Additional Coding Opportunities in Cache-Aided Networks Mich` ele - PowerPoint PPT Presentation

Additional Coding Opportunities in Cache-Aided Networks Mich` ele Wigger Telecom ParisTech Joint Work with S. Saeedi-Bidokhti, S. Kamel, M. Sarkiss, S. Shamai, R. Timo, and A. Yener WiOpt 2017 May 17, 2017

Caching in Networks Database cache cache cache 2

Caching in a One-To-Many Broadcast Network Database cache cache cache [Maddah-Ali, Niesen ’14] 3

Caching in a One-To-Many Broadcast Network Database Wireless cache cache cache 3

Model data data database: data encoder broadcast network cache cache cache … user user user 4

Model data data database: data encoder cache cache cache … • Caching Phase: demands not yet known 4

Model data data database: Demands data encoder cache cache cache • Caching Phase: demands not yet known • Delivery Phase: demands announced 4

Model data data database: Demands data encoder Encoder X broadcast network p ( y 1 , . . . , y K | x ) Y 1 Y 2 Y K cache cache cache … user user user • Caching Phase: demands not yet known • Delivery Phase: demands announced 4

Model data data database: data encoder broadcast network cache cache cache … user user user • Caching Phase: demands not yet known • Delivery Phase: demands announced • Under all possible demands, files need to be sent reliably 4

Model R data data database: data encoder Encoder broadcast network cache cache cache … user user user • Caching Phase: demands not yet known • Delivery Phase: demands announced • Under all possible demands, files need to be sent reliably • Largest data-rate R in function of cache rates M 1 , . . . , M K ? 4

Easy Bounds • Local caching gain: M k − M 0 R ( M 1 , . . . , M K ) ≥ R ( M 0 1 , . . . , M 0 k K ) + max D k ∈{ 1 ,..., K } (Gain only from local cache memory) • Perfect global caching gain: � K k = 1 M k − � K k = 1 M 0 R ( M 1 , . . . , M K ) ≤ R ( M 0 1 , . . . , M 0 k K ) + D (Gain as if each receiver had access to all caches) 5

Coded Caching data data database: data encoder cache cache cache user user user … • Noise-free bit-pipe • Equal cache sizes M 1 = M 2 = . . . = M K = M Related results in [Maddah-Ali, Niesen ’14], [Yu, Maddah-Ali, Avestimehr ’16], [Ji, Tulino, Liorcha, Caire ’15], [Pedarsani, Maddah-Ali, Niesen ’16], [Wang, Lim, Gastpar ’16], [Amiri, Yang, Gunduz ’16] ... 6

Coded Caching data data database: encoder data cache cache user user still need [Maddah-Ali, Niesen ’14] 7

Coded Caching data data database: encoder data cache cache user user still need [Maddah-Ali, Niesen ’14] 7

Coded Caching data data database: encoder data cache cache user user [Maddah-Ali, Niesen ’14] 7

Coded Caching data data database: data encoder 4 3 cache Data rate R cache user user 2 1 Coded caching Traditional caching [Maddah-Ali, Niesen ’14] 0 0 1 2 3 Cache size M / D 7

Noisy Broadcast Networks data data database: data encoder Encoder broadcast network cache cache cache … user user user Cache memories are even more useful in heterogeneous networks 8

Noisy Broadcast Networks data data database: data encoder Encoder degraded broadcast network cache cache cache … user user user Cache memories are even more useful in heterogeneous networks 8

Challenges • Noisy channel outputs • Heterogeneous users: different channel qualities & cache sizes • Rate Bottleneck caused by weaker receivers Solutions • Cache assignment based on channel qualities • Joint cache-channel coding 9

Erasure Broadcast Networks data data database: data encoder Encoder X � K � 1 � 2 Y 1 Y 2 Y K cache cache cache … user user user • Binary input X � X with probability 1 − ǫ k • Output Y k = ? with probability ǫ k • 1 ≥ ǫ 1 ≥ ǫ 2 ≥ ǫ 3 ≥ . . . ≥ ǫ K ≥ 0 10

