Pub Date : 2014-11-03DOI: 10.1109/ITW.2015.7133146
Or Ordentlich, O. Shayevitz
A lossy source code C with rate R for a discrete memoryless source S is called subset-universal if for every 0 <; R' <; R, almost every subset of 2nR' of its codewords achieves average distortion close to the source's distortion-rate function D(R'). In this paper we prove the asymptotic existence of such codes. Moreover, we show the asymptotic existence of a code that is subset-universal with respect to all sources with the same alphabet.
{"title":"Subset-universal lossy compression","authors":"Or Ordentlich, O. Shayevitz","doi":"10.1109/ITW.2015.7133146","DOIUrl":"https://doi.org/10.1109/ITW.2015.7133146","url":null,"abstract":"A lossy source code C with rate R for a discrete memoryless source S is called subset-universal if for every 0 <; R' <; R, almost every subset of 2nR' of its codewords achieves average distortion close to the source's distortion-rate function D(R'). In this paper we prove the asymptotic existence of such codes. Moreover, we show the asymptotic existence of a code that is subset-universal with respect to all sources with the same alphabet.","PeriodicalId":174797,"journal":{"name":"2015 IEEE Information Theory Workshop (ITW)","volume":"437 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114117390","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 : 2014-11-02DOI: 10.1109/ITW.2015.7133137
Nir Elkayam, M. Feder
Achievable and converse bounds for general channels and mismatched decoding are derived. The direct (achievable) bound is derived using random coding and the analysis is tight up to factor 2. The converse is given in term of the achievable bound and the factor between them is given. This gives performance of the best rate-R code with possible mismatched decoding metric over a general channel, up to the factor that is identified. In the matched case we show that the converse equals the minimax meta-converse of Polyanskiy et al. [1].
{"title":"Achievable and converse bounds over a general channel and general decoding metric","authors":"Nir Elkayam, M. Feder","doi":"10.1109/ITW.2015.7133137","DOIUrl":"https://doi.org/10.1109/ITW.2015.7133137","url":null,"abstract":"Achievable and converse bounds for general channels and mismatched decoding are derived. The direct (achievable) bound is derived using random coding and the analysis is tight up to factor 2. The converse is given in term of the achievable bound and the factor between them is given. This gives performance of the best rate-R code with possible mismatched decoding metric over a general channel, up to the factor that is identified. In the matched case we show that the converse equals the minimax meta-converse of Polyanskiy et al. [1].","PeriodicalId":174797,"journal":{"name":"2015 IEEE Information Theory Workshop (ITW)","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123203577","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 : 2014-11-02DOI: 10.1109/ITW.2015.7133119
Andrea Grigorescu, H. Boche, R. Schaefer, H. Poor
The compound broadcast channel with confidential messages (BCC) generalizes the BCC by modeling the uncertainty of the channel. For the compound BCC, it is known only that the actual channel realization belongs to a pre-specified uncertainty set of channels and that it is constant during the entire transmission. For reliable and secure communication it is necessary to operate at a rate pair within the compound BCC capacity region. Therefore, the question of whether small variations of the uncertainty set lead to large losses of the compound BCC capacity region is of interest, and this problem is studied here. In particular, it is shown that the compound BCC model is robust, i.e., the capacity region depends continuously on the uncertainty set.
{"title":"Capacity region continuity of the compound broadcast channel with confidential messages","authors":"Andrea Grigorescu, H. Boche, R. Schaefer, H. Poor","doi":"10.1109/ITW.2015.7133119","DOIUrl":"https://doi.org/10.1109/ITW.2015.7133119","url":null,"abstract":"The compound broadcast channel with confidential messages (BCC) generalizes the BCC by modeling the uncertainty of the channel. For the compound BCC, it is known only that the actual channel realization belongs to a pre-specified uncertainty set of channels and that it is constant during the entire transmission. For reliable and secure communication it is necessary to operate at a rate pair within the compound BCC capacity region. Therefore, the question of whether small variations of the uncertainty set lead to large losses of the compound BCC capacity region is of interest, and this problem is studied here. In particular, it is shown that the compound BCC model is robust, i.e., the capacity region depends continuously on the uncertainty set.","PeriodicalId":174797,"journal":{"name":"2015 IEEE Information Theory Workshop (ITW)","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131009443","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 : 2014-10-31DOI: 10.1109/ITW.2015.7133087
Yauhen Yakimenka, Vitaly Skachek
The l-th stopping redundancy ρι(C) of the binary [n, k, d] code C, 1 ≤ l ≤ d, is defined as the minimum number of rows in the parity-check matrix of C, such that the smallest stopping set is of size at least l. The stopping redundancy ρ(C) is defined as ρd(C). In this work, we improve on the probabilistic analysis of stopping redundancy, proposed by Han, Siegel and Vardy, which yields the best bounds known today. In our approach, we judiciously select the first few rows in the parity-check matrix, and then continue with the probabilistic method. By using similar techniques, we improve also on the best known bounds on ρι(C), for 1 ≤ l ≤ d. Our approach is compared to the existing methods by numerical computations.
