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 THANKS