IEEE Trans. Inf. Theory最新文献

Corrections to "On the Separability of Parallel MISO Broadcast Channels Under Partial CSIT: A Degrees of Freedom Region Perspective" 对“局部CSIT下平行MISO广播信道的可分性:一个自由度区域视角”的修正

IEEE Trans. Inf. Theory Pub Date : 2020-09-21 DOI: 10.1109/TIT.2020.3015638

Hamdi Joudeh, B. Clerckx

引用次数: 0

Efficiently Decoding Reed-Muller Codes From Random Errors 从随机错误中有效解码Reed-Muller码

IEEE Trans. Inf. Theory Pub Date : 2017-04-01 DOI: 10.1109/TIT.2017.2671410

Ramprasad Saptharishi, Amir Shpilka, Ben lee Volk

{"title":"Efficiently Decoding Reed-Muller Codes From Random Errors","authors":"Ramprasad Saptharishi, Amir Shpilka, Ben lee Volk","doi":"10.1109/TIT.2017.2671410","DOIUrl":"https://doi.org/10.1109/TIT.2017.2671410","url":null,"abstract":"Reed–Muller (RM) codes encode an $m$ -variate polynomial of degree at most $r$ by evaluating it on all points in ${0,1}^{m}$ . We denote this code by $RM(r,m)$ . The minimum distance of $RM(r,m)$ is $2^{m-r}$ and so it cannot correct more than half that number of errors in the worst case. For random errors one may hope for a better result. In this paper we give an efficient algorithm (in the block length $n=2^{m}$ ) for decoding random errors in RM codes far beyond the minimum distance. Specifically, for low-rate codes (of degree $r=o(sqrt {m})$ ), we can correct a random set of $(1/2-o(1))n$ errors with high probability. For high rate codes (of degree $m-r$ for $r=o(sqrt {m/log m})$ ), we can correct roughly $m^{r/2}$ errors. More generally, for any integer $r$ , our algorithm can correct any error pattern in $RM(m-(2r+2),m)$ , for which the same erasure pattern can be corrected in $RM(m-(r+1),m)$ . The results above are obtained by applying recent results of Abbe, Shpilka, and Wigderson (STOC, 2015) and Kudekar et al. (STOC, 2016) regarding the ability of RM codes to correct random erasures. The algorithm is based on solving a carefully defined set of linear equations and thus it is significantly different than other algorithms for decoding RM codes that are based on the recursive structure of the code. It can be seen as a more explicit proof of a result of Abbe et al. that shows a reduction from correcting erasures to correcting errors, and it also bares some similarities with the error-locating pair method of Pellikaan, Duursma, and Kotter that generalizes the Berlekamp–Welch algorithm for decoding Reed–Solomon codes.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"30 1","pages":"1954-1960"},"PeriodicalIF":0.0,"publicationDate":"2017-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78823493","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}

引用次数: 4

Restricted q-Isometry Properties Adapted to Frames for Nonconvex lq-Analysis 适用于非凸lq分析框架的受限q等距性质

IEEE Trans. Inf. Theory Pub Date : 2016-02-20 DOI: 10.1109/TIT.2016.2573312

Junhong Lin, Song Li

{"title":"Restricted q-Isometry Properties Adapted to Frames for Nonconvex lq-Analysis","authors":"Junhong Lin, Song Li","doi":"10.1109/TIT.2016.2573312","DOIUrl":"https://doi.org/10.1109/TIT.2016.2573312","url":null,"abstract":"This paper discusses reconstruction of signals from few measurements in the situation that signals are sparse or approximately sparse in terms of a general frame via the $l_q$-analysis optimization with $0<qleq 1$. We first introduce a notion of restricted $q$-isometry property ($q$-RIP) adapted to a dictionary, which is a natural extension of the standard $q$-RIP, and establish a generalized $q$-RIP condition for approximate reconstruction of signals via the $l_q$-analysis optimization. We then determine how many random, Gaussian measurements are needed for the condition to hold with high probability. The resulting sufficient condition is met by fewer measurements for smaller $q$ than when $q=1$. The introduced generalized $q$-RIP is also useful in compressed data separation. In compressed data separation, one considers the problem of reconstruction of signals' distinct subcomponents, which are (approximately) sparse in morphologically different dictionaries, from few measurements. With the notion of generalized $q$-RIP, we show that under an usual assumption that the dictionaries satisfy a mutual coherence condition, the $l_q$ split analysis with $0<qleq1 $ can approximately reconstruct the distinct components from fewer random Gaussian measurements with small $q$ than when $q=1$","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"56 1","pages":"4733-4747"},"PeriodicalIF":0.0,"publicationDate":"2016-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73899628","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}

引用次数: 18

Distortion Rate Function of Sub-Nyquist Sampled Gaussian Sources 子奈奎斯特采样高斯源的失真率函数