Single Weak Receiver Degrades Performance 4 3 . 5 3 Data rate R 2 . 5 2 1 . 5 1 0 . 5 Coded caching ( ǫ 1 = ǫ 2 = . . . ǫ K = 0 . 2) 0 0 0 . 2 0 . 4 0 . 6 0 . 8 1 1 . 2 1 . 4 1 . 6 1 . 8 2 2 . 2 2 . 4 2 . 6 2 . 8 3 Cache size M / D 11

Single Weak Receiver Degrades Performance 4 3 . 5 3 Data rate R 2 . 5 2 1 . 5 1 0 . 5 Coded caching ( ǫ 1 = ǫ 2 = . . . ǫ K = 0 . 2) Coded caching ( ǫ 1 = 0 . 8, ǫ 2 = . . . ǫ K = 0 . 2) 0 0 0 . 2 0 . 4 0 . 6 0 . 8 1 1 . 2 1 . 4 1 . 6 1 . 8 2 2 . 2 2 . 4 2 . 6 2 . 8 3 Cache size M / D 11

Single Weak Receiver Degrades Performance 4 3 . 5 3 Data rate R 2 . 5 2 1 . 5 1 Coded caching ( ǫ 1 = ǫ 2 = . . . ǫ K = 0 . 2) 0 . 5 Coded caching ( ǫ 1 = 0 . 8, ǫ 2 = . . . ǫ K = 0 . 2) Upper Bound with equal caches ( ǫ 1 = 0 . 8, ǫ 2 = . . . ǫ K = 0 . 2) 0 0 0 . 2 0 . 4 0 . 6 0 . 8 1 1 . 2 1 . 4 1 . 6 1 . 8 2 2 . 2 2 . 4 2 . 6 2 . 8 3 Cache size M / D 11

Is Degradation Inherent? Can it be Circumvented? • Is performance degradation really fundamental? • Not if cache sizes had properly been assigned/designed! Assign more cache memory to weak receiver! Library: Encoder K 1 2 cache cache cache … Decoder Decoder Decoder 12

Performance when Cache Memory can be freely Assigned 4 3 . 5 3 Data rate R 2 . 5 2 1 . 5 1 Coded caching ( ǫ 1 = ǫ 2 = . . . ǫ K = 0 . 2) Coded caching ( ǫ 1 = 0 . 8, ǫ 2 = . . . ǫ K = 0 . 2) 0 . 5 Upper Bound with equal caches ( ǫ 1 = 0 . 8, ǫ 2 = . . . ǫ K = 0 . 2) Our New Coding Scheme ( ǫ 1 = 0 . 8, ǫ 2 = . . . ǫ K = 0 . 2) 0 0 0 . 2 0 . 4 0 . 6 0 . 8 1 1 . 2 1 . 4 1 . 6 1 . 8 2 2 . 2 2 . 4 2 . 6 2 . 8 3 Average cache size M Total / D / K • Careful cache assignment + new coding allows to mitigate loss! 13

Coding Schemes for Unequal Cache Assignment data data database: data encoder M D cache user user • State of the art (coded caching + erasure BC code): R − M R D + ≤ 1 (local caching gain) 1 − ǫ 1 1 − ǫ 2 • Piggyback coding (joint cache-channel coding) 14

Piggyback coding user 2 user 1 user 1 needs knowing user 2 needs X n ( , ) for user 2 for user 1 15

Piggyback coding user 2 user 1 user 1 needs knowing user 2 needs X n ( , ) for user 2 for user 1 15

Piggyback coding user 2 user 1 user 1 needs knowing user 2 needs X n ( , ) for user 2 for user 1 � � , R − M + R − M R D D max ≤ 1 (global caching gain) 1 − ǫ 2 1 − ǫ 1 1 − ǫ 2 15

Network with Weak Receivers with Caches Library: Encoder cache cache … Decoder Decoder Decoder • Weak and strong receivers with ǫ w ≥ ǫ s • Equal cache size M at all weak receivers 16

