Pub Date : 2007-06-24DOI: 10.1109/ISIT.2007.4557510
P. Solé, V. Sison
In this paper, bounds are derived on the minimum homogeneous distance of the image of a linear block code over the Galois ring GR(pr ,m), with respect to any basis of GR(pr, m). These bounds depend on the parameters of GR(pr , m), the minimum Hamming distance of the block code, and the average value of the homogeneous weight applied on the base ring Zpr. Examples are given of Galois ring codes that meet these bounds.
{"title":"Bounds on the Minimum Homogeneous Distance of the pr-ary Image of Linear Block Codes over the Galois Ring GR(pr, m)","authors":"P. Solé, V. Sison","doi":"10.1109/ISIT.2007.4557510","DOIUrl":"https://doi.org/10.1109/ISIT.2007.4557510","url":null,"abstract":"In this paper, bounds are derived on the minimum homogeneous distance of the image of a linear block code over the Galois ring GR(pr ,m), with respect to any basis of GR(pr, m). These bounds depend on the parameters of GR(pr , m), the minimum Hamming distance of the block code, and the average value of the homogeneous weight applied on the base ring Zpr. Examples are given of Galois ring codes that meet these bounds.","PeriodicalId":92224,"journal":{"name":"International Symposium on Information Theory and its Applications. International Symposium on Information Theory and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2007-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78903061","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 : 2007-06-24DOI: 10.1109/ISIT.2007.4557335
Kai Li, Xiaodong Wang, A. Ashikhmin
We investigate the extrinsic information transfer (EXIT) functions of Hadamard codes in the context of repeat- zigzag Hadamard (RZH) codes with parallel decoding. The derived EXIT functions can serve as an effective tool for designing low-rate IRZH codes with parallel decoding in BIAWGN channels.
{"title":"EXIT Functions of Hadamard Components in Repeat-Zigzag-Hadamard (RZH) Codes","authors":"Kai Li, Xiaodong Wang, A. Ashikhmin","doi":"10.1109/ISIT.2007.4557335","DOIUrl":"https://doi.org/10.1109/ISIT.2007.4557335","url":null,"abstract":"We investigate the extrinsic information transfer (EXIT) functions of Hadamard codes in the context of repeat- zigzag Hadamard (RZH) codes with parallel decoding. The derived EXIT functions can serve as an effective tool for designing low-rate IRZH codes with parallel decoding in BIAWGN channels.","PeriodicalId":92224,"journal":{"name":"International Symposium on Information Theory and its Applications. International Symposium on Information Theory and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2007-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74254149","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 : 2007-06-24DOI: 10.1109/ISIT.2007.4557097
M. Gärtner, H. Bölcskei
We analyze the outage characteristics of correlated Ricean fading, coherent multiple-input multiple-output (MIMO) channels. In particular, we establish the notion of a "critical rate", below which communication at zero outage is possible and above which the channel appears as Ricean fading. The critical rate is shown to depend on the "angle" between the subspace spanned by the Ricean component of the channel matrix and the subspace spanned by the correlation matrix of the Rayleigh fading component. A nonzero critical rate is possible only if the correlation matrix of the Rayleigh fading component is rank- deficient. Finally, we provide a complete characterization of the optimum diversity-multiplexing tradeoff for correlated Ricean fading MIMO channels taking into account the existence of the critical rate and thereby establishing the notion of a critical multiplexing gain.
{"title":"On the \"Critical Rate\" in Ricean MIMO Channels","authors":"M. Gärtner, H. Bölcskei","doi":"10.1109/ISIT.2007.4557097","DOIUrl":"https://doi.org/10.1109/ISIT.2007.4557097","url":null,"abstract":"We analyze the outage characteristics of correlated Ricean fading, coherent multiple-input multiple-output (MIMO) channels. In particular, we establish the notion of a \"critical rate\", below which communication at zero outage is possible and above which the channel appears as Ricean fading. The critical rate is shown to depend on the \"angle\" between the subspace spanned by the Ricean component of the channel matrix and the subspace spanned by the correlation matrix of the Rayleigh fading component. A nonzero critical rate is possible only if the correlation matrix of the Rayleigh fading component is rank- deficient. Finally, we provide a complete characterization of the optimum diversity-multiplexing tradeoff for correlated Ricean fading MIMO channels taking into account the existence of the critical rate and thereby establishing the notion of a critical multiplexing gain.","PeriodicalId":92224,"journal":{"name":"International Symposium on Information Theory and its Applications. International Symposium on Information Theory and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2007-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86302465","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.2006.261581
A. Yao
Summary form only given,as follows. In past decades, the theory of computational complexity has fl ourished in terms of both the revelation of its internal structures and the unfolding of its numerous applications. In this talk we discuss several persistent and interwoven themes underlying many of these accomplishments. In particular we shall focus on the interplay between communication and computation which has a key role in these developments. We also speculate on promising future directions in the study of computational and communication complexity.
