RELIABLE COMMUNICATION 1 IN THE PRESENCE OFLIMITEDADVERSARIES

Background – Communication Scenario 2 AliceBob Calvin Bad guy EncoderDecoder (Adversarial) Noisy Channel Message Decoded message Codeword Received word

Background – Related Work 3 “Benchmark” channel models One extreme: oblivious adversary q=2 (binary) R p “ large ” q R p 1 1 (AVC capacity) “Like noisy” NOT BAD! (AVC capacity/folklore)

Background – Related Work 4 “Benchmark” channel models The other extreme: omniscient adversary One extreme: oblivious adversary q=2 (binary) R p “ large ” q R p 1 1 [Sha48] [Reed- Solomon]/[Singleton] [McERRW77] [Gilbert Varshamov] Calvin WHAT? He knows “everything”! “ intermediate ” q p 1 0.5

Background – Related Work 5 Weaker channel models List-decoding - weakened reconstruction goal q=2 (binary) R p “ large ” q R p 1 1 [Sha48] Computationally efficient list-decoding schemes LOOK!

Background – Related Work 6 Weaker channel models List-decoding - weakened reconstruction goal q=2 (binary) R p “ large ” q R p 1 1 Smith-Guruswami Computationally efficient encoding/decoding schemes Computationally bounded adversaries - weakened adversary power Calvin LOOK! Micali-Sudan

Background – Related Work 8 Weaker channel models AVCs with common randomness between Alice and Bob Omniscient jammer with noiseless feedback Calvin AliceBob q=2 (binary) R p [Sha48] [McERRW77] [Gilbert Varshamov] [Berlekamp] 1/3 “ large ” q R p 1 0.5

Calvin 9 Causal adversaries Between oblivious and omniscient adversaries 011?10??????? * ? 14 Transmitted Word Tampered Word CurrentFuture Calvin

10 Causal adversaries Between oblivious and omniscient adversaries Causal large alphabet Delayed adversary Causal “ large ” q R p Delayed q=2 R p [Sha48] Delayed “ large ” q (additive) R p 1 1 R p 1 1 d 0.5 Delayed “ large ” q (overwrite)

11 Causal adversaries Capacity

12 Causal adversaries Between oblivious and omniscient adversaries Analysis of all possible causal adversarial behaviours 1 One possible adversarial trajectory (Slopes are bounded)

Analysis of all possible causal adversarial behaviours Proof techniques overview - Converse: “Babble-and-push” attack 13 Causal adversaries 011?10??????? ? 14 Transmitted Word Tampered Word Babbling phasePushing phase

Proof techniques overview - Converse: “Babble-and-push” attack 14 Causal adversaries Transmitted Word Tampered Word 1… … … Selected Word 1… Pushing phase 1.Construct a set of codewords based on corrupted bits transmitted so far 2.Select one codeword from the set and then “push” the transmitted codeword towards the selected one Pushing phase

Proof techniques overview - Converse: “Babble-and-push” attack 15 Causal adversaries Transmitted Word Tampered Word 1… … … Selected Word 1… Pushing phase 1.Construct a set of codewords based on corrupted bits transmitted so far 2.Select one codeword from the set and then “push” the transmitted codeword towards the selected one Pushing phase The tampered word lies in midway between the transmitted word and selected word.

Proof techniques overview - Converse: “Babble-and-push” attack 16 Causal adversaries Those codewords with prefix different from the observed prefix are discarded.

17 Causal adversaries 011?10??????? ? 14 Transmitted Word Tampered Word List-decoding condition Proof techniques overview - Converse: “Babble-and-push” attack Energy-bounding condition Babbling phasePushing phase

Proof techniques overview - Converse: “Babble-and-push” attack 18 Causal adversaries Using stochastic encoders instead of deterministic encoders illustrated in previous slides Message

19 Causal adversaries Calvin

Proof techniques overview - Converse: “Babble-and-push” attack 20 Causal adversaries Proof techniques overview – Achievability 1 Trajectory of the “babble-and-push strategy” Possible decoding points

Proof techniques overview - Converse: “Babble-and-push” attack 21 Causal adversaries Proof techniques overview – Achievability Encoder: concatenated stochastic codes

22 Causal adversaries Proof techniques overview – Achievability Encoder: concatenated stochastic codes

23 Causal adversaries Proof techniques overview – Achievability Encoder: concatenated stochastic codes Decoding process: list-decoding + unique decoding Obtain a list of messages List-decoding phase Unique decoding phase

24 Causal adversaries Proof techniques overview – Achievability Encoder: concatenated stochastic codes Decoding process: list-decoding + unique decoding Obtain a list of messages List-decoding phase Unique decoding phase Encodings Consistency Checking If two words differ in a limited number of positions, they are said to be consistent.

25 Causal adversaries Proof techniques overview – Achievability Encoder: concatenated stochastic codes Decoding process: list-decoding + unique decoding List of “right mega sub-codewords” Fail in consistency checking… Received “right mega sub-codeword”

26 Causal adversaries Proof techniques overview – Achievability Encoder: concatenated stochastic codes Decoding process: list-decoding + unique decoding With high probability, Bob succeeds in decoding Pass consistency checking! Received “right mega sub-codeword”

27 Limited-view adversaries: Multipath networks with large-alphabet symbols Adversary can see a certain fraction and jam another fraction Myopic adversaries: Adversary has (non-causal) view of a noisy version of Alice's transmission

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