Pub Date : 2015-06-25DOI: 10.1109/ITW.2015.7133162
V. Kostina, Yury Polyanskiy, S. Verdú
We investigate the minimum transmitted energy required to reproduce k source samples with a given fidelity after transmission over a memoryless Gaussian channel. In particular, we analyze the reduction in transmitted energy that accrues thanks to the availability of noiseless feedback. Allowing a nonvanishing excess distortion probability ∈ boosts the asymptotic fundamental limit by a factor of 1-∈, with or without feedback. If feedback is available, achieving guaranteed distortion with finite average energy is possible.
{"title":"Transmitting k samples over the Gaussian channel: Energy-distortion tradeoff","authors":"V. Kostina, Yury Polyanskiy, S. Verdú","doi":"10.1109/ITW.2015.7133162","DOIUrl":"https://doi.org/10.1109/ITW.2015.7133162","url":null,"abstract":"We investigate the minimum transmitted energy required to reproduce k source samples with a given fidelity after transmission over a memoryless Gaussian channel. In particular, we analyze the reduction in transmitted energy that accrues thanks to the availability of noiseless feedback. Allowing a nonvanishing excess distortion probability ∈ boosts the asymptotic fundamental limit by a factor of 1-∈, with or without feedback. If feedback is available, achieving guaranteed distortion with finite average energy is possible.","PeriodicalId":174797,"journal":{"name":"2015 IEEE Information Theory Workshop (ITW)","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125149166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-06-25DOI: 10.1109/ITW.2015.7133092
S. Engelberg, O. Keren
Transmission across asynchronous communication channels can be subjected to delay injection attacks. Delay injection attacks cause arbitrary skews - arbitrary numbers of transmitted signals can arrive after the first signal of the next transmission has arrived. The (common) assumption that all signals form the ith transmission arrive at the decoder before any signal from the (i + 2)th transmission arrives is called a no switch assumption. This paper presents a self-synchronizing zero-latency coding scheme that requires no acknowledge and can perfectly decode any transmission distorted by an arbitrary skew that obeys the no switch assumption.
{"title":"Zero-latency zero-error codes for parallel asynchronous channels with arbitrary skews","authors":"S. Engelberg, O. Keren","doi":"10.1109/ITW.2015.7133092","DOIUrl":"https://doi.org/10.1109/ITW.2015.7133092","url":null,"abstract":"Transmission across asynchronous communication channels can be subjected to delay injection attacks. Delay injection attacks cause arbitrary skews - arbitrary numbers of transmitted signals can arrive after the first signal of the next transmission has arrived. The (common) assumption that all signals form the ith transmission arrive at the decoder before any signal from the (i + 2)th transmission arrives is called a no switch assumption. This paper presents a self-synchronizing zero-latency coding scheme that requires no acknowledge and can perfectly decode any transmission distorted by an arbitrary skew that obeys the no switch assumption.","PeriodicalId":174797,"journal":{"name":"2015 IEEE Information Theory Workshop (ITW)","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126046010","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-06-25DOI: 10.1109/ITW.2015.7133127
N. Pietro, Nour Basha, J. Boutros
The recently discovered family of generalized low-density (GLD) lattices brings new mathematical challenges to coding theorists and practitioners. Given the excellent performance of integer GLD lattices in high dimensions and motivated by the simple lattice structure used for fast iterative decoding, this paper is a first attempt to analyze GLD lattices for asymptotically large dimensions. Firstly, we describe non-binary GLD codes and show their asymptotic goodness in terms of minimum Hamming distance. Secondly, we consider a GLD lattice ensemble built via Construction A from non-binary GLD codes, and analyze their goodness with respect to Poltyrev limit on the Gaussian channel. Finally, at large dimensions and using a large code alphabet, we prove that infinite GLD lattice constellations attain Poltyrev capacity limit under maximum likelihood decoding.