{"title":"Refined upper bounds on stopping redundancy of binary linear codes","authors":"Yauhen Yakimenka, Vitaly Skachek","doi":"10.1109/ITW.2015.7133087","DOIUrl":"https://doi.org/10.1109/ITW.2015.7133087","url":null,"abstract":"The l-th stopping redundancy ρ<sub>ι</sub>(C) of the binary [n, k, d] code C, 1 ≤ l ≤ d, is defined as the minimum number of rows in the parity-check matrix of C, such that the smallest stopping set is of size at least l. The stopping redundancy ρ(C) is defined as ρ<sub>d</sub>(C). In this work, we improve on the probabilistic analysis of stopping redundancy, proposed by Han, Siegel and Vardy, which yields the best bounds known today. In our approach, we judiciously select the first few rows in the parity-check matrix, and then continue with the probabilistic method. By using similar techniques, we improve also on the best known bounds on ρ<sub>ι</sub>(C), for 1 ≤ l ≤ d. Our approach is compared to the existing methods by numerical computations.","PeriodicalId":174797,"journal":{"name":"2015 IEEE Information Theory Workshop (ITW)","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133406894","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 : 2014-10-31DOI: 10.1109/ITW.2015.7133132
H. M. Kiah, Gregory J. Puleo, O. Milenkovic
We consider the problem of assembling a sequence based on a collection of its substrings observed through a noisy channel. This problem of reconstructing sequences from traces was first investigated in the noiseless setting under the name of “Markov type” analysis. Here, we explain the connection between the problem and the problem of DNA synthesis and sequencing, and introduce the notion of a DNA storage channel. We analyze the number of sequence equivalence classes under the channel mapping and propose new asymmetric coding techniques to combat the effects of synthesis noise. In our analysis, we make use of Ehrhart theory for rational polytopes.
{"title":"Codes for DNA storage channels","authors":"H. M. Kiah, Gregory J. Puleo, O. Milenkovic","doi":"10.1109/ITW.2015.7133132","DOIUrl":"https://doi.org/10.1109/ITW.2015.7133132","url":null,"abstract":"We consider the problem of assembling a sequence based on a collection of its substrings observed through a noisy channel. This problem of reconstructing sequences from traces was first investigated in the noiseless setting under the name of “Markov type” analysis. Here, we explain the connection between the problem and the problem of DNA synthesis and sequencing, and introduce the notion of a DNA storage channel. We analyze the number of sequence equivalence classes under the channel mapping and propose new asymmetric coding techniques to combat the effects of synthesis noise. In our analysis, we make use of Ehrhart theory for rational polytopes.","PeriodicalId":174797,"journal":{"name":"2015 IEEE Information Theory Workshop (ITW)","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114242987","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 : 2014-10-30DOI: 10.1109/ITW.2015.7133108
A. Ganesan, S. Jaggi, Venkatesh Saligrama
Group testing with inhibitors (GTI) introduced by Farach at al. is studied in this paper. There are three types of items, d defectives, r inhibitors and n-d-r normal items in a population of n items. The presence of any inhibitor in a test can prevent the expression of a defective. For this model, we propose a probabilistic non-adaptive pooling design with a low complexity decoding algorithm. We show that the sample complexity of the number of tests required for guaranteed recovery with vanishing error probability using the proposed algorithm scales as T = O(d log n) and equation in the regimes r = O(d) and d = o(r) respectively. In the former regime, the number of tests meets the lower bound order while in the latter regime, the number of tests is shown to exceed the lower bound order by a log r over d multiplicative factor. The decoding complexity of the proposed decoding algorithm scales as O(nT).
