Pub Date : 2016-07-10DOI: 10.1109/ISIT.2016.7541637
E. Rosnes, Michael Helmling
In this work, we present an explicit construction of valid inequalities (using no auxiliary variables) for the convex hull of the so-called constant-weight embedding of a single parity-check (SPC) code over any prime field. The construction is based on classes of building blocks that are assembled to form the left-hand side of an inequality according to several rules. In the case of almost doubly-symmetric valid classes we prove that the resulting inequalities are all facet-defining, while we conjecture this to be true if and only if the class is valid and symmetric. Such sets of inequalities have not appeared in the literature before, have a strong theoretical interest, and can be used to develop an efficient (relaxed) adaptive linear programming decoder for general (non-SPC) linear codes over prime fields.
{"title":"Constructing valid convex hull inequalities for single parity-check codes over prime fields","authors":"E. Rosnes, Michael Helmling","doi":"10.1109/ISIT.2016.7541637","DOIUrl":"https://doi.org/10.1109/ISIT.2016.7541637","url":null,"abstract":"In this work, we present an explicit construction of valid inequalities (using no auxiliary variables) for the convex hull of the so-called constant-weight embedding of a single parity-check (SPC) code over any prime field. The construction is based on classes of building blocks that are assembled to form the left-hand side of an inequality according to several rules. In the case of almost doubly-symmetric valid classes we prove that the resulting inequalities are all facet-defining, while we conjecture this to be true if and only if the class is valid and symmetric. Such sets of inequalities have not appeared in the literature before, have a strong theoretical interest, and can be used to develop an efficient (relaxed) adaptive linear programming decoder for general (non-SPC) linear codes over prime fields.","PeriodicalId":198767,"journal":{"name":"2016 IEEE International Symposium on Information Theory (ISIT)","volume":"732 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133183688","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 : 2016-07-10DOI: 10.1109/ISIT.2016.7541504
S. Bross, A. Lapidoth
The Rate-and-State capacity of a state-dependent channel with a state-cognizant encoder is the highest possible rate of communication over the channel when the decoder-in addition to reliably decoding the data-must also reconstruct the state sequence with some required fidelity. Feedback from the channel output to the encoder is shown to increase this capacity even for channels that are memoryless with memoryless states. This capacity is calculated here for such channels with feedback when the state reconstruction fidelity is measured using a single-letter distortion function and the state sequence is revealed to the encoder in one of two different ways: strictly-causally or causally.
{"title":"Conveying data and State with feedback","authors":"S. Bross, A. Lapidoth","doi":"10.1109/ISIT.2016.7541504","DOIUrl":"https://doi.org/10.1109/ISIT.2016.7541504","url":null,"abstract":"The Rate-and-State capacity of a state-dependent channel with a state-cognizant encoder is the highest possible rate of communication over the channel when the decoder-in addition to reliably decoding the data-must also reconstruct the state sequence with some required fidelity. Feedback from the channel output to the encoder is shown to increase this capacity even for channels that are memoryless with memoryless states. This capacity is calculated here for such channels with feedback when the state reconstruction fidelity is measured using a single-letter distortion function and the state sequence is revealed to the encoder in one of two different ways: strictly-causally or causally.","PeriodicalId":198767,"journal":{"name":"2016 IEEE International Symposium on Information Theory (ISIT)","volume":"134 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133242107","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 : 2016-07-10DOI: 10.1109/ISIT.2016.7541804
Ahmed Hindy, Aria Nosratinia
A modified version of Costa's dirty paper channel is studied, in which both the input signal and the state experience stationary and ergodic time-varying fading. The fading coefficients are assumed to be known exclusively at the receiver. An inner bound of the achievable rates using lattice codes is derived and compared to an outer bound of the capacity. For a wide range of fading distributions, the gap to capacity is within a constant value that does not depend on either the power of the input signal or the state. The results presented in this paper are applied to a class of ergodic fading broadcast channels with receive channel state information, where the achievable rate region is shown to be close to capacity under certain configurations.