{"title":"Non-binary GLD codes and their lattices","authors":"N. Pietro, Nour Basha, J. Boutros","doi":"10.1109/ITW.2015.7133127","DOIUrl":"https://doi.org/10.1109/ITW.2015.7133127","url":null,"abstract":"The recently discovered family of generalized low-density (GLD) lattices brings new mathematical challenges to coding theorists and practitioners. Given the excellent performance of integer GLD lattices in high dimensions and motivated by the simple lattice structure used for fast iterative decoding, this paper is a first attempt to analyze GLD lattices for asymptotically large dimensions. Firstly, we describe non-binary GLD codes and show their asymptotic goodness in terms of minimum Hamming distance. Secondly, we consider a GLD lattice ensemble built via Construction A from non-binary GLD codes, and analyze their goodness with respect to Poltyrev limit on the Gaussian channel. Finally, at large dimensions and using a large code alphabet, we prove that infinite GLD lattice constellations attain Poltyrev capacity limit under maximum likelihood decoding.","PeriodicalId":174797,"journal":{"name":"2015 IEEE Information Theory Workshop (ITW)","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128190229","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-06-25DOI: 10.1109/ITW.2015.7133094
Jingge Zhu, M. Gastpar
The classical modulo-lattice construction of Erez et al. has been successfully applied to several coding problems under Gaussian noise, including coding for computation over multiple-access channels (MAC). For the latter problem, an alternative construction can be developed by extending a recently proposed nested linear code to Gaussian case. In this note, it is shown that using the nested linear code with judiciously chosen input distributions, the original compute-and-forward result is recovered and larger computation rates are achievable. In particular we show that the Gaussian input distribution is not optimal in general for the computation problem over Gaussian MAC. Among other results, new achievable rates for the Gaussian two-way relay channel (TWRC) are given.
{"title":"Compute-and-forward using nested linear codes for the Gaussian MAC","authors":"Jingge Zhu, M. Gastpar","doi":"10.1109/ITW.2015.7133094","DOIUrl":"https://doi.org/10.1109/ITW.2015.7133094","url":null,"abstract":"The classical modulo-lattice construction of Erez et al. has been successfully applied to several coding problems under Gaussian noise, including coding for computation over multiple-access channels (MAC). For the latter problem, an alternative construction can be developed by extending a recently proposed nested linear code to Gaussian case. In this note, it is shown that using the nested linear code with judiciously chosen input distributions, the original compute-and-forward result is recovered and larger computation rates are achievable. In particular we show that the Gaussian input distribution is not optimal in general for the computation problem over Gaussian MAC. Among other results, new achievable rates for the Gaussian two-way relay channel (TWRC) are given.","PeriodicalId":174797,"journal":{"name":"2015 IEEE Information Theory Workshop (ITW)","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128217443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-06-25DOI: 10.1109/ITW.2015.7133088
Xishuo Liu, S. Draper
LP-decodable multipermutation codes are a class of multipermutation codes that can be decoded using linear programming (LP). These codes are defined using linearly constrained multipermutation matrices, which are binary matrices that satisfy particular row sum and column sum constraints. Although generic LP solvers are capable of solving the LP decoding problem, they are not efficient in general because they do not leverage structures of the problem. This motivates us to study efficient decoding algorithms. In this paper, we focus on encoding and decoding algorithms for LP-decodable multipermutation codes. We first describe an algorithm that “ranks” multipermutations. In other words, it maps consecutive integers, one by one, to an ordered list of multipermutations. By leveraging this algorithm, we develop an encoding algorithm for a code proposed by Shieh and Tsai. Regarding decoding algorithms we propose an iterative decoding algorithm based on the alternating direction method of multipliers (ADMM), each iteration of which can be solved efficiently using off-the-shelf techniques. Finally, we study decoding performances of different decoders via simulation.
