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Algorithms
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Coding Theory and Its Application
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Coding Theory and Its Application

A special issue of Algorithms (ISSN 1999-4893).

Deadline for manuscript submissions: closed (30 July 2019) | Viewed by 21173

Special Issue Editors

Dr. Gianluigi Liva

E-Mail Website
Guest Editor
Institute of Communication and Navigation, German Aerospace Center (DLR), 82234 Wessling, Germany
Interests: codes on graphs; low-density parity-check codes; polar codes; coding for wireless communications; coding for optical links
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Alexandre Graell i Amat

E-Mail Website
Guest Editor
Department of Electrical Engineering, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden
Interests: coding theory and its application to distributed storage and computing, privacy, and optical communications
Special Issues, Collections and Topics in MDPI journals
Prof. Antonia Wachter-Zeh

E-Mail Website
Guest Editor
Institute for Communications Engineering, Technical University of Munich, 80333 Munich, Germany
Interests: error-correcting codes and their application to security; communication systems; and data storage

Special Issue Information

Dear Colleagues,

We are glad to announce the upcoming Special Issue dedicated to coding theory and its applications. This Special Issue aims to provide a unified, comprehensive view of recent advances in channel coding in the context of a broad range of both well-established and emerging applications. While historically tightly related to the problem of protecting communication links, channel codes offer solutions to a large class of challenges, spanning from the efficient storage of information over distributed network nodes to quantum computer attack-resilient encryption algorithms, protocol design for high-throughput uncoordinated medium access control, DNA storage, speeding up distributed computing tasks, and secret key generation—just to mention a few.

Researchers active in the analysis, design, and application of schemes based on channel codes are highly encouraged to submit their recent original findings. 

Dr. Gianluigi Liva
Prof. Alexandre Graell i Amat
Prof. Antonia Wachter-Zeh
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Algorithms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Error correcting codes for high throughput communication systems
  • Error correcting codes for machine-type communications
  • Coding for storage
  • Code-based cryptosystems
  • Coding for multi-user communications
  • Coding for secrecy and privacy
  • Application of coding techniques to compressive sensing and group testing
  • Coding for distributed computing
  • Coding for optical communications

Published Papers (5 papers)

