Pub Date : 2008-08-15DOI: 10.1109/ITA.2008.4601072
G. Shamir
A pattern of a sequence is a sequence of integer indices with each index describing the order of first occurrence of the respective symbol in the original sequence. Several recent works studied entropy and entropy rate of patterns. Specifically, in a recent paper, tight general bounds on the block entropy of patterns of sequences generated by independent and identically distributed (i.i.d.) sources were derived. In this paper, precise approximations are given to the pattern block entropies for patterns of sequences generated by i.i.d. uniform and monotonic distributions, including distributions over the integers, and the geometric distribution. Numerical non-asymptotic bounds on the pattern block entropies of these distributions are provided even for very short blocks, and even for distributions that have infinite i.i.d. entropy rates. Conditional index entropy is also studied for distributions over smaller alphabets.
{"title":"Pattern entropy - revisited","authors":"G. Shamir","doi":"10.1109/ITA.2008.4601072","DOIUrl":"https://doi.org/10.1109/ITA.2008.4601072","url":null,"abstract":"A pattern of a sequence is a sequence of integer indices with each index describing the order of first occurrence of the respective symbol in the original sequence. Several recent works studied entropy and entropy rate of patterns. Specifically, in a recent paper, tight general bounds on the block entropy of patterns of sequences generated by independent and identically distributed (i.i.d.) sources were derived. In this paper, precise approximations are given to the pattern block entropies for patterns of sequences generated by i.i.d. uniform and monotonic distributions, including distributions over the integers, and the geometric distribution. Numerical non-asymptotic bounds on the pattern block entropies of these distributions are provided even for very short blocks, and even for distributions that have infinite i.i.d. entropy rates. Conditional index entropy is also studied for distributions over smaller alphabets.","PeriodicalId":345196,"journal":{"name":"2008 Information Theory and Applications Workshop","volume":"99 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127256078","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 : 2008-08-15DOI: 10.1109/ITA.2008.4601047
Upamanyu Madhow
The millimeter wave band from 60-95 GHz offers large swathes of unlicensed and semi-unlicensed spectrum, which may well form the basis for the next revolution in wireless communication, in which wireless catches up with wires.With the rapid scaling of silicon processes, low-cost implementations for radio frequency front-ends are on the horizon. A key challenge now is to parlay these breakthroughs into innovative system concepts. We review three such concepts here.Millimeter wave MIMO: The small carrier wavelength enables spatial multiplexing in line-of-sight environments, potentially resulting in point-to-point outdoor wireless links at optical speeds (40 Gbps) using bandwidths of the order of 5 GHz. Directional multihop networking: Indoor Gigabit wireless links based on 60 GHz unlicensed spectrum are subject to disruption due to line-of-sight blockage by obstacles such as furniture and humans. We show that a multihop architecture with a small number of relays assures full network connectivity. All-digital multiGigabit baseband: Since high-speed analog-to- digital conversion (ADC) is costly and power-hungry, in order to design all-digital baseband processing that can be implemented inexpensively by riding Moore's law, we must be able to perform signal processing with sloppy ADC. We discuss Shannon-theoretic limits and signal processing challenges in this context.
{"title":"MultiGigabit millimeter wave communication: System concepts and challenges","authors":"Upamanyu Madhow","doi":"10.1109/ITA.2008.4601047","DOIUrl":"https://doi.org/10.1109/ITA.2008.4601047","url":null,"abstract":"The millimeter wave band from 60-95 GHz offers large swathes of unlicensed and semi-unlicensed spectrum, which may well form the basis for the next revolution in wireless communication, in which wireless catches up with wires.With the rapid scaling of silicon processes, low-cost implementations for radio frequency front-ends are on the horizon. A key challenge now is to parlay these breakthroughs into innovative system concepts. We review three such concepts here.Millimeter wave MIMO: The small carrier wavelength enables spatial multiplexing in line-of-sight environments, potentially resulting in point-to-point outdoor wireless links at optical speeds (40 Gbps) using bandwidths of the order of 5 GHz. Directional multihop networking: Indoor Gigabit wireless links based on 60 GHz unlicensed spectrum are subject to disruption due to line-of-sight blockage by obstacles such as furniture and humans. We show that a multihop architecture with a small number of relays assures full network connectivity. All-digital multiGigabit baseband: Since high-speed analog-to- digital conversion (ADC) is costly and power-hungry, in order to design all-digital baseband processing that can be implemented inexpensively by riding Moore's law, we must be able to perform signal processing with sloppy ADC. We discuss Shannon-theoretic limits and signal processing challenges in this context.","PeriodicalId":345196,"journal":{"name":"2008 Information Theory and Applications Workshop","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125538519","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 : 2008-05-09DOI: 10.1109/ITA.2008.4601092
O. Somekh, O. Simeone, B. M. Zaidel, H. Poor, S. Shamai
The open problem of calculating the limiting spectrum (or its Shannon transform) of increasingly large random Hermitian finite-band matrices is described. In general, these matrices include a finite number of non-zero diagonals around their main diagonal regardless of their size. Two different communication setups which may be modeled using such matrices are presented: a simple cellular uplink channel, and a time varying inter-symbol interference channel. Selected recent information-theoretic works dealing directly with such channels are reviewed. Finally, several characteristics of the still unknown limiting spectrum of such matrices are listed, and some reflections are touched upon.