{"title":"Encoding and decoding algorithms for LP-decodable multipermutation codes","authors":"Xishuo Liu, S. Draper","doi":"10.1109/ITW.2015.7133088","DOIUrl":"https://doi.org/10.1109/ITW.2015.7133088","url":null,"abstract":"LP-decodable multipermutation codes are a class of multipermutation codes that can be decoded using linear programming (LP). These codes are defined using linearly constrained multipermutation matrices, which are binary matrices that satisfy particular row sum and column sum constraints. Although generic LP solvers are capable of solving the LP decoding problem, they are not efficient in general because they do not leverage structures of the problem. This motivates us to study efficient decoding algorithms. In this paper, we focus on encoding and decoding algorithms for LP-decodable multipermutation codes. We first describe an algorithm that “ranks” multipermutations. In other words, it maps consecutive integers, one by one, to an ordered list of multipermutations. By leveraging this algorithm, we develop an encoding algorithm for a code proposed by Shieh and Tsai. Regarding decoding algorithms we propose an iterative decoding algorithm based on the alternating direction method of multipliers (ADMM), each iteration of which can be solved efficiently using off-the-shelf techniques. Finally, we study decoding performances of different decoders via simulation.","PeriodicalId":174797,"journal":{"name":"2015 IEEE Information Theory Workshop (ITW)","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125642384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-06-25DOI: 10.1109/ITW.2015.7133147
J. Belfiore, Y. Hong, E. Viterbo
In this paper we introduce the two-modular Fourier transform of a binary function f : R → R defined over a finite commutative ring R = F2[X]/φ(X), where F2[X] is the ring of polynomials with binary coefficients and φ(X) is a polynomial of degree n, which is not a multiple of X. We also introduce the corresponding inverse Fourier transform. We then prove the corresponding convolution theorem.
{"title":"Harmonic analysis of binary functions","authors":"J. Belfiore, Y. Hong, E. Viterbo","doi":"10.1109/ITW.2015.7133147","DOIUrl":"https://doi.org/10.1109/ITW.2015.7133147","url":null,"abstract":"In this paper we introduce the two-modular Fourier transform of a binary function f : R → R defined over a finite commutative ring R = F2[X]/φ(X), where F2[X] is the ring of polynomials with binary coefficients and φ(X) is a polynomial of degree n, which is not a multiple of X. We also introduce the corresponding inverse Fourier transform. We then prove the corresponding convolution theorem.","PeriodicalId":174797,"journal":{"name":"2015 IEEE Information Theory Workshop (ITW)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130142798","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-06-25DOI: 10.1109/ITW.2015.7133154
Or Ordentlich, U. Erez, B. Nazer
We consider a Gaussian multiple-access channel where each user's message is identified with a vector of elements from a finite field, and the receiver's goal is to decode a linear combination of these finite field vectors. It is further assumed that each transmitter can causally observe the channel's output through a clean feedback link. We propose a novel coding scheme for this setup, which can be seen as an extension of the Cover-Leung scheme for the computation problem. This scheme is shown to achieve computation rates higher than the best known computation rates for the same scenario without feedback. In particular, for the symmetric two-user Gaussian multiple-access channel, the proposed scheme attains a symmetric computation rate greater than 1/2 log(3/4 + SNR).
{"title":"On compute-and-forward with feedback","authors":"Or Ordentlich, U. Erez, B. Nazer","doi":"10.1109/ITW.2015.7133154","DOIUrl":"https://doi.org/10.1109/ITW.2015.7133154","url":null,"abstract":"We consider a Gaussian multiple-access channel where each user's message is identified with a vector of elements from a finite field, and the receiver's goal is to decode a linear combination of these finite field vectors. It is further assumed that each transmitter can causally observe the channel's output through a clean feedback link. We propose a novel coding scheme for this setup, which can be seen as an extension of the Cover-Leung scheme for the computation problem. This scheme is shown to achieve computation rates higher than the best known computation rates for the same scenario without feedback. In particular, for the symmetric two-user Gaussian multiple-access channel, the proposed scheme attains a symmetric computation rate greater than 1/2 log(3/4 + SNR).","PeriodicalId":174797,"journal":{"name":"2015 IEEE Information Theory Workshop (ITW)","volume":"216 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114356728","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-06-25DOI: 10.1109/ITW.2015.7133163
Peter Gazi, Stefano Tessaro
Secret-key constructions are often proved secure in a model where one or more underlying components are replaced by an idealized oracle accessible to the attacker. This model gives rise to information-theoretic security analyses, and several advances have been made in this area over the last few years. This paper provides a systematic overview of what is achievable in this model, and how existing works fit into this view.
