Pub Date : 2006-07-09DOI: 10.1109/ISIT.2006.262094
C. Kellett, S. Weller
In this paper we present an abstraction of the extrinsic information transfer (EXIT) chart as the interconnection of two nonlinear systems in feedback with each other. We present results on the stability of fixed points for such a dynamical system and use this framework to rederive the well-known stability condition, connecting this to the one-dimensional dynamical system describing the fractions of erasure for low-density parity-check (LDPC) codes on the binary erasure channel (BEC). We observe that the error threshold corresponds to a fixed point bifurcation for this one-dimensional system, and show that this information can be visualized using a well-known tool from control theory: the root locus plot. We further show that these bifurcations can be seen by examining the EXIT chart
{"title":"Bifurcations and EXIT charts for the Binary Erasure Channel","authors":"C. Kellett, S. Weller","doi":"10.1109/ISIT.2006.262094","DOIUrl":"https://doi.org/10.1109/ISIT.2006.262094","url":null,"abstract":"In this paper we present an abstraction of the extrinsic information transfer (EXIT) chart as the interconnection of two nonlinear systems in feedback with each other. We present results on the stability of fixed points for such a dynamical system and use this framework to rederive the well-known stability condition, connecting this to the one-dimensional dynamical system describing the fractions of erasure for low-density parity-check (LDPC) codes on the binary erasure channel (BEC). We observe that the error threshold corresponds to a fixed point bifurcation for this one-dimensional system, and show that this information can be visualized using a well-known tool from control theory: the root locus plot. We further show that these bifurcations can be seen by examining the EXIT chart","PeriodicalId":115298,"journal":{"name":"2006 IEEE International Symposium on Information Theory","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116235822","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 : 2006-07-09DOI: 10.1109/ISIT.2006.262131
L. Budaghyan, C. Carlet, P. Felke, G. Leander
We exhibit an infinite class of almost perfect nonlinear quadratic polynomials from F2n to F2n (n ges 12, n divisible by 3 but not by 9). We prove that these functions are EA-inequivalent to any power function and that they are CCZ-inequivalent to any Gold function. In a forthcoming full paper, we shall also prove that at least some of these functions are CCZ-inequivalent to any Kasami function
{"title":"An infinite class of quadratic APN functions which are not equivalent to power mappings","authors":"L. Budaghyan, C. Carlet, P. Felke, G. Leander","doi":"10.1109/ISIT.2006.262131","DOIUrl":"https://doi.org/10.1109/ISIT.2006.262131","url":null,"abstract":"We exhibit an infinite class of almost perfect nonlinear quadratic polynomials from F2n to F2n (n ges 12, n divisible by 3 but not by 9). We prove that these functions are EA-inequivalent to any power function and that they are CCZ-inequivalent to any Gold function. In a forthcoming full paper, we shall also prove that at least some of these functions are CCZ-inequivalent to any Kasami function","PeriodicalId":115298,"journal":{"name":"2006 IEEE International Symposium on Information Theory","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125096683","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 : 2006-07-09DOI: 10.1109/ISIT.2006.261750
P. Harremoës, C. Vignat
In this paper we are interested in n-dimensional uniform distributions on a triangle and a sphere. We show that their marginal distributions are maximizers of Renyi entropy under a constraint of variance and expectation in the respective cases of the sphere and of the triangle. Moreover, using an example, we show that a distribution on a triangle with (uniform) maximum entropy marginals may have an arbitrary small entropy. As a last result, we address the asymptotic behavior of these results and provide a link to the de Finetti theorem
{"title":"Rényi Entropies of Projections","authors":"P. Harremoës, C. Vignat","doi":"10.1109/ISIT.2006.261750","DOIUrl":"https://doi.org/10.1109/ISIT.2006.261750","url":null,"abstract":"In this paper we are interested in n-dimensional uniform distributions on a triangle and a sphere. We show that their marginal distributions are maximizers of Renyi entropy under a constraint of variance and expectation in the respective cases of the sphere and of the triangle. Moreover, using an example, we show that a distribution on a triangle with (uniform) maximum entropy marginals may have an arbitrary small entropy. As a last result, we address the asymptotic behavior of these results and provide a link to the de Finetti theorem","PeriodicalId":115298,"journal":{"name":"2006 IEEE International Symposium on Information Theory","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122705136","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 : 2006-07-09DOI: 10.1109/ISIT.2006.261635