{"title":"On the spectrum of large random hermitian finite-band matrices","authors":"O. Somekh, O. Simeone, B. M. Zaidel, H. Poor, S. Shamai","doi":"10.1109/ITA.2008.4601092","DOIUrl":"https://doi.org/10.1109/ITA.2008.4601092","url":null,"abstract":"The open problem of calculating the limiting spectrum (or its Shannon transform) of increasingly large random Hermitian finite-band matrices is described. In general, these matrices include a finite number of non-zero diagonals around their main diagonal regardless of their size. Two different communication setups which may be modeled using such matrices are presented: a simple cellular uplink channel, and a time varying inter-symbol interference channel. Selected recent information-theoretic works dealing directly with such channels are reviewed. Finally, several characteristics of the still unknown limiting spectrum of such matrices are listed, and some reflections are touched upon.","PeriodicalId":345196,"journal":{"name":"2008 Information Theory and Applications Workshop","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133105978","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 : 2008-05-07DOI: 10.1109/ISIT.2008.4595189
M. Wigger, M. Gastpar
A generic intuition says that the pre-log, or multi-plexing gain, cannot be larger than the minimum of the number of transmit and receive dimensions. This suggests that for the scalar broadcast channel, the pre-log cannot exceed one. By contrast, in this note, we show that when the noises are anti-correlated and feedback is present, then a pre-log of two can be attained. In other words, in this special case, in the limit of high SNR, the scalar Gaussian broadcast channel turns into two parallel AWGN channels. Achievability is established via a coding strategy due to Schalkwijk, Kailath, and Ozarow.
{"title":"The pre-log of Gaussian broadcast with feedback can be two","authors":"M. Wigger, M. Gastpar","doi":"10.1109/ISIT.2008.4595189","DOIUrl":"https://doi.org/10.1109/ISIT.2008.4595189","url":null,"abstract":"A generic intuition says that the pre-log, or multi-plexing gain, cannot be larger than the minimum of the number of transmit and receive dimensions. This suggests that for the scalar broadcast channel, the pre-log cannot exceed one. By contrast, in this note, we show that when the noises are anti-correlated and feedback is present, then a pre-log of two can be attained. In other words, in this special case, in the limit of high SNR, the scalar Gaussian broadcast channel turns into two parallel AWGN channels. Achievability is established via a coding strategy due to Schalkwijk, Kailath, and Ozarow.","PeriodicalId":345196,"journal":{"name":"2008 Information Theory and Applications Workshop","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129611142","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 : 2008-04-23DOI: 10.1109/ITA.2008.4601053
Chandra Nair, Z. Wang
We study the best known general inner bound (K. Marton, January, 2003) and outer bound (C. Nair et al., January, 2007) for the capacity region of the two user discrete memory less channel.We prove that a seemingly stronger outer bound is identical to a weaker form of the outer bound that was also presented in (C. Nair et al., January, 2007). We are able to further express the best outer bound in a form that is computable, i.e. there are bounds on the cardinalities of the auxiliary random variables. The inner and outer bounds coincide for all channels for which the capacity region is known and it is not known whether the regions described by these bounds are same or different. We present a channel, where assuming a certain conjecture backed by simulations and partial theoretical results, one can show that the bounds are different.
我们研究了最著名的两个用户离散内存少信道容量区域的一般内界(K. Marton, 2003年1月)和外界(C. Nair等人，2007年1月)。我们证明了一个看似更强的外界与(C. Nair et al.， January, 2007)中也提出的一个较弱形式的外界是相同的。我们能够进一步以可计算的形式表达最佳外界，即辅助随机变量的基数有边界。对于已知容量区域的所有信道，内界和外界都是一致的，并且不知道这些边界所描述的区域是相同还是不同。我们提出了一个通道，其中假设由模拟和部分理论结果支持的某些猜想，可以表明边界是不同的。
{"title":"On the inner and outer bounds for 2-receiver discrete memoryless broadcast channels","authors":"Chandra Nair, Z. Wang","doi":"10.1109/ITA.2008.4601053","DOIUrl":"https://doi.org/10.1109/ITA.2008.4601053","url":null,"abstract":"We study the best known general inner bound (K. Marton, January, 2003) and outer bound (C. Nair et al., January, 2007) for the capacity region of the two user discrete memory less channel.We prove that a seemingly stronger outer bound is identical to a weaker form of the outer bound that was also presented in (C. Nair et al., January, 2007). We are able to further express the best outer bound in a form that is computable, i.e. there are bounds on the cardinalities of the auxiliary random variables. The inner and outer bounds coincide for all channels for which the capacity region is known and it is not known whether the regions described by these bounds are same or different. We present a channel, where assuming a certain conjecture backed by simulations and partial theoretical results, one can show that the bounds are different.","PeriodicalId":345196,"journal":{"name":"2008 Information Theory and Applications Workshop","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125783078","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 : 2008-01-02DOI: 10.1109/ITA.2008.4601084
V. Annapureddy, V. Veeravalli
New upper bounds on the sum capacity of the two-user Gaussian interference channel are derived. Using these bounds, it is shown that treating interference as noise achieves the sum capacity if the interference levels are below certain thresholds.
