain stays constant!
• Global gain scales Linearly
Efficient online caching must capture the GLOBAL GAIN.
In this talk: Coded Least Recently Sent
• We propose coded LRS to
exploit global gain
Coded
Coded
• Cache any uncashed requested
file
• Partially!
• Randomly
• Uniformly
• No matter who requested!
• Cache is full:
•
Evict least recently sent
Optimality of Coded LRS
Set of Equi-Popular N Files
With prob. p
Theorem (Coded LRS)
Local Gain
K User
Global (coding) Gain:
Scales with K
Sketch of Proof
Partially Cached
files
popular files
Users
Demands
No Caching Gain
Enjoys code cashing gain
Challenges:
• Load for uncached demands are bounded by a constant number.
• Number of uncached demands is governed by a complicated
Markov chain.
• Big gain for the partially cached demands.
Performance Evaluation
• Real-Life demand time series extracted From Netflix Prize Data
(10 millions demands, over one year period)
• Dynamic Variation of the Users’ Demand
Performance Evaluation
Size of Each Isolated Cache
• Significant gain due to coded global gain
Conclusion
• For cache networks, LRU is NOT optimal.
• Introduced online coded caching (Coded LRS).
• Significant gain over LRU
• Proved coded LRS is approximately optimal under some
conditions
•
Validated the result for real-life time series of requests
extracted from Netflix.
Further Reading
•
Maddah-Ali and Niesen, “Fundamental Limits of Caching”, Sept 2012 (IEEE Trans.
On Information theory, March 2014).
•
Maddah-Ali and Niesen, “Distributed Caching Attains Order-Optimal MemoryRate Trade-offs”, Jan. 2013 ( to Appear in ACM/IEEE Trans. On Networking, 2014).
•
Niesen and Maddah-Ali “Coded Caching with Non-Uniform Demands”, Jun. 2013.
(Submitted to IEEE Trans. On Information Theory).
•
Pedarsani, Maddah-Ali, and Niesen, “Online Coded Caching”, Nov. 2013
(Submitted to ACM/IEEE Trans. on Networking).
•
Karamchandani, Niesen, Maddah-Ali, and Diggavi “Hierarchical Coded Caching”,
Jan. 2014 (Submitted to IEEE Trans. On Information Theory).