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Research

14 pages, 680 KiB  
Article
A New Coding Paradigm for the Primitive Relay Channel
by Marco Mondelli, S. Hamed Hassani and Rüdiger Urbanke
Algorithms 2019, 12(10), 218; https://doi.org/10.3390/a12100218 - 18 Oct 2019
Cited by 4 | Viewed by 3023
Abstract
We consider the primitive relay channel, where the source sends a message to the relay and to the destination, and the relay helps the communication by transmitting an additional message to the destination via a separate channel. Two well-known coding techniques have been [...] Read more.
We consider the primitive relay channel, where the source sends a message to the relay and to the destination, and the relay helps the communication by transmitting an additional message to the destination via a separate channel. Two well-known coding techniques have been introduced for this setting: decode-and-forward and compress-and-forward. In decode-and-forward, the relay completely decodes the message and sends some information to the destination; in compress-and-forward, the relay does not decode, and it sends a compressed version of the received signal to the destination using Wyner–Ziv coding. In this paper, we present a novel coding paradigm that provides an improved achievable rate for the primitive relay channel. The idea is to combine compress-and-forward and decode-and-forward via a chaining construction. We transmit over pairs of blocks: in the first block, we use compress-and-forward; and, in the second block, we use decode-and-forward. More specifically, in the first block, the relay does not decode, it compresses the received signal via Wyner–Ziv, and it sends only part of the compression to the destination. In the second block, the relay completely decodes the message, it sends some information to the destination, and it also sends the remaining part of the compression coming from the first block. By doing so, we are able to strictly outperform both compress-and-forward and decode-and-forward. Note that the proposed coding scheme can be implemented with polar codes. As such, it has the typical attractive properties of polar coding schemes, namely, quasi-linear encoding and decoding complexity, and error probability that decays at super-polynomial speed. As a running example, we take into account the special case of the erasure relay channel, and we provide a comparison between the rates achievable by our proposed scheme and the existing upper and lower bounds. Full article
(This article belongs to the Special Issue Coding Theory and Its Application)
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34 pages, 549 KiB  
Article
A Finite Regime Analysis of Information Set Decoding Algorithms
by Marco Baldi, Alessandro Barenghi, Franco Chiaraluce, Gerardo Pelosi and Paolo Santini
Algorithms 2019, 12(10), 209; https://doi.org/10.3390/a12100209 - 01 Oct 2019
Cited by 30 | Viewed by 4125
Abstract
Decoding of random linear block codes has been long exploited as a computationally hard problem on which it is possible to build secure asymmetric cryptosystems. In particular, both correcting an error-affected codeword, and deriving the error vector corresponding to a given syndrome were [...] Read more.
Decoding of random linear block codes has been long exploited as a computationally hard problem on which it is possible to build secure asymmetric cryptosystems. In particular, both correcting an error-affected codeword, and deriving the error vector corresponding to a given syndrome were proven to be equally difficult tasks. Since the pioneering work of Eugene Prange in the early 1960s, a significant research effort has been put into finding more efficient methods to solve the random code decoding problem through a family of algorithms known as information set decoding. The obtained improvements effectively reduce the overall complexity, which was shown to decrease asymptotically at each optimization, while remaining substantially exponential in the number of errors to be either found or corrected. In this work, we provide a comprehensive survey of the information set decoding techniques, providing finite regime temporal and spatial complexities for them. We exploit these formulas to assess the effectiveness of the asymptotic speedups obtained by the improved information set decoding techniques when working with code parameters relevant for cryptographic purposes. We also delineate computational complexities taking into account the achievable speedup via quantum computers and similarly assess such speedups in the finite regime. To provide practical grounding to the choice of cryptographically relevant parameters, we employ as our validation suite the ones chosen by cryptosystems admitted to the second round of the ongoing standardization initiative promoted by the US National Institute of Standards and Technology. Full article
(This article belongs to the Special Issue Coding Theory and Its Application)
30 pages, 1194 KiB  
Article
Coarsely Quantized Decoding and Construction of Polar Codes Using the Information Bottleneck Method
by Syed Aizaz Ali Shah, Maximilian Stark and Gerhard Bauch
Algorithms 2019, 12(9), 192; https://doi.org/10.3390/a12090192 - 10 Sep 2019
Cited by 12 | Viewed by 4518
Abstract
The information bottleneck method is a generic clustering framework from the field of machine learning which allows compressing an observed quantity while retaining as much of the mutual information it shares with the quantity of primary relevance as possible. The framework was recently [...] Read more.
The information bottleneck method is a generic clustering framework from the field of machine learning which allows compressing an observed quantity while retaining as much of the mutual information it shares with the quantity of primary relevance as possible. The framework was recently used to design message-passing decoders for low-density parity-check codes in which all the arithmetic operations on log-likelihood ratios are replaced by table lookups of unsigned integers. This paper presents, in detail, the application of the information bottleneck method to polar codes, where the framework is used to compress the virtual bit channels defined in the code structure and show that the benefits are twofold. On the one hand, the compression restricts the output alphabet of the bit channels to a manageable size. This facilitates computing the capacities of the bit channels in order to identify the ones with larger capacities. On the other hand, the intermediate steps of the compression process can be used to replace the log-likelihood ratio computations in the decoder with table lookups of unsigned integers. Hence, a single procedure produces a polar encoder as well as its tailored, quantized decoder. Moreover, we also use a technique called message alignment to reduce the space complexity of the quantized decoder obtained using the information bottleneck framework. Full article
(This article belongs to the Special Issue Coding Theory and Its Application)
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23 pages, 903 KiB  
Article
Protograph LDPC Code Design for Asynchronous Random Access
by Federico Clazzer, Balázs Matuz, Sachini Jayasooriya, Mahyar Shirvanimoghaddam and Sarah J. Johnson
Algorithms 2019, 12(8), 170; https://doi.org/10.3390/a12080170 - 15 Aug 2019
Cited by 5 | Viewed by 4082
Abstract
This work addresses the physical layer channel code design for an uncoordinated, frame- and slot-asynchronous random access protocol. Starting from the observation that collisions between two users yield very specific interference patterns, we define a surrogate channel model and propose different protograph low-density [...] Read more.
This work addresses the physical layer channel code design for an uncoordinated, frame- and slot-asynchronous random access protocol. Starting from the observation that collisions between two users yield very specific interference patterns, we define a surrogate channel model and propose different protograph low-density parity-check code designs. The proposed codes are both tested in a setup where the physical layer is abstracted, as well as on a more realistic channel model, where finite-length physical layer simulations of the entire asynchronous random access scheme, including decoding, are carried out. We find that the abstracted physical layer model overestimates the performance when short blocks are considered. Additionally, the optimized codes show gains in supported channel traffic, a measure of the number of terminals that can be concurrently accommodated on the channel, of around 17% at a packet loss rate of 10 − 2 w.r.t. off-the-shelf codes. Full article
(This article belongs to the Special Issue Coding Theory and Its Application)
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15 pages, 1527 KiB  
Article
Soft Iterative Decoding Algorithms for Rateless Codes in Satellite Systems
by Meixiang Zhang, Satya Chan and Sooyoung Kim
Algorithms 2019, 12(8), 151; https://doi.org/10.3390/a12080151 - 29 Jul 2019
Cited by 2 | Viewed by 3965
Abstract
The satellite system is one of the most efficient means for broadcasting due to its wide service coverage as well as the fact that it can provide high data rate services by using high frequency bands. However, there are a number of problems [...] Read more.
The satellite system is one of the most efficient means for broadcasting due to its wide service coverage as well as the fact that it can provide high data rate services by using high frequency bands. However, there are a number of problems in the satellite system, such as a long round trip delay (RTD) and heterogeneity of the channel conditions of the earth stations. Even though utilizing adaptive coding and modulation (ACM) is almost mandatory for the satellite systems using high frequency bands due to the serious rain fading, the long RTD makes it difficult to quickly respond to channel quality information, resulting in a decrease in the efficiency of ACM. A high heterogeneity of earth stations caused by a wide service coverage also makes it difficult to apply a uniform transmission mode, and thus satellite systems require receiver-dependent transmission modes. A rateless code can be an effective means to compensate for these disadvantages of satellite systems compared to terrestrial wireless systems. This paper presents soft iterative decoding algorithms for efficient application of rateless codes in satellite systems and demonstrates that rateless codes can be effectively used for hybrid automatic repeat request schemes. Full article
(This article belongs to the Special Issue Coding Theory and Its Application)
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