S. Savari, G. Kramer
The capacity region for multiple unicast sessions on a bidirectional ring network is established and is shown to be achieved by routing. The proof uses recently developed progressive d-separating edge set bounds, new extensions of these bounds, as well as tools from the literature on the multicommodity flow problem
{"title":"The Multimessage Unicast Capacity Region for Bidirectional Ring Networks","authors":"S. Savari, G. Kramer","doi":"10.1109/ISIT.2006.261635","DOIUrl":"https://doi.org/10.1109/ISIT.2006.261635","url":null,"abstract":"The capacity region for multiple unicast sessions on a bidirectional ring network is established and is shown to be achieved by routing. The proof uses recently developed progressive d-separating edge set bounds, new extensions of these bounds, as well as tools from the literature on the multicommodity flow problem","PeriodicalId":115298,"journal":{"name":"2006 IEEE International Symposium on Information Theory","volume":"333 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122749681","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 : 2006-07-09DOI: 10.1109/ISIT.2006.261903
B. Falkowski, C. C. Lozano, S. Rahardja
Hardware calculation of generalized fastest linearly independent arithmetic (LIA) expansions using systolic processor is presented in this paper. The relation between the forward flow graph of a particular LIA transform and the systolic processor structure for its spectra calculation is given. In general, a particular systolic hardware structure can be used for more than one fastest LIA transforms with appropriate reordering of inputs and/or outputs
{"title":"Generalized Fastest LIA Transform Spectra Calculation by Systolic Processor","authors":"B. Falkowski, C. C. Lozano, S. Rahardja","doi":"10.1109/ISIT.2006.261903","DOIUrl":"https://doi.org/10.1109/ISIT.2006.261903","url":null,"abstract":"Hardware calculation of generalized fastest linearly independent arithmetic (LIA) expansions using systolic processor is presented in this paper. The relation between the forward flow graph of a particular LIA transform and the systolic processor structure for its spectra calculation is given. In general, a particular systolic hardware structure can be used for more than one fastest LIA transforms with appropriate reordering of inputs and/or outputs","PeriodicalId":115298,"journal":{"name":"2006 IEEE International Symposium on Information Theory","volume":"133 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122835637","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 : 2006-07-09DOI: 10.1109/ISIT.2006.261849
Jaewoo Jung, J. Gibson
In 1960 Campbell derived a quantity that he called coefficient rate which is expressible in terms of the entropy of the process power spectral density. Later, Yang, et al showed that the spectral entropy is proportional to the logarithm of the equivalent bandwidth of the smallest frequency band containing most of the energy. Gibson, et al also showed that for discrete time AR(1) sequences, Campbell's coefficient rate and Shannon's entropy rate power are equal but that the equality does not hold for higher order AR processes. In this paper, we derive a new expression for Campbell's coefficient rate in terms of the parametrized version of the rate distortion function of a Gaussian random process with a given power spectral density subject to the MSE fidelity criterion. We also derive expressions for the entropy rate power and coefficient rate in terms of the slope of the rate distortion function for the given source and for a source with flat power spectral density
{"title":"The Interpretation of Spectral Entropy Based Upon Rate Distortion Functions","authors":"Jaewoo Jung, J. Gibson","doi":"10.1109/ISIT.2006.261849","DOIUrl":"https://doi.org/10.1109/ISIT.2006.261849","url":null,"abstract":"In 1960 Campbell derived a quantity that he called coefficient rate which is expressible in terms of the entropy of the process power spectral density. Later, Yang, et al showed that the spectral entropy is proportional to the logarithm of the equivalent bandwidth of the smallest frequency band containing most of the energy. Gibson, et al also showed that for discrete time AR(1) sequences, Campbell's coefficient rate and Shannon's entropy rate power are equal but that the equality does not hold for higher order AR processes. In this paper, we derive a new expression for Campbell's coefficient rate in terms of the parametrized version of the rate distortion function of a Gaussian random process with a given power spectral density subject to the MSE fidelity criterion. We also derive expressions for the entropy rate power and coefficient rate in terms of the slope of the rate distortion function for the given source and for a source with flat power spectral density","PeriodicalId":115298,"journal":{"name":"2006 IEEE International Symposium on Information Theory","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122903109","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 : 2006-07-09DOI: 10.1109/ISIT.2006.261636