New Gains of Caching · 10 − 2 5 4 . 5 Data rate R 4 3 . 5 Nested piggyback coding Coded caching with BC code 3 Amiri&Gunduz-2017 Upper bound 2 . 5 0 0 . 5 1 1 . 5 2 2 . 5 3 3 . 5 4 4 . 5 5 Cache size M / D · 10 − 2 4 weak, and 16 strong users, ǫ w = 0 . 8, ǫ s = 0 . 2 M R ≈ R 0 + γ local γ MN γ new D ���� ���� no-cache scales with # strong users [Saeedi-Bidokhti, Wigger, Timo-2016, Amiri&Gunduz-2017] 17

Cache Assignment data data database: data encoder broadcast network cache cache … user user user cache M 1 M 2 M K M 1 + . . . + M K ≤ M Total R ( M Total ) ? 18

Bounds on the Rate-Memory Tradeoff 2 . 5 2 Data rate R 1 . 5 1 0 . 5 Upper bound on uniform cache assignment 0 0 0 . 5 1 1 . 5 2 2 . 5 3 3 . 5 4 4 . 5 5 5 . 5 6 6 . 5 7 7 . 5 Total cache budget M Total / D Erasure broadcast network ǫ 1 = 0 . 9 , ǫ 2 = 0 . 6 , ǫ 3 = 0 . 1 , ǫ 4 = 0 . 05 [Saeedi-Bidokhti, Wigger, Yener-2017] 19

Bounds on the Rate-Memory Tradeoff 2 . 5 2 Data rate R 1 . 5 1 0 . 5 Cache assignment and new coding Upper bound on uniform cache assignment 0 0 0 . 5 1 1 . 5 2 2 . 5 3 3 . 5 4 4 . 5 5 5 . 5 6 6 . 5 7 7 . 5 Total cache budget M Total / D Erasure broadcast network ǫ 1 = 0 . 9 , ǫ 2 = 0 . 6 , ǫ 3 = 0 . 1 , ǫ 4 = 0 . 05 [Saeedi-Bidokhti, Wigger, Yener-2017] 19

Bounds on the Rate-Memory Tradeoff 2 . 5 2 Data rate R 1 . 5 1 0 . 5 Cache assignment and new coding Upper bound Upper bound on uniform cache assignment 0 0 0 . 5 1 1 . 5 2 2 . 5 3 3 . 5 4 4 . 5 5 5 . 5 6 6 . 5 7 7 . 5 Total cache budget M Total / D Erasure broadcast network ǫ 1 = 0 . 9 , ǫ 2 = 0 . 6 , ǫ 3 = 0 . 1 , ǫ 4 = 0 . 05 [Saeedi-Bidokhti, Wigger, Yener-2017] 19

Bounds on the Rate-Memory Tradeoff 2 . 5 slope = 1 K 2 Data rate R 1 . 5 1 slope = 1 0 . 5 Cache assignment and new coding Upper bound Upper bound on uniform cache assignment 0 0 0 . 5 1 1 . 5 2 2 . 5 3 3 . 5 4 4 . 5 5 5 . 5 6 6 . 5 7 7 . 5 Total cache budget M Total / D Erasure broadcast network ǫ 1 = 0 . 9 , ǫ 2 = 0 . 6 , ǫ 3 = 0 . 1 , ǫ 4 = 0 . 05 [Saeedi-Bidokhti, Wigger, Yener-2017] 19

Bounds on the Rate-Memory Tradeoff 4 3 . 5 3 Data rate R 2 . 5 2 1 . 5 1 Cache assignment and generalized piggyback coding 0 . 5 Upper bound Upper bound on uniform cache assignment 0 0 1 2 3 4 5 6 7 8 9 10 Total cache budget M Total / D Gaussian broadcast network N 1 = 4 , N 2 = 2 , N 3 = 1 , N 4 = 0 . 5 [Saeedi-Bidokhti, Wigger, Yener-2017] 19