{"title":"Non-adaptive group testing with inhibitors","authors":"A. Ganesan, S. Jaggi, Venkatesh Saligrama","doi":"10.1109/ITW.2015.7133108","DOIUrl":"https://doi.org/10.1109/ITW.2015.7133108","url":null,"abstract":"Group testing with inhibitors (GTI) introduced by Farach at al. is studied in this paper. There are three types of items, d defectives, r inhibitors and n-d-r normal items in a population of n items. The presence of any inhibitor in a test can prevent the expression of a defective. For this model, we propose a probabilistic non-adaptive pooling design with a low complexity decoding algorithm. We show that the sample complexity of the number of tests required for guaranteed recovery with vanishing error probability using the proposed algorithm scales as T = O(d log n) and equation in the regimes r = O(d) and d = o(r) respectively. In the former regime, the number of tests meets the lower bound order while in the latter regime, the number of tests is shown to exceed the lower bound order by a log r over d multiplicative factor. The decoding complexity of the proposed decoding algorithm scales as O(nT).","PeriodicalId":174797,"journal":{"name":"2015 IEEE Information Theory Workshop (ITW)","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131913684","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 : 2014-10-27DOI: 10.1109/ITW.2015.7133090
Martina Cardone, Daniela Tuninetti, R. Knopp
In ISIT2012 Brahma, Özgür and Fragouli conjectured that in a half-duplex diamond relay network (a Gaussian noise network without a direct source-destination link and with N non-interfering relays) an approximately optimal relay scheduling (achieving the cut-set upper bound to within a constant gap uniformly over all channel gains) exists with at most N + 1 active states (only N + 1 out of the 2N possible relay listen-transmit configurations have a strictly positive probability). Such relay scheduling policies are said to be simple. In ITW2013 we conjectured that simple relay policies are optimal for any half-duplex Gaussian multi-relay network, that is, simple schedules are not a consequence of the diamond network's sparse topology. In this paper we formally prove the conjecture beyond Gaussian networks. In particular, for any memoryless half-duplex N-relay network for which the cut-set bound is approximately optimal to within a constant gap under some conditions (satisfied for example by Gaussian networks), an optimal schedule exists with at most N + 1 active states. The key step of our proof is to write the minimum of a submodular function by means of its Lovász extension and use the greedy algorithm for submodular polyhedra to highlight structural properties of the optimal solution. This, together with the saddle-point property of min-max problems and the existence of optimal basic feasible solutions in linear programs, proves the claim.
{"title":"The approximate optimality of simple schedules for half-duplex multi-relay networks","authors":"Martina Cardone, Daniela Tuninetti, R. Knopp","doi":"10.1109/ITW.2015.7133090","DOIUrl":"https://doi.org/10.1109/ITW.2015.7133090","url":null,"abstract":"In ISIT2012 Brahma, Özgür and Fragouli conjectured that in a half-duplex diamond relay network (a Gaussian noise network without a direct source-destination link and with N non-interfering relays) an approximately optimal relay scheduling (achieving the cut-set upper bound to within a constant gap uniformly over all channel gains) exists with at most N + 1 active states (only N + 1 out of the 2N possible relay listen-transmit configurations have a strictly positive probability). Such relay scheduling policies are said to be simple. In ITW2013 we conjectured that simple relay policies are optimal for any half-duplex Gaussian multi-relay network, that is, simple schedules are not a consequence of the diamond network's sparse topology. In this paper we formally prove the conjecture beyond Gaussian networks. In particular, for any memoryless half-duplex N-relay network for which the cut-set bound is approximately optimal to within a constant gap under some conditions (satisfied for example by Gaussian networks), an optimal schedule exists with at most N + 1 active states. The key step of our proof is to write the minimum of a submodular function by means of its Lovász extension and use the greedy algorithm for submodular polyhedra to highlight structural properties of the optimal solution. This, together with the saddle-point property of min-max problems and the existence of optimal basic feasible solutions in linear programs, proves the claim.","PeriodicalId":174797,"journal":{"name":"2015 IEEE Information Theory Workshop (ITW)","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134276621","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 : 2014-10-14DOI: 10.1109/ITW.2015.7133080
Yi-Peng Wei, S. Ulukus
Information-theoretic work for wiretap channels is mostly based on random coding schemes. Designing practical coding schemes to achieve information-theoretic security is an important problem. By applying two recently developed techniques for polar codes, namely, universal polar coding and polar coding for asymmetric channels, we propose a polar coding scheme to achieve the secrecy capacity of the general wiretap channel.