Yunnan Wu
Previous studies have proposed a practical network coding scheme for multicasting information in packet networks, which buffers received packets and outputs random linear mixtures of packets in the buffer. To analyze the performance of such a scheme, this paper introduces a continuous-time trellis, which models the packet transmissions in a practical asynchronous network. The continuous-time trellis represents an extension of a discrete-time trellis that was used in prior theoretical studies to model a synchronized network. The asymptotic throughput of the practical network coding scheme is characterized via an analysis of the asymptotic s-T connectivity in the trellis
{"title":"A Trellis Connectivity Analysis of Random Linear Network Coding with Buffering","authors":"Yunnan Wu","doi":"10.1109/ISIT.2006.261636","DOIUrl":"https://doi.org/10.1109/ISIT.2006.261636","url":null,"abstract":"Previous studies have proposed a practical network coding scheme for multicasting information in packet networks, which buffers received packets and outputs random linear mixtures of packets in the buffer. To analyze the performance of such a scheme, this paper introduces a continuous-time trellis, which models the packet transmissions in a practical asynchronous network. The continuous-time trellis represents an extension of a discrete-time trellis that was used in prior theoretical studies to model a synchronized network. The asymptotic throughput of the practical network coding scheme is characterized via an analysis of the asymptotic s-T connectivity in the trellis","PeriodicalId":115298,"journal":{"name":"2006 IEEE International Symposium on Information Theory","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131442093","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 : 2006-07-09DOI: 10.1109/ISIT.2006.261993
S. Forchhammer, Torben V. Laursen
A stationary model is presented for the two-dimensional (2-D) no isolated bits (n.i.b.) constraint over an extended alphabet defined by the elements within 1 by 2 blocks. This block-wise model is based on a set of sufficient conditions for a Pickard random field (PRF) over an m-ary alphabet. Iterative techniques are applied as part of determining the model parameters. Given two Markov chains describing a boundary, an algorithm is presented which determines whether a certain PRF consistent with the boundary exists. Iterative scaling is used as part of the algorithm, which also determines the conditional probabilities yielding the maximum entropy for the given boundary description if a solution exists. Optimizing over the parameters for a class of boundaries with certain symmetry properties, an entropy of 0.9156 is achieved for the n.i.b. constraint, providing a lower bound. An algorithm for iterative search for a PRF solution starting from a set of conditional probabilities is also presented
{"title":"A Model for the Two-Dimensional No Isolated Bits Constraint","authors":"S. Forchhammer, Torben V. Laursen","doi":"10.1109/ISIT.2006.261993","DOIUrl":"https://doi.org/10.1109/ISIT.2006.261993","url":null,"abstract":"A stationary model is presented for the two-dimensional (2-D) no isolated bits (n.i.b.) constraint over an extended alphabet defined by the elements within 1 by 2 blocks. This block-wise model is based on a set of sufficient conditions for a Pickard random field (PRF) over an m-ary alphabet. Iterative techniques are applied as part of determining the model parameters. Given two Markov chains describing a boundary, an algorithm is presented which determines whether a certain PRF consistent with the boundary exists. Iterative scaling is used as part of the algorithm, which also determines the conditional probabilities yielding the maximum entropy for the given boundary description if a solution exists. Optimizing over the parameters for a class of boundaries with certain symmetry properties, an entropy of 0.9156 is achieved for the n.i.b. constraint, providing a lower bound. An algorithm for iterative search for a PRF solution starting from a set of conditional probabilities is also presented","PeriodicalId":115298,"journal":{"name":"2006 IEEE International Symposium on Information Theory","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132581819","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 : 2006-07-09DOI: 10.1109/ISIT.2006.261779