{"title":"Lattice strategies for the ergodic fading dirty paper channel","authors":"Ahmed Hindy, Aria Nosratinia","doi":"10.1109/ISIT.2016.7541804","DOIUrl":"https://doi.org/10.1109/ISIT.2016.7541804","url":null,"abstract":"A modified version of Costa's dirty paper channel is studied, in which both the input signal and the state experience stationary and ergodic time-varying fading. The fading coefficients are assumed to be known exclusively at the receiver. An inner bound of the achievable rates using lattice codes is derived and compared to an outer bound of the capacity. For a wide range of fading distributions, the gap to capacity is within a constant value that does not depend on either the power of the input signal or the state. The results presented in this paper are applied to a class of ergodic fading broadcast channels with receive channel state information, where the achievable rate region is shown to be close to capacity under certain configurations.","PeriodicalId":198767,"journal":{"name":"2016 IEEE International Symposium on Information Theory (ISIT)","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124108501","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 : 2016-07-10DOI: 10.1109/ISIT.2016.7541791
Ahmed Hareedy, Chinmayi Lanka, Clayton Schoeny, L. Dolecek
Transmission channels underlying modern memory systems, e.g., Flash memories, possess a significant amount of asymmetry. While existing LDPC codes optimized for symmetric, AWGN-like channels are being actively considered for Flash applications, we demonstrate that, due to channel asymmetry, such approaches are fairly inadequate. We propose a new, general, combinatorial framework for the analysis and design of non-binary LDPC (NB-LDPC) codes for asymmetric channels. We introduce a refined definition of absorbing sets, which we call general absorbing sets (GASs), and an important subclass of GASs, which we refer to as general absorbing sets of type two (GASTs). Additionally, we study the combinatorial properties of GASTs. We then present the weight consistency matrix (WCM), which succinctly captures key properties in a GAST. Based on these new concepts, we then develop a general code optimization framework, and demonstrate its effectiveness on the realistic highly-asymmetric normal-Laplace mixture (NLM) Flash channel. Our optimized codes enjoy over one order (resp., half of an order) of magnitude performance gain in the uncorrectable BER (UBER) relative to the unoptimized codes (resp. the codes optimized for symmetric channels).
{"title":"The weight consistency matrix framework for general non-binary LDPC code optimization: Applications in flash memories","authors":"Ahmed Hareedy, Chinmayi Lanka, Clayton Schoeny, L. Dolecek","doi":"10.1109/ISIT.2016.7541791","DOIUrl":"https://doi.org/10.1109/ISIT.2016.7541791","url":null,"abstract":"Transmission channels underlying modern memory systems, e.g., Flash memories, possess a significant amount of asymmetry. While existing LDPC codes optimized for symmetric, AWGN-like channels are being actively considered for Flash applications, we demonstrate that, due to channel asymmetry, such approaches are fairly inadequate. We propose a new, general, combinatorial framework for the analysis and design of non-binary LDPC (NB-LDPC) codes for asymmetric channels. We introduce a refined definition of absorbing sets, which we call general absorbing sets (GASs), and an important subclass of GASs, which we refer to as general absorbing sets of type two (GASTs). Additionally, we study the combinatorial properties of GASTs. We then present the weight consistency matrix (WCM), which succinctly captures key properties in a GAST. Based on these new concepts, we then develop a general code optimization framework, and demonstrate its effectiveness on the realistic highly-asymmetric normal-Laplace mixture (NLM) Flash channel. Our optimized codes enjoy over one order (resp., half of an order) of magnitude performance gain in the uncorrectable BER (UBER) relative to the unoptimized codes (resp. the codes optimized for symmetric channels).","PeriodicalId":198767,"journal":{"name":"2016 IEEE International Symposium on Information Theory (ISIT)","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114500407","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 : 2016-07-10DOI: 10.1109/ISIT.2016.7541524
Moein Falahatgar, Ashkan Jafarpour, A. Orlitsky, Venkatadheeraj Pichapati, A. Suresh
Estimating the number of defective elements of a set has various biological applications including estimating the prevalence of a disease or disorder. Group testing has been shown to be more efficient than scrutinizing each element separately for defectiveness. In group testing, we query a subset of elements and the result of the query will be defective if the subset contains at least one defective element. We present an adaptive, randomized group-testing algorithm to estimate the number of defective elements with near-optimal number of queries. Our algorithm uses at most 2 log log d + O(1/δ2 log 1/ε) queries and estimates the number of defective elements d up to a multiplicative factor of 1 ± δ, with error probability ≤ ε. Also, we show an information-theoretic lower bound (1 - ε) log log d - 1 on the necessary number of queries any adaptive algorithm makes to estimate the number of defective elements for constant δ.