{"title":"Secret-key cryptography from ideal primitives: A systematic overview","authors":"Peter Gazi, Stefano Tessaro","doi":"10.1109/ITW.2015.7133163","DOIUrl":"https://doi.org/10.1109/ITW.2015.7133163","url":null,"abstract":"Secret-key constructions are often proved secure in a model where one or more underlying components are replaced by an idealized oracle accessible to the attacker. This model gives rise to information-theoretic security analyses, and several advances have been made in this area over the last few years. This paper provides a systematic overview of what is achievable in this model, and how existing works fit into this view.","PeriodicalId":174797,"journal":{"name":"2015 IEEE Information Theory Workshop (ITW)","volume":"361 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124546648","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-06-25DOI: 10.1109/ITW.2015.7133155
Ignacio Cascudo
Given a linear error correcting code C, its m-th power is defined as the linear span of the set of all coordinate-wise products of m (not necessarily distinct) codewords in C. The study of powers of codes (and especially squares) is relevant in a number of recent results in several areas of cryptography where we need to bound certain parameters (such as the dimension and the minimum distance) of both a linear code and some power of it simultaneously. These areas include most notably secret sharing and multiparty computation, but also two-party cryptography and public key cryptography. In this paper, some of these applications will be discussed together with several recent results and some open challenges.
{"title":"Powers of codes and applications to cryptography","authors":"Ignacio Cascudo","doi":"10.1109/ITW.2015.7133155","DOIUrl":"https://doi.org/10.1109/ITW.2015.7133155","url":null,"abstract":"Given a linear error correcting code C, its m-th power is defined as the linear span of the set of all coordinate-wise products of m (not necessarily distinct) codewords in C. The study of powers of codes (and especially squares) is relevant in a number of recent results in several areas of cryptography where we need to bound certain parameters (such as the dimension and the minimum distance) of both a linear code and some power of it simultaneously. These areas include most notably secret sharing and multiparty computation, but also two-party cryptography and public key cryptography. In this paper, some of these applications will be discussed together with several recent results and some open challenges.","PeriodicalId":174797,"journal":{"name":"2015 IEEE Information Theory Workshop (ITW)","volume":"245 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124298664","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-06-25DOI: 10.1109/ITW.2015.7133103
Ayush Jain, R. Bansal
In this paper, we bound the number of phrases of the sliding window Lempel-Ziv (SWLZ) algorithm using an upper bound on the expected number of phrases in the fixed database Lempel-Ziv (FDLZ) algorithm for a class of φ-mixing sources which includes Markov sources, unifilar sources and finite state sources as special cases, as developed by Yang and Kieffer [1]. We use this bound to obtain a point-wise upper bound on the redundancy rate of SWLZ algorithm to be 2H(log2log2nw/log2nw) + O(log2log2log2nw/log2nw). Here H is the entropy rate of the source and nw is the window size.
{"title":"Point-wise analysis of redundancy in SWLZ algorithm for φ-mixing sources","authors":"Ayush Jain, R. Bansal","doi":"10.1109/ITW.2015.7133103","DOIUrl":"https://doi.org/10.1109/ITW.2015.7133103","url":null,"abstract":"In this paper, we bound the number of phrases of the sliding window Lempel-Ziv (SWLZ) algorithm using an upper bound on the expected number of phrases in the fixed database Lempel-Ziv (FDLZ) algorithm for a class of φ-mixing sources which includes Markov sources, unifilar sources and finite state sources as special cases, as developed by Yang and Kieffer [1]. We use this bound to obtain a point-wise upper bound on the redundancy rate of SWLZ algorithm to be 2H(log<sub>2</sub>log<sub>2</sub>n<sub>w</sub>/log<sub>2</sub>n<sub>w</sub>) + O(log<sub>2</sub>log<sub>2</sub>log<sub>2</sub>n<sub>w</sub>/log<sub>2</sub>n<sub>w</sub>). Here H is the entropy rate of the source and n<sub>w</sub> is the window size.","PeriodicalId":174797,"journal":{"name":"2015 IEEE Information Theory Workshop (ITW)","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126790904","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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