A. Amraoui, A. Montanari, R. Urbanke
We show that the finite-length scaling parameters for irregular LDPC codes when used over the binary erasure channel can be computed without resorting to "covariance evolution". We provide simple expressions that can be evaluated using solely the degree distributions and the characteristics of the fixed point of density evolution
{"title":"Analytic Determination of Scaling Parameters","authors":"A. Amraoui, A. Montanari, R. Urbanke","doi":"10.1109/ISIT.2006.261779","DOIUrl":"https://doi.org/10.1109/ISIT.2006.261779","url":null,"abstract":"We show that the finite-length scaling parameters for irregular LDPC codes when used over the binary erasure channel can be computed without resorting to \"covariance evolution\". We provide simple expressions that can be evaluated using solely the degree distributions and the characteristics of the fixed point of density evolution","PeriodicalId":115298,"journal":{"name":"2006 IEEE International Symposium on Information Theory","volume":"254 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132822718","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 : 2006-07-09DOI: 10.1109/ISIT.2006.261748
M. Griot, A. Casado, Wen-Yen Weng, H. Chan, J. Basak, E. Yablonovitch, I. Verbauwhede, B. Jalali, R. Wesel
This paper presents trellis codes for the Z channel designed to maintain a relatively low ones density. These codes have applications in pulse-position modulation systems and as a solution for uncoordinated communication on the binary OR multiple-access channel (MAC). In this paper we consider the latter application to demonstrate the performance of the codes. The OR channel provides an unusual opportunity where single-user decoding permits operation at about 70% of the full multiple-access channel sum capacity. The interleaver-division multiple access technique applied in this paper should approach that performance with turbo solutions. However, the current paper focuses on very low latency codes with simple decoding, intended for very high speed (gigabits per second) applications. Namely, it focuses on nonlinear trellis codes that provide about 30% of the full multiple-access sum capacity at high speeds and with very low latency. These trellis codes are designed specifically for the Z-channel that arises in a multiple-user OR channel, when the other users are treated as noise. In order to optimize the sum-capacity of the OR-MAC, the trellis code transmits codewords with a ones density much less than 50%. Also, a union bound technique that predicts the performance of these codes is presented. Results from simulations and a working FPGA implementation are shown
{"title":"Trellis Codes with Low Ones Density for the OR Multiple Access Channel","authors":"M. Griot, A. Casado, Wen-Yen Weng, H. Chan, J. Basak, E. Yablonovitch, I. Verbauwhede, B. Jalali, R. Wesel","doi":"10.1109/ISIT.2006.261748","DOIUrl":"https://doi.org/10.1109/ISIT.2006.261748","url":null,"abstract":"This paper presents trellis codes for the Z channel designed to maintain a relatively low ones density. These codes have applications in pulse-position modulation systems and as a solution for uncoordinated communication on the binary OR multiple-access channel (MAC). In this paper we consider the latter application to demonstrate the performance of the codes. The OR channel provides an unusual opportunity where single-user decoding permits operation at about 70% of the full multiple-access channel sum capacity. The interleaver-division multiple access technique applied in this paper should approach that performance with turbo solutions. However, the current paper focuses on very low latency codes with simple decoding, intended for very high speed (gigabits per second) applications. Namely, it focuses on nonlinear trellis codes that provide about 30% of the full multiple-access sum capacity at high speeds and with very low latency. These trellis codes are designed specifically for the Z-channel that arises in a multiple-user OR channel, when the other users are treated as noise. In order to optimize the sum-capacity of the OR-MAC, the trellis code transmits codewords with a ones density much less than 50%. Also, a union bound technique that predicts the performance of these codes is presented. Results from simulations and a working FPGA implementation are shown","PeriodicalId":115298,"journal":{"name":"2006 IEEE International Symposium on Information Theory","volume":"87 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132208256","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：