{"title":"Polar coding for the general wiretap channel","authors":"Yi-Peng Wei, S. Ulukus","doi":"10.1109/ITW.2015.7133080","DOIUrl":"https://doi.org/10.1109/ITW.2015.7133080","url":null,"abstract":"Information-theoretic work for wiretap channels is mostly based on random coding schemes. Designing practical coding schemes to achieve information-theoretic security is an important problem. By applying two recently developed techniques for polar codes, namely, universal polar coding and polar coding for asymmetric channels, we propose a polar coding scheme to achieve the secrecy capacity of the general wiretap channel.","PeriodicalId":174797,"journal":{"name":"2015 IEEE Information Theory Workshop (ITW)","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115235802","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 : 2014-07-16DOI: 10.1109/ITW.2015.7133115
Sarah R. Allen, R. O'Donnell
Let X1, ..., Xn be joint {±1}-valued random variables. It is known that conditioning on a random subset of O(1/ε2) of them reduces their average pairwise covariance to below ε (in expectation). We conjecture that O(1/ε2) can be improved to O(1/ε). The motivation for the problem and our conjectured improvement comes from the theory of global correlation rounding for convex relaxation hierarchies. We suggest attempting the conjecture in the case that X1, ..., Xn are the leaves of an information flow tree. We prove the conjecture in the case that the information flow tree is a caterpillar graph (similar to a two-state hidden Markov model).
{"title":"Conditioning and covariance on caterpillars","authors":"Sarah R. Allen, R. O'Donnell","doi":"10.1109/ITW.2015.7133115","DOIUrl":"https://doi.org/10.1109/ITW.2015.7133115","url":null,"abstract":"Let X<sub>1</sub>, ..., X<sub>n</sub> be joint {±1}-valued random variables. It is known that conditioning on a random subset of O(1/ε<sup>2</sup>) of them reduces their average pairwise covariance to below ε (in expectation). We conjecture that O(1/ε<sup>2</sup>) can be improved to O(1/ε). The motivation for the problem and our conjectured improvement comes from the theory of global correlation rounding for convex relaxation hierarchies. We suggest attempting the conjecture in the case that X<sub>1</sub>, ..., X<sub>n</sub> are the leaves of an information flow tree. We prove the conjecture in the case that the information flow tree is a caterpillar graph (similar to a two-state hidden Markov model).","PeriodicalId":174797,"journal":{"name":"2015 IEEE Information Theory Workshop (ITW)","volume":"86 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132519597","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 : 2014-01-31DOI: 10.1109/ITW.2015.7133133
C. Kourtellaris, C. Charalambous
We consider a unit memory channel, called Binary State Symmetric Channel (BSSC), in which the channel state is the modulo2 addition of the current channel input and the previous channel output. We derive closed form expressions for the capacity and corresponding channel input distribution for the BSSC with and without feedback and transmission cost. We also show that the capacity of the BSSC, with or without feedback, is achieved by a first order symmetric Markov process.
{"title":"Capacity of Binary State Symmetric Channel with and without feedback and transmission cost","authors":"C. Kourtellaris, C. Charalambous","doi":"10.1109/ITW.2015.7133133","DOIUrl":"https://doi.org/10.1109/ITW.2015.7133133","url":null,"abstract":"We consider a unit memory channel, called Binary State Symmetric Channel (BSSC), in which the channel state is the modulo2 addition of the current channel input and the previous channel output. We derive closed form expressions for the capacity and corresponding channel input distribution for the BSSC with and without feedback and transmission cost. We also show that the capacity of the BSSC, with or without feedback, is achieved by a first order symmetric Markov process.","PeriodicalId":174797,"journal":{"name":"2015 IEEE Information Theory Workshop (ITW)","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115380152","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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