{"title":"Some perspectives on computational and communication complexity","authors":"A. Yao","doi":"10.1109/ISIT.2006.261581","DOIUrl":"https://doi.org/10.1109/ISIT.2006.261581","url":null,"abstract":"Summary form only given,as follows. In past decades, the theory of computational complexity has fl ourished in terms of both the revelation of its internal structures and the unfolding of its numerous applications. In this talk we discuss several persistent and interwoven themes underlying many of these accomplishments. In particular we shall focus on the interplay between communication and computation which has a key role in these developments. We also speculate on promising future directions in the study of computational and communication complexity.","PeriodicalId":92224,"journal":{"name":"International Symposium on Information Theory and its Applications. International Symposium on Information Theory and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81783374","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.2006.261584
D. Geman
Summary form only given, as follows. Image interpretation, which is effortless and instantaneous for human beings, is the grand challenge of computer vision. The dream is to build a "description machine" which produces a rich semantic description of the underly
{"title":"In search of a unifying theory for image interpretation","authors":"D. Geman","doi":"10.1109/ISIT.2006.261584","DOIUrl":"https://doi.org/10.1109/ISIT.2006.261584","url":null,"abstract":"Summary form only given, as follows. Image interpretation, which is effortless and instantaneous for human beings, is the grand challenge of computer vision. The dream is to build a \"description machine\" which produces a rich semantic description of the underly","PeriodicalId":92224,"journal":{"name":"International Symposium on Information Theory and its Applications. International Symposium on Information Theory and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85259982","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.2006.261623
M. Burnashev, I. Dumer
Recursive decoding is studied for Reed-Muller (RM) codes used on a binary symmetric channel. Decoding is performed beyond the bounded distance radius d/2 and corrects most error patterns of weight up to (d ln d)/2. In our analysis, coding is decomposed into consecutive steps, with one information bit derived in each step. Then the error probability of each step is defined by the recursive recalculations of the Bernoulli random variables. We derive the exponential moments of the recalculated random variables. As a result, tight exponential bounds on the output error probability are obtained for the two recursive algorithms considered in the paper. For both algorithms, the derived error exponents almost coincide with simulation results.
{"title":"Error exponents for recursive decoding of Reed-Muller codes","authors":"M. Burnashev, I. Dumer","doi":"10.1109/ISIT.2006.261623","DOIUrl":"https://doi.org/10.1109/ISIT.2006.261623","url":null,"abstract":"Recursive decoding is studied for Reed-Muller (RM) codes used on a binary symmetric channel. Decoding is performed beyond the bounded distance radius d/2 and corrects most error patterns of weight up to (d ln d)/2. In our analysis, coding is decomposed into consecutive steps, with one information bit derived in each step. Then the error probability of each step is defined by the recursive recalculations of the Bernoulli random variables. We derive the exponential moments of the recalculated random variables. As a result, tight exponential bounds on the output error probability are obtained for the two recursive algorithms considered in the paper. For both algorithms, the derived error exponents almost coincide with simulation results.","PeriodicalId":92224,"journal":{"name":"International Symposium on Information Theory and its Applications. International Symposium on Information Theory and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81958141","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.2006.261576
M. Gärtner, H. Bölcskei
A significant body of results on space-time and space-frequency coding for single-user channels is available in the literature. In contrast, space-time/frequency coding for multiple-access channels (MACs) seems largely unexplored. Building on the framework in Gallager, IEEE Trans. IT, 1985 for characterizing the dominant error event regions in single-antenna additive white Gaussian noise (AWGN) MACs, we derive rate-dependent space-time/frequency code design criteria for fading multiantenna MACs with perfect channel state information at the receiver. It is demonstrated that, depending on the transmission rate tuple, joint designs taking the presence of multiple users explicitly into account may be necessary. Our results furthermore allow to identify the rate regions where, for each user, employing codes designed for the single-user case is optimal. Finally, we show that the number of receive antennas has a significant impact on the dominant error event regions and hence, plays an important role in the code design criteria. As a byproduct of our analysis, we find that the classical code design criteria (based on pairwise error probabilities) are recovered using a completely different approach aimed at minimizing the probability of encountering a bad effective channel realization.
