https://www.dagstuhl.de/16321

### 07. – 12. August 2016, Dagstuhl-Seminar 16321

# Coding Theory in the Time of Big Data

## Organisatoren

Martin Bossert (Universität Ulm, DE)

Eimear Byrne (University College Dublin, IE)

Emina Soljanin (Rutgers University – Piscataway, US)

## Auskunft zu diesem Dagstuhl-Seminar erteilt

## Dokumente

Dagstuhl Report, Volume 6, Issue 8

Motivationstext

Teilnehmerliste

Dagstuhl's Impact: Dokumente verfügbar

## Summary

The Dagstuhl Seminar 16321 *Coding Theory in the Time of Big Data*, held in August 7-12, 2016, was the third of a series of Dagstuhl seminars relating modern aspects of coding theory and its applications in computer science. The overarching technical theme was on how fundamentals of coding theory could be applied to data storage and transmission in the context of big data and conversely, on emerging topics in coding theory arising from such applications.
In Dagstuhl Seminar 11461 the main topics discussed were list decoding, codes on graphs, network coding and the relations between them. The themes of distributed storage, network coding and polar codes were central to Dagstuhl Seminar 13351.

The conference was organised into six main working groups, as listed below:

- Distributed Storage & Index Coding,
- Private Information Retrieval for Storage Codes,
- DNA-Based Storage,
- Age & Delay of Information.
- Code-Based Cryptography,
- Rank-Metric Codes.

The amount of data that is being stored is scaling at a rapid pace making efficient data storage an important problem that inspires several lines of scientific research. During the seminar, several discussions were conducted on the theme of using classical and new techniques from coding theory to store/compute data efficiently in distributed storage systems. A number of open problems were identified, such as the design of codes with optimal repair bandwidth, fundamental trade-offs between storage & communication cost, applications to content distribution networks, connections between fundamental limits of storage/caching and the index coding problem and applications of coding theory for parallel computing. A theoretical framework and numerical simulation for the long term reliability of a distributed storage system were presented by Luby.

DNA-based storage was recently proposed to address new challenges to handle extremely high volume recording media to propose new compression methods for non-traditional data formats. Since DNA may be easily replicated and a massive amount of information stored reliably with minimal space requirements, it has enormous potential as a method of big data storage. This was the focus of the DNA working group. Problems such read and write cost, insertion and deletion errors arising in sequences, error reduction were discussed. Milenkovic gave an introductory talk describing several problems associated with whole genome, sequencing read, RNA-seq and ChiP-seq data compression, and outlined the first portable DNA-based rewritable and random access storage system.

Private information retrieval (PIR) enables a user to retrieve a data item from a database without disclosing the identity of the item retrieved, while the data itself may be public. The PIR working group considered this problem in the context of storage codes, in particular for dynamic coded storage and adversarial PIR, with some extensions to asynchronized systems, batch codes and private keyword search. Hollanti gave a tutorial overview of recent results in the area.

Age of information is a metric for status updating systems, where a monitor is interested in staying timely about the status of a source. The optimal updating strategy that minimizes the average age exists when the updating rate is constrained by limited network resources. Streaming source coding problems can be applied to the problem of age analysis. The main focus the Age & Delay working group was to introduce the age of information concept to participating coding theorists and explore potential age and delay problems in coding and storage. An adaptive arithmetic coding scheme was proposed as a potential solution to avoid huge decoding delay. Several possible delay problems in file downloading from multiple servers were discussed. Two PhD students, Zhong and Najm gave a tutorial overview of the topic.

Code-based crypto-systems are some of the very few that resist quantum-based attacks. In the case subfield subcodes such as the Goppa or Srivastava codes no successful attack is known yet. Moderate-density parity-check (MDPC) codes have been proposed for key size reduction in such crytposystems. The group identified open problems such as investigating other subfield subcodes and attacks on MDPC structured codes. An overview was presented by Bossert.

Rank-metric codes have applications in random network coding, coded-caching and in code-based cryptography. The working group focussed on maximum rank distance (MRD) codes, specifically their classifications and on algebraic methods for constructing and decoding families of them. New nontrivial classifications were obtained. Further research directions on the classification problem were identified such as adapting semi-field theory techniques and searches for codes with high symmetry. Given the known limitation of list decoders for Gabidulin codes, the group worked on adapting decoders for Gabidulin codes to recent families of MRD codes. Sheekey presented recent results on MRD codes and described links to semifields.

A total of 44 researchers participated in the seminar across these working groups. In addition, several participants took the opportunity to collaborate with others on specific related projects. There were 16 talks in total, several related to storage of big data and others on topics such as maximum rank distance codes, chip-to-chip communication, the MDS conjecture, the SAGE computer algebra system, age of information, the edge removal problem, convolutional codes and network coding. Among the talks given were some tutorial presentations, aimed at introducing researchers to fundamentals of a related working group. The working groups focussed on identifying and addressing new and/or important open problems in the area. Age & Delay, PIR for storage codes and DNA-based storage were new topics to many participants and generated considerable interest.

**Summary text license**

Creative Commons BY 3.0 Unported license

Martin Bossert, Eimear Byrne, and Emina Soljanin

## Dagstuhl-Seminar Series

- 18511: "Algebraic Coding Theory for Networks, Storage, and Security" (2018)
- 13351: "Coding Theory" (2013)
- 11461: "Coding Theory" (2011)

## Classification

- Data Structures / Algorithms / Complexity
- Networks
- Security / Cryptology

## Keywords

- Error-correction
- Coding theory
- Algebraic coding theory
- Distributed storage
- Index coding
- Caching problems
- Streaming algorithms
- Cryptography
- Information theory
- Randomized algorithms
- Complexity theory.