估计一组缺陷元素的数量有各种各样的生物学应用，包括估计疾病或失调的患病率。小组测试已被证明比单独检查每个元素的缺陷更有效。在组测试中，我们查询元素的子集，如果子集包含至少一个有缺陷的元素，那么查询的结果将是有缺陷的。我们提出了一种自适应的随机组测试算法，以接近最优的查询数量来估计缺陷元素的数量。我们的算法最多使用2 log log d + O(1/δ2 log 1/ε)查询，并估计缺陷元素的数量d达到1±δ的乘因子，误差概率≤ε。此外，我们还给出了一个信息理论下界(1 - ε) log log d - 1关于任何自适应算法为估计常数δ缺陷元素的数量而进行的必要查询次数的下界。
{"title":"Estimating the number of defectives with group testing","authors":"Moein Falahatgar, Ashkan Jafarpour, A. Orlitsky, Venkatadheeraj Pichapati, A. Suresh","doi":"10.1109/ISIT.2016.7541524","DOIUrl":"https://doi.org/10.1109/ISIT.2016.7541524","url":null,"abstract":"Estimating the number of defective elements of a set has various biological applications including estimating the prevalence of a disease or disorder. Group testing has been shown to be more efficient than scrutinizing each element separately for defectiveness. In group testing, we query a subset of elements and the result of the query will be defective if the subset contains at least one defective element. We present an adaptive, randomized group-testing algorithm to estimate the number of defective elements with near-optimal number of queries. Our algorithm uses at most 2 log log d + O(1/δ2 log 1/ε) queries and estimates the number of defective elements d up to a multiplicative factor of 1 ± δ, with error probability ≤ ε. Also, we show an information-theoretic lower bound (1 - ε) log log d - 1 on the necessary number of queries any adaptive algorithm makes to estimate the number of defective elements for constant δ.","PeriodicalId":198767,"journal":{"name":"2016 IEEE International Symposium on Information Theory (ISIT)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114956173","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 : 2016-07-10DOI: 10.1109/ISIT.2016.7541564
Linjia Chang, Avhishek Chatterjee, L. Varshney
Due to process variation in nanoscale manufacturing, there may be permanently missing connections in information processing hardware. Due to timing errors in circuits, there may be missed messages in intra-chip communications, equivalent to transiently missing connections. In this work, we investigate the performance of message-passing LDPC decoders in the presence of missing connections. We prove concentration and convergence theorems that validate the use of density evolution performance analysis. Arbitrarily small error probability is not possible under miswiring, but we find suitably defined decoding thresholds for communication systems with binary erasure channels and peeling decoders, as well as binary symmetric channels and Gallager A decoders. We see that decoding is robust to missing connections, as decoding thresholds degrade smoothly.
{"title":"LDPC decoders with missing connections","authors":"Linjia Chang, Avhishek Chatterjee, L. Varshney","doi":"10.1109/ISIT.2016.7541564","DOIUrl":"https://doi.org/10.1109/ISIT.2016.7541564","url":null,"abstract":"Due to process variation in nanoscale manufacturing, there may be permanently missing connections in information processing hardware. Due to timing errors in circuits, there may be missed messages in intra-chip communications, equivalent to transiently missing connections. In this work, we investigate the performance of message-passing LDPC decoders in the presence of missing connections. We prove concentration and convergence theorems that validate the use of density evolution performance analysis. Arbitrarily small error probability is not possible under miswiring, but we find suitably defined decoding thresholds for communication systems with binary erasure channels and peeling decoders, as well as binary symmetric channels and Gallager A decoders. We see that decoding is robust to missing connections, as decoding thresholds degrade smoothly.","PeriodicalId":198767,"journal":{"name":"2016 IEEE International Symposium on Information Theory (ISIT)","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123219903","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 : 2016-07-10DOI: 10.1109/ISIT.2016.7541738
Karim A. Banawan, S. Ulukus
We investigate the secure degrees of freedom (s.d.o.f.) of two new channel models: broadcast channel with combating helpers and interference channel with selfish users. In the first model, over a classical broadcast channel with confidential messages (BCCM), there are two helpers, each associated with one of the receivers. In the second model, over a classical interference channel with confidential messages (ICCM), there is a helper and users are selfish. The goal of introducing these channel models is to investigate various malicious interactions that arise in networks, including active adversaries. By casting each problem as an extensive-form game and applying recursive real interference alignment, we show that, for the first model, the combating intentions of the helpers are neutralized and the full s.d.o.f. is retained; for the second model, selfishness precludes secure communication and no s.d.o.f. is achieved.
