TY - GEN
T1 - Efficient and explicit coding for interactive communication
AU - Gelles, Ran
AU - Moitra, Ankur
AU - Sahai, Amit
PY - 2011
Y1 - 2011
N2 - We revisit the problem of reliable interactive communication over a noisy channel, and obtain the first fully explicit (randomized) efficient constant-rate emulation procedure for reliable interactive communication. Our protocol works for any discrete memory less noisy channel with constant capacity, and fails with exponentially small probability in the total length of the protocol. Following a work by Schulman [Schulman 1993] our simulation uses a tree-code, yet as opposed to the non-constructive absolute tree-code used by Schulman, we introduce a relaxation in the notion of goodness for a tree code and define a potent tree code. This relaxation allows us to construct an explicit emulation procedure for any two-party protocol. Our results also extend to the case of interactive multiparty communication. We show that a randomly generated tree code (with suitable constant alphabet size) is an efficiently decodable potent tree code with overwhelming probability. Furthermore we are able to partially derandomize this result by means of epsilon-biased distributions using only O(N) random bits, where N is the depth of the tree.
AB - We revisit the problem of reliable interactive communication over a noisy channel, and obtain the first fully explicit (randomized) efficient constant-rate emulation procedure for reliable interactive communication. Our protocol works for any discrete memory less noisy channel with constant capacity, and fails with exponentially small probability in the total length of the protocol. Following a work by Schulman [Schulman 1993] our simulation uses a tree-code, yet as opposed to the non-constructive absolute tree-code used by Schulman, we introduce a relaxation in the notion of goodness for a tree code and define a potent tree code. This relaxation allows us to construct an explicit emulation procedure for any two-party protocol. Our results also extend to the case of interactive multiparty communication. We show that a randomly generated tree code (with suitable constant alphabet size) is an efficiently decodable potent tree code with overwhelming probability. Furthermore we are able to partially derandomize this result by means of epsilon-biased distributions using only O(N) random bits, where N is the depth of the tree.
KW - derandomization
KW - interactive communication with noise
KW - tree codes
UR - http://www.scopus.com/inward/record.url?scp=84863326122&partnerID=8YFLogxK
U2 - 10.1109/FOCS.2011.51
DO - 10.1109/FOCS.2011.51
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AN - SCOPUS:84863326122
SN - 9780769545714
T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
SP - 768
EP - 777
BT - Proceedings - 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011
T2 - 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011
Y2 - 22 October 2011 through 25 October 2011
ER -