{"title":"Sum capacity of the Gaussian interference channel in the low interference regime","authors":"V. Annapureddy, V. Veeravalli","doi":"10.1109/ITA.2008.4601084","DOIUrl":"https://doi.org/10.1109/ITA.2008.4601084","url":null,"abstract":"New upper bounds on the sum capacity of the two-user Gaussian interference channel are derived. Using these bounds, it is shown that treating interference as noise achieves the sum capacity if the interference levels are below certain thresholds.","PeriodicalId":345196,"journal":{"name":"2008 Information Theory and Applications Workshop","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114331039","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 : 2007-10-30DOI: 10.1109/ITA.2008.4601037
S. Guha, B. Erkmen, J. Shapiro
Determining the ultimate classical information carrying capacity of electromagnetic waves requires quantum-mechanical analysis to properly account for the bosonic nature of these waves. Recent work has established capacity theorems for bosonic single-user, broadcast, and wiretap channels, under the presumption of two minimum output entropy conjectures. Despite considerable accumulated evidence that supports the validity of these conjectures, they have yet to be proven. Here we show that the preceding minimum output entropy conjectures are simple consequences of an entropy photon-number inequality, which is a conjectured quantum-mechanical analog of the entropy power inequality from classical information theory.
{"title":"The Entropy Photon-Number Inequality and its consequences","authors":"S. Guha, B. Erkmen, J. Shapiro","doi":"10.1109/ITA.2008.4601037","DOIUrl":"https://doi.org/10.1109/ITA.2008.4601037","url":null,"abstract":"Determining the ultimate classical information carrying capacity of electromagnetic waves requires quantum-mechanical analysis to properly account for the bosonic nature of these waves. Recent work has established capacity theorems for bosonic single-user, broadcast, and wiretap channels, under the presumption of two minimum output entropy conjectures. Despite considerable accumulated evidence that supports the validity of these conjectures, they have yet to be proven. Here we show that the preceding minimum output entropy conjectures are simple consequences of an entropy photon-number inequality, which is a conjectured quantum-mechanical analog of the entropy power inequality from classical information theory.","PeriodicalId":345196,"journal":{"name":"2008 Information Theory and Applications Workshop","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125875648","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 : 1900-01-01DOI: 10.1109/ITA.2008.4601035
Vinith Misra, V. K. Goyal, L. Varshney
In traditional modes of lossy compression, attaining low distortion letter-by-letter on a vector of source letters X1N=(X1, X2,..., XN)isinRopfN is the implicit aim. We consider here instead the goal of estimating at the destination a function G(X1N) of the source data under the constraint that each Xi must be separately scalar quantized. The design of optimal fixed- and variable-rate scalar quantizers is considered under the assumptions of high-resolution quantization theory, yielding optimal point densities for regular quantizers. Additionally, we consider how performance scales with N for certain classes of functions. This demonstrates potentially large improvement from consideration of G in the quantizer design.
{"title":"High-resolution distributed functional quantization","authors":"Vinith Misra, V. K. Goyal, L. Varshney","doi":"10.1109/ITA.2008.4601035","DOIUrl":"https://doi.org/10.1109/ITA.2008.4601035","url":null,"abstract":"In traditional modes of lossy compression, attaining low distortion letter-by-letter on a vector of source letters X<sub>1</sub> <sup>N</sup>=(X<sub>1</sub>, X<sub>2</sub>,..., X<sub>N</sub>)isinRopf<sup>N</sup> is the implicit aim. We consider here instead the goal of estimating at the destination a function G(X<sub>1</sub> <sup>N</sup>) of the source data under the constraint that each X<sub>i</sub> must be separately scalar quantized. The design of optimal fixed- and variable-rate scalar quantizers is considered under the assumptions of high-resolution quantization theory, yielding optimal point densities for regular quantizers. Additionally, we consider how performance scales with N for certain classes of functions. This demonstrates potentially large improvement from consideration of G in the quantizer design.","PeriodicalId":345196,"journal":{"name":"2008 Information Theory and Applications Workshop","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114324960","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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