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Verifying and decoding in constant depth
 In Proceedings of the ThirtyNinth Annual ACM Symposium on Theory of Computing
, 2007
"... We develop a general approach for improving the efficiency of a computationally bounded receiver interacting with a powerful and possibly malicious sender. The key idea we use is that of delegating some of the receiver’s computation to the (potentially malicious) sender. This idea was recently intro ..."
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Cited by 15 (4 self)
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that are locally (list)decodable by constantdepth circuits of size polylogarithmic in the length of the codeword. Using the tight connection between locally listdecodable codes and averagecase complexity, we obtain a new, more efficient, worstcase to averagecase reduction for languages in EXP.
The Complexity of Local List Decoding
"... We study the complexity of locally listdecoding binary error correcting codes with good parameters (that are polynomially related to information theoretic bounds). We show that computing majority over Θ(1/ǫ) bits is essentially equivalent to locally listdecoding binary codes from relative distance ..."
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Cited by 4 (1 self)
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efficient (in terms of circuit size and depth) localdecoder that uses majority gates of fanin Θ(1/ǫ). Using known lower bounds for computing majority by constant depth circuits, our results imply that every constantdepth decoder for such a code must have size almost exponential in 1/ǫ (this extends even
Verifying and Decoding in Constant Depth Shafi Goldwasser *CSAIL, MIT and
"... Another, less immediate senderreceiver setting arises in considering error correcting codes. By taking the sender to be a (potentially corrupted) codeword and the receiver to be a decoder, we obtain explicit families of codes that are locally (list)decodable by constantdepth circuits of size poly ..."
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Another, less immediate senderreceiver setting arises in considering error correcting codes. By taking the sender to be a (potentially corrupted) codeword and the receiver to be a decoder, we obtain explicit families of codes that are locally (list)decodable by constantdepth circuits of size
Context Coding of Depth Map Images Under the PiecewiseConstant Image Model Representation
"... Abstract — This paper introduces an efficient method for lossless compression of depth map images, using the representation of a depth image in terms of three entities: 1) the crackedges; 2) the constant depth regions enclosed by them; and 3) the depth value over each region. The starting represen ..."
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Cited by 4 (3 self)
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, the vertical and horizontal crackedges separating the constant depth regions are transmitted by 2D context coding using optimally pruned context trees. Both the encoder and decoder can reconstruct the regions of constant depth from the transmitted crackedge image. The depth value in a given region is encoded
Locally Decodable Codes with 2 queries and Polynomial Identity Testing for depth 3 circuits
 ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY, REPORT NO. 44 (2005)
, 2005
"... In this work we study two, seemingly unrelated, notions. Locally Decodable Codes (LDCs) are codes that allow the recovery of each message bit from a constant number of entries of the codeword. Polynomial Identity Testing (PIT) is one of the fundamental problems of algebraic complexity: we are given ..."
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Cited by 47 (14 self)
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In this work we study two, seemingly unrelated, notions. Locally Decodable Codes (LDCs) are codes that allow the recovery of each message bit from a constant number of entries of the codeword. Polynomial Identity Testing (PIT) is one of the fundamental problems of algebraic complexity: we are given
The complexity of constructing pseudorandom generators from hard functions
 COMPUTATIONAL COMPLEXITY
, 2004
"... We study the complexity of constructing pseudorandom generators (PRGs) from hard functions, focussing on constantdepth circuits. We show that, starting from a function f: {0, 1} l → {0, 1} computable in alternating time O(l) with O(1) alternations that is hard on average (i.e. there is a constant ..."
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Cited by 42 (9 self)
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within the polynomial time hierarchy. These negative results are obtained by showing that polynomialsize constantdepth circuits cannot compute good extractors and listdecodable codes.
Cryptography with Constant Input Locality (Extended Abstract)
"... We study the following natural question: Which cryptographic primitives (if any) can be realized by functions with constant input locality, namely functions in which every bit of the input influences only a constant number of bits of the output? This continues the study of cryptography in low compl ..."
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Cited by 12 (3 self)
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generators, commitments, and semanticallysecure publickey encryption schemes whose input locality is constant. Moreover, these constructions also enjoy constant output locality. Therefore, they give rise to cryptographic hardware that has constantdepth, constant fanin and constant fanout. As a byproduct
Protecting Circuits from Computationally Bounded and Noisy Leakage ∗
, 2014
"... Physical computational devices leak sidechannel information that may, and often does, reveal secret internal states. We present a general transformation that compiles any circuit into a circuit with the same functionality but resilience against welldefined classes of leakage. Our construction requ ..."
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that the apparatus is limited in the amount of output bits per iteration and the ability to decode certain linear encodings. While our results apply in general to such leakage classes, in particular, we obtain security against: • Constantdepth circuits leakage, where the leakage function is computed by an AC 0
Bit Allocation and Encoded View Selection for Optimal Multiview Image Representation
"... Abstract—Novel coding tools have been proposed recently to encode texture and depth maps of multiview images, exploiting interview correlations, for depthimagebased rendering (DIBR). However, the important associated bit allocation problem for DIBR remains open: for chosen view coding and synthes ..."
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and synthesis tools, how to allocate bits among texture and depth maps across encoded views, so that the fidelity of a set of V views reconstructed at the decoder is maximized, for a fixed bitrate budget? In this paper, we present an optimization strategy to select subset of texture and depth maps
On Dependent Bit Allocation for Multiview Image Coding With DepthImageBased Rendering
, 2011
"... The encoding of both texture and depth maps of multiview images, captured by a set of spatially correlated cameras, is important for any 3D visual communication system based on depthimagebased rendering (DIBR). In this paper, we address the problem of efficient bit allocation among texture and de ..."
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Cited by 12 (5 self)
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and depth maps of multiview images. More specifically, suppose we are given a coding tool to encode texture and depth maps at the encoder and a viewsynthesis tool to construct intermediate views at the decoder using neighboring encoded texture and depth maps. Our goal is to determine how to best select
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