{"title":"Multiuser Space-Time/Frequency Code Design","authors":"M. Gärtner, H. Bölcskei","doi":"10.1109/ISIT.2006.261576","DOIUrl":"https://doi.org/10.1109/ISIT.2006.261576","url":null,"abstract":"A significant body of results on space-time and space-frequency coding for single-user channels is available in the literature. In contrast, space-time/frequency coding for multiple-access channels (MACs) seems largely unexplored. Building on the framework in Gallager, IEEE Trans. IT, 1985 for characterizing the dominant error event regions in single-antenna additive white Gaussian noise (AWGN) MACs, we derive rate-dependent space-time/frequency code design criteria for fading multiantenna MACs with perfect channel state information at the receiver. It is demonstrated that, depending on the transmission rate tuple, joint designs taking the presence of multiple users explicitly into account may be necessary. Our results furthermore allow to identify the rate regions where, for each user, employing codes designed for the single-user case is optimal. Finally, we show that the number of receive antennas has a significant impact on the dominant error event regions and hence, plays an important role in the code design criteria. As a byproduct of our analysis, we find that the classical code design criteria (based on pairwise error probabilities) are recovered using a completely different approach aimed at minimizing the probability of encountering a bad effective channel realization.","PeriodicalId":92224,"journal":{"name":"International Symposium on Information Theory and its Applications. International Symposium on Information Theory and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76227485","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.2006.261881
Tie Liu, P. Viswanath
We prove a new extremal inequality, motivated by the vector Gaussian broadcast channel and the distributed source coding with a single quadratic distortion constraint problem. As a corollary, this inequality yields a generalization of the classical vector entropy-power inequality (EPI). As another corollary, this inequality sheds insight into maximizing differential entropy of a sum of jointly distributed random variables, generalizing a classical result of Cover and Zhang.
{"title":"An Extremal Inequality Motivated by Multiterminal Information Theoretic Problems","authors":"Tie Liu, P. Viswanath","doi":"10.1109/ISIT.2006.261881","DOIUrl":"https://doi.org/10.1109/ISIT.2006.261881","url":null,"abstract":"We prove a new extremal inequality, motivated by the vector Gaussian broadcast channel and the distributed source coding with a single quadratic distortion constraint problem. As a corollary, this inequality yields a generalization of the classical vector entropy-power inequality (EPI). As another corollary, this inequality sheds insight into maximizing differential entropy of a sum of jointly distributed random variables, generalizing a classical result of Cover and Zhang.","PeriodicalId":92224,"journal":{"name":"International Symposium on Information Theory and its Applications. International Symposium on Information Theory and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76382399","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.2006.261599
H. Permuter, T. Weissman, A. Goldsmith
We consider channel coding with feedback for the general case where the feedback may be an arbitrary deterministic function of the output samples. Under the assumption that the channel states take values in a finite alphabet, we find an achievable rate and an upper bound on the capacity. We conclude by showing that when the channel is indecomposable, and has no intersymbol interference, its capacity is given by the limit of the maximum of the (normalized) directed information between the input XN and the output YN, i.e. C = limNrarrinfin/1N max I(XN rarr YN), where the maximization is over the causal conditioning probability Q(xN||kN-) defined in this paper
对于反馈可能是输出样本的任意确定性函数的一般情况，我们考虑带反馈的信道编码。在信道状态取值为有限字母的假设下，我们找到了一个可实现的速率和容量的上界。当信道不可分解且无码间干扰时，其容量由输入XN与输出YN之间(归一化)有向信息的最大值的极限给出，即C = limNrarrinfin/1N max I(XN rarr YN)，其中最大值大于本文定义的因果条件概率Q(XN ||kN-)
{"title":"Capacity of Finite-State Channels with Time-Invariant Deterministic Feedback","authors":"H. Permuter, T. Weissman, A. Goldsmith","doi":"10.1109/ISIT.2006.261599","DOIUrl":"https://doi.org/10.1109/ISIT.2006.261599","url":null,"abstract":"We consider channel coding with feedback for the general case where the feedback may be an arbitrary deterministic function of the output samples. Under the assumption that the channel states take values in a finite alphabet, we find an achievable rate and an upper bound on the capacity. We conclude by showing that when the channel is indecomposable, and has no intersymbol interference, its capacity is given by the limit of the maximum of the (normalized) directed information between the input XN and the output YN, i.e. C = limNrarrinfin/1N max I(XN rarr YN), where the maximization is over the causal conditioning probability Q(xN||kN-) defined in this paper","PeriodicalId":92224,"journal":{"name":"International Symposium on Information Theory and its Applications. International Symposium on Information Theory and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72876099","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.2006.261582
A. Vardy
Summary form only given, as follows. We will survey the fi eld of algebraic and combinatorial coding theory, in an attempt to answer the question in the title. In particular, we shall revisit classical problems that are yet unsolved, review promising advances in the past decade, elaborate upon recent connections to other areas, and speculate what may lie ahead for the fi eld.
{"title":"What's New and Exciting in Algebraic and Combinatorial Coding Theory?","authors":"A. Vardy","doi":"10.1109/ISIT.2006.261582","DOIUrl":"https://doi.org/10.1109/ISIT.2006.261582","url":null,"abstract":"Summary form only given, as follows. We will survey the fi eld of algebraic and combinatorial coding theory, in an attempt to answer the question in the title. In particular, we shall revisit classical problems that are yet unsolved, review promising advances in the past decade, elaborate upon recent connections to other areas, and speculate what may lie ahead for the fi eld.","PeriodicalId":92224,"journal":{"name":"International Symposium on Information Theory and its Applications. International Symposium on Information Theory and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83945964","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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