Coding scheme for interactive communication is the first to near optimality on three classical measures.
Error-correcting codes are one of the glories of the information age: They're what guarantee the flawless transmission of digital information over the airwaves or through copper wire, even in the presence of the corrupting influences that engineers call "noise."
But classical error-correcting codes work best with large chunks of data: The bigger the chunk, the higher the rate at which it can be transmitted error-free. In the Internet age, however, distributed computing is becoming more and more common, with devices repeatedly exchanging small chunks of data over long periods of time.
So for the last 20 years, researchers have been investigating interactive-coding schemes, which address the problem of long sequences of short exchanges. Like classical error-correcting codes, interactive codes are evaluated according to three criteria: How much noise can they tolerate? What's the maximum transmission rate they afford? And how time-consuming are the encoding and decoding processes?
At the IEEE Symposium on Foundations of Computer Science this month, MIT graduate students past and present will describe the first interactive coding scheme to approach the optimum on all three measures.
"Previous to this work, it was known how to get two out of three of these things to be optimal," says Mohsen Ghaffari, a graduate student in electrical engineering and computer science and one of the paper's two co-authors. "This paper achieves all three of them."
Moreover, where Claude Shannon's groundbreaking 1948 analysis of error-correcting codes considered the case of random noise, in which every bit of transmitted data has the same chance of being corrupted, Ghaffari and his collaborator — Bernhard Haeupler, who did his graduate work at MIT and is now an assistant professor at Carnegie Mellon University — consider the more stringent case of "adversarial noise," in which an antagonist is trying to interfere with transmission in the most disruptive way possible.
"We don't know what type of random noise will be the one that actually captures reality," Ghaffari explains. "If we knew the best one, we would just use that. But generally, we don't know. So you try to generate a coding that is as general as possible." A coding scheme that could thwart an active adversary would also thwart any type of random noise.
Error-correcting codes — both classical and interactive — work by adding some extra information to the message to be transmitted. They might, for instance, tack on some bits that describe arithmetic relationships between the message bits. Both the message bits and the extra bits are liable to corruption, so decoding a message — extracting the true sequence of message bits from the sequence that arrives at the receiver — is usually a process of iterating back and forth between the message bits and the extra bits, trying to iron out discrepancies.
In interactive communication, the maximum tolerable error rate is one-fourth: If the adversary can corrupt more than a quarter of the bits sent, perfectly reliable communication is impossible. Some prior interactive-coding schemes, Ghaffari explains, could handle that error rate without requiring too many extra bits. But the decoding process was prohibitively complex.
Making a list
To keep the complexity down, Ghaffari and Haeupler adopted a technique called list decoding. Rather than iterating back and forth between message bits and extra bits until the single most probable interpretation emerges, their algorithm iterates just long enough to create a list of likely candidates. At the end of their mutual computation, each of the interacting devices may have a list with hundreds of entries.
But each device, while it has only imperfect knowledge of the messages sent by the other, has perfect knowledge of the messages it sent. So if, at the computation's end, the devices simply exchange lists, each has enough additional information to zero in on the optimal decoding.
The maximum tolerable error rate for an interactive-coding scheme — one-fourth — is a theoretical result. The minimum length of an encoded message and the minimum decoding complexity, on the other hand, are surmises based on observation.
But Ghaffari and Haeupler's decoding algorithm is nearly linear, meaning that its execution time is roughly proportional to the length of the messages exchanged.
But linear relationships are still defined by constants: y = x is a linear relationship, but so is y = 1,000,000,000x. A linear algorithm that takes an extra second of computation for each additional bit of data it considers isn't as good as a linear algorithm that takes an extra microsecond.
Written by Larry Hardesty, MIT News Office
Andrew Carleen | Eurek Alert!
New Technologies for A/V Analysis and Search
13.04.2017 | Fraunhofer-Institut für Digitale Medientechnologie IDMT
On patrol in social networks
25.01.2017 | Fraunhofer-Institut für Arbeitswirtschaft und Organisation IAO
An international team of scientists has proposed a new multi-disciplinary approach in which an array of new technologies will allow us to map biodiversity and the risks that wildlife is facing at the scale of whole landscapes. The findings are published in Nature Ecology and Evolution. This international research is led by the Kunming Institute of Zoology from China, University of East Anglia, University of Leicester and the Leibniz Institute for Zoo and Wildlife Research.
Using a combination of satellite and ground data, the team proposes that it is now possible to map biodiversity with an accuracy that has not been previously...
Heatwaves in the Arctic, longer periods of vegetation in Europe, severe floods in West Africa – starting in 2021, scientists want to explore the emissions of the greenhouse gas methane with the German-French satellite MERLIN. This is made possible by a new robust laser system of the Fraunhofer Institute for Laser Technology ILT in Aachen, which achieves unprecedented measurement accuracy.
Methane is primarily the result of the decomposition of organic matter. The gas has a 25 times greater warming potential than carbon dioxide, but is not as...
Hydrogen is regarded as the energy source of the future: It is produced with solar power and can be used to generate heat and electricity in fuel cells. Empa researchers have now succeeded in decoding the movement of hydrogen ions in crystals – a key step towards more efficient energy conversion in the hydrogen industry of tomorrow.
As charge carriers, electrons and ions play the leading role in electrochemical energy storage devices and converters such as batteries and fuel cells. Proton...
Scientists from the Excellence Cluster Universe at the Ludwig-Maximilians-Universität Munich have establised "Cosmowebportal", a unique data centre for cosmological simulations located at the Leibniz Supercomputing Centre (LRZ) of the Bavarian Academy of Sciences. The complete results of a series of large hydrodynamical cosmological simulations are available, with data volumes typically exceeding several hundred terabytes. Scientists worldwide can interactively explore these complex simulations via a web interface and directly access the results.
With current telescopes, scientists can observe our Universe’s galaxies and galaxy clusters and their distribution along an invisible cosmic web. From the...
Temperature measurements possible even on the smallest scale / Molecular ruby for use in material sciences, biology, and medicine
Chemists at Johannes Gutenberg University Mainz (JGU) in cooperation with researchers of the German Federal Institute for Materials Research and Testing (BAM)...
19.06.2017 | Event News
13.06.2017 | Event News
13.06.2017 | Event News
23.06.2017 | Physics and Astronomy
23.06.2017 | Physics and Astronomy
23.06.2017 | Information Technology