We consider fault-tolerant boolean formulas in which the output of a faulty gate is short-circuited to one of the gate's inputs. A recent result by Kalai et al. [FOCS 2012] converts any boolean formula into a resi...
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ISBN:
(纸本)9783959771160
We consider fault-tolerant boolean formulas in which the output of a faulty gate is short-circuited to one of the gate's inputs. A recent result by Kalai et al. [FOCS 2012] converts any boolean formula into a resilient formula of polynomial size that works correctly if less than a fraction 1/6 of the gates (on every input-to-output path) are faulty. We improve the result of Kalai et al., and show how to efficiently fortify any boolean formula against a fraction 1/5 of short-circuit gates per path, with only a polynomial blowup in size. We additionally show that it is impossible to obtain formulas with higher resilience and sub-exponential growth in size. Towards our results, we consider interactive coding schemes when noiseless feedback is present;these produce resilient boolean formulas via a Karchmer-Wigderson relation. We develop a coding scheme that resists up to a fraction 1/5 of corrupted transmissions in each direction of the interactive channel. We further show that such a level of noise is maximal for coding schemes with sub-exponential blowup in communication. Our coding scheme takes a surprising inspiration from Blockchain technology.
In 2005, the Consultative Committee for Space Data Systems (CCSDS) approved a new Recommendation (CCSDS 122.0-B-1) for Image Data Compression. Our group has designed a new file syntax for the Recommendation. The propo...
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ISBN:
(纸本)9780819469069
In 2005, the Consultative Committee for Space Data Systems (CCSDS) approved a new Recommendation (CCSDS 122.0-B-1) for Image Data Compression. Our group has designed a new file syntax for the Recommendation. The proposal consists of adding embedded headers. Such modification provides scalability by quality, spatial location, resolution and component. The main advantages of our proposal are: 1) the definition of multiple types of progression order, which enhances abilities in transmission scenarios, and 2) the support for the extraction and decoding of specific windows of interest without needing to decode the complete code-stream. In this paper we evaluate the performance of our proposal. First we measure the impact of the embedded headers in the encoded stream. Second we compare the compression performance of our technique to JPEG2000.
interactive error correcting codes can protect interactive communication protocols against a constant fraction of adversarial errors, while incurring only a constant multiplicative overhead in the total communication....
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ISBN:
(纸本)9781450369794
interactive error correcting codes can protect interactive communication protocols against a constant fraction of adversarial errors, while incurring only a constant multiplicative overhead in the total communication. What is the maximum fraction of errors that such codes can protect against? For the non-adaptive channel, where the parties must agree in advance on the order in which they communicate, Braverman and Rao prove that the maximum error resilience is 1/4 (STOC, 2011). Ghaffari, Haeupler, and Sudan (STOC, 2014) consider the adaptive channel, where the order in which the parties communicate may not be fixed, and give a clever protocol that is resilient to a 2/7 fraction of errors. This was believed to be optimal. We revisit this result, and show how to overcome the 2/7 barrier. Specifically, we show that, over the adaptive channel, every twoparty communication protocol can be converted to a protocol that is resilient to 7/24 > 2/7 fraction of errors with only a constant multiplicative overhead to the total communication. The protocol is obtained by a novel implementation of a feedback mechanism over the adaptive channel.
We study the effect of noise on the n-party beeping model. In this model, in every round, each party may decide to either 'beep' or not. All parties hear a beep if and only if at least one party beeps. The bee...
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ISBN:
(纸本)9781450375825
We study the effect of noise on the n-party beeping model. In this model, in every round, each party may decide to either 'beep' or not. All parties hear a beep if and only if at least one party beeps. The beeping model is becoming increasingly popular, as it offers a very simple abstraction of wireless networks and is very well suited for studying biological phenomena. Still, the noise resilience of the beeping model is yet to be understood. Our main result is a lower bound, showing that making protocols in the beeping model resilient to noise may have a large performance overhead. Specifically, we give a protocol that works over the (noiseless) beeping model, and prove that any scheme that simulates this protocol over the beeping model with correlated stochastic noise will blow up the number of rounds by an O(logn) multiplicative factor. We complement this result by a matching upper bound, constructing a noise-resilient simulation scheme with O(logn) overhead for any noiseless beeping protocol.
We consider fault-tolerant boolean formulas in which the output of a faulty gate is short-circuited to one of the gate's inputs. A recent result by Kalai et al. [FOCS 2012] converts any boolean formula into a resi...
详细信息
We consider fault-tolerant boolean formulas in which the output of a faulty gate is short-circuited to one of the gate's inputs. A recent result by Kalai et al. [FOCS 2012] converts any boolean formula into a resilient formula of polynomial size thatworks correctly if less than 1/6 of the gates (on every input-to-output path) are faulty. We improve the result of Kalai et al., and show how to efficiently fortify any boolean formula against a fraction of 1/5 of short-circuit gates per path, with only a polynomial blowup in size. We additionally show that it is impossible to obtain formulas with higher resilience and sub-exponential growth in size. Towards our results, we consider interactive coding schemes when noiseless feedback is present;these produce resilient boolean formulas via a Karchmer-Wigderson relation. We develop a coding scheme that resists corruptions in up to a fraction of 1/5 of the transmissions in each direction of the interactive channel. We further show that such a level of noise is maximal for coding schemes whose communication blowup is sub-exponential. Our coding scheme has taken a surprising inspiration from Blockchain technology.
We consider fault-tolerant boolean formulas in which the output of a faulty gate is short-circuited to one of the gate's inputs. A recent result by Kalai et al. [FOCS 2012] converts any boolean formula into a resi...
详细信息
ISBN:
(纸本)9783959771160
We consider fault-tolerant boolean formulas in which the output of a faulty gate is short-circuited to one of the gate's inputs. A recent result by Kalai et al. [FOCS 2012] converts any boolean formula into a resilient formula of polynomial size that works correctly if less than a fraction 1/6 of the gates (on every input-to-output path) are faulty. We improve the result of Kalai et al., and show how to efficiently fortify any boolean formula against a fraction 1/5 of short-circuit gates per path, with only a polynomial blowup in size. We additionally show that it is impossible to obtain formulas with higher resilience and sub-exponential growth in *** our results, we consider interactive coding schemes when noiseless feedback is present; these produce resilient boolean formulas via a Karchmer-Wigderson relation. We develop a coding scheme that resists up to a fraction 1/5 of corrupted transmissions in each direction of the interactive channel. We further show that such a level of noise is maximal for coding schemes with sub-exponential blowup in communication. Our coding scheme takes a surprising inspiration from Blockchain technology.
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