{"title":"Secrecy in broadcast channel with combating helpers and interference channel with selfish users","authors":"Karim A. Banawan, S. Ulukus","doi":"10.1109/ISIT.2016.7541738","DOIUrl":"https://doi.org/10.1109/ISIT.2016.7541738","url":null,"abstract":"We investigate the secure degrees of freedom (s.d.o.f.) of two new channel models: broadcast channel with combating helpers and interference channel with selfish users. In the first model, over a classical broadcast channel with confidential messages (BCCM), there are two helpers, each associated with one of the receivers. In the second model, over a classical interference channel with confidential messages (ICCM), there is a helper and users are selfish. The goal of introducing these channel models is to investigate various malicious interactions that arise in networks, including active adversaries. By casting each problem as an extensive-form game and applying recursive real interference alignment, we show that, for the first model, the combating intentions of the helpers are neutralized and the full s.d.o.f. is retained; for the second model, selfishness precludes secure communication and no s.d.o.f. is achieved.","PeriodicalId":198767,"journal":{"name":"2016 IEEE International Symposium on Information Theory (ISIT)","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123566442","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 : 2016-07-10DOI: 10.1109/ISIT.2016.7541347
Lucien Lapierre, P. Lisoněk
We study vectorial bent functions with Dillon-type exponents. These functions have attracted attention because they are hyperbent whenever they are bent, and they achieve the highest possible algebraic degree among all bent functions on the same domain. In low dimensions we determine the simplest possible forms of such functions when they map to GF(4). We prove non-existence results for certain monomial and multinomial bent functions mapping to large codomains.
{"title":"On vectorial bent functions with Dillon-type exponents","authors":"Lucien Lapierre, P. Lisoněk","doi":"10.1109/ISIT.2016.7541347","DOIUrl":"https://doi.org/10.1109/ISIT.2016.7541347","url":null,"abstract":"We study vectorial bent functions with Dillon-type exponents. These functions have attracted attention because they are hyperbent whenever they are bent, and they achieve the highest possible algebraic degree among all bent functions on the same domain. In low dimensions we determine the simplest possible forms of such functions when they map to GF(4). We prove non-existence results for certain monomial and multinomial bent functions mapping to large codomains.","PeriodicalId":198767,"journal":{"name":"2016 IEEE International Symposium on Information Theory (ISIT)","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121936449","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 : 2016-07-10DOI: 10.1109/ISIT.2016.7541588
Li Gao, M. Junge, Nicholas Laracuente
Using a suitable algebraic setup, we find new estimates of the quantum capacity and the potential quantum capacity for non-degradable channels obtained by random unitaries associated with a finite group. This approach can be generalized to quantum groups and uses new tools from operator algebras and interpolation of Rényi-type entropies. As an application, we obtain new estimates for the depolarizing channel in high dimension.
{"title":"Operator algebra approach to quantum capacities","authors":"Li Gao, M. Junge, Nicholas Laracuente","doi":"10.1109/ISIT.2016.7541588","DOIUrl":"https://doi.org/10.1109/ISIT.2016.7541588","url":null,"abstract":"Using a suitable algebraic setup, we find new estimates of the quantum capacity and the potential quantum capacity for non-degradable channels obtained by random unitaries associated with a finite group. This approach can be generalized to quantum groups and uses new tools from operator algebras and interpolation of Rényi-type entropies. As an application, we obtain new estimates for the depolarizing channel in high dimension.","PeriodicalId":198767,"journal":{"name":"2016 IEEE International Symposium on Information Theory (ISIT)","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122122650","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 : 2016-07-10DOI: 10.1109/ISIT.2016.7541301
N. Alon, Jehoshua Bruck, Farzad Farnoud, Siddhartha Jain
We study the tandem duplication distance between binary sequences and their roots. This distance is motivated by genomic tandem duplication mutations and counts the smallest number of tandem duplication events that are required to take one sequence to another. We consider both exact and approximate tandem duplications, the latter leading to a combined duplication/Hamming distance. The paper focuses on the maximum value of the duplication distance to the root. For exact duplication, denoting the maximum distance to the root of a sequence of length n by f(n), we prove that f(n) = Θ(n). For the case of approximate duplication, where a β-fraction of symbols may be duplicated incorrectly, we show using the Plotkin bound that the maximum distance has a sharp transition from linear to logarithmic in n at β = 1/2.
{"title":"On the duplication distance of binary strings","authors":"N. Alon, Jehoshua Bruck, Farzad Farnoud, Siddhartha Jain","doi":"10.1109/ISIT.2016.7541301","DOIUrl":"https://doi.org/10.1109/ISIT.2016.7541301","url":null,"abstract":"We study the tandem duplication distance between binary sequences and their roots. This distance is motivated by genomic tandem duplication mutations and counts the smallest number of tandem duplication events that are required to take one sequence to another. We consider both exact and approximate tandem duplications, the latter leading to a combined duplication/Hamming distance. The paper focuses on the maximum value of the duplication distance to the root. For exact duplication, denoting the maximum distance to the root of a sequence of length n by f(n), we prove that f(n) = Θ(n). For the case of approximate duplication, where a β-fraction of symbols may be duplicated incorrectly, we show using the Plotkin bound that the maximum distance has a sharp transition from linear to logarithmic in n at β = 1/2.","PeriodicalId":198767,"journal":{"name":"2016 IEEE International Symposium on Information Theory (ISIT)","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124510373","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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