IEEE Trans. Inf. Theory Pub Date : 2016-01-01 DOI: 10.1109/TIT.2015.2485271

A. Kipnis, A. Goldsmith, Yonina C. Eldar, T. Weissman

{"title":"Distortion Rate Function of Sub-Nyquist Sampled Gaussian Sources","authors":"A. Kipnis, A. Goldsmith, Yonina C. Eldar, T. Weissman","doi":"10.1109/TIT.2015.2485271","DOIUrl":"https://doi.org/10.1109/TIT.2015.2485271","url":null,"abstract":"The amount of information lost in sub-Nyquist sampling of a continuous-time Gaussian stationary process is quantified. We consider a combined source coding and sub-Nyquist reconstruction problem in which the input to the encoder is a noisy sub-Nyquist sampled version of the analog source. We first derive an expression for the mean squared error in the reconstruction of the process from a noisy and information rate-limited version of its samples. This expression is a function of the sampling frequency and the average number of bits describing each sample. It is given as the sum of two terms: minimum mean square error in estimating the source from its noisy but otherwise fully observed sub-Nyquist samples, and a second term obtained by reverse waterfilling over an average of spectral densities associated with the polyphase components of the source. We extend this result to multi-branch uniform sampling, where the samples are available through a set of parallel channels with a uniform sampler and a pre-sampling filter in each branch. Further optimization to reduce distortion is then performed over the pre-sampling filters, and an optimal set of pre-sampling filters associated with the statistics of the input signal and the sampling frequency is found. This results in an expression for the minimal possible distortion achievable under any analog-to-digital conversion scheme involving uniform sampling and linear filtering. These results thus unify the Shannon–Whittaker–Kotelnikov sampling theorem and Shannon rate-distortion theory for Gaussian sources.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"15 1","pages":"401-429"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75209497","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}

引用次数: 55

ℓp-Regularized Least Squares (0 p正则化最小二乘(0

IEEE Trans. Inf. Theory Pub Date : 2016-01-01 DOI: 10.1109/TIT.2015.2501362

Masahiro Yukawa, S. Amari

{"title":"ℓp-Regularized Least Squares (0","authors":"Masahiro Yukawa, S. Amari","doi":"10.1109/TIT.2015.2501362","DOIUrl":"https://doi.org/10.1109/TIT.2015.2501362","url":null,"abstract":"This paper elucidates the underlying structures of ℓp-regularized least squares problems in the nonconvex case of 0 <; p <; 1. The difference between two formulations is highlighted (which does not occur in the convex case of p = 1): 1) an ℓp-constrained optimization (Pcp) and 2) an ℓp-penalized (unconstrained) optimization (Lλp). It is shown that the solution path of (Lλp) is discontinuous and also a part of the solution path of (Pcp). As an alternative to the solution path, a critical path is considered, which is a maximal continuous curve consisting of critical points. Critical paths are piecewise smooth, as can be seen from the viewpoint of the variational method, and generally contain non-optimal points, such as saddle points and local maxima as well as global/local minima. Our study reveals multiplicity (non-monotonicity) in the correspondence between the regularization parameters of (Pcp) and (Lλp ). Two particular paths of critical points connecting the origin and an ordinary least squares (OLS) solution are studied further. One is a main path starting at an OLS solution, and the other is a greedy path starting at the origin. Part of the greedy path can be constructed with a generalized Minkowskian gradient. This paper of greedy path leads to a nontrivial close-link between the optimization problem of ℓp-regularized least squares and the greedy method of orthogonal matching pursuit.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"186 1","pages":"488-502"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88441933","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}

引用次数: 17

Secure Degrees of Freedom for the MIMO Wire-Tap Channel With a Multi-Antenna Cooperative Jammer 带多天线协同干扰器的MIMO线接信道的安全自由度

IEEE Trans. Inf. Theory Pub Date : 2015-12-22 DOI: 10.1109/TIT.2017.2738011

Mohamed S. Nafea, A. Yener

{"title":"Secure Degrees of Freedom for the MIMO Wire-Tap Channel With a Multi-Antenna Cooperative Jammer","authors":"Mohamed S. Nafea, A. Yener","doi":"10.1109/TIT.2017.2738011","DOIUrl":"https://doi.org/10.1109/TIT.2017.2738011","url":null,"abstract":"In this paper, a multiple antenna wire-tap channel in the presence of a multi-antenna cooperative jammer is studied. In particular, the secure degrees of freedom (s.d.o.f.) of this channel is established, with $N_t$ antennas at the transmitter, $N_r$ antennas at the legitimate receiver, and $N_e$ antennas at the eavesdropper, for all possible values of the number of antennas, $N_c$, at the cooperative jammer. In establishing the result, several different ranges of $N_c$ need to be considered separately. The lower and upper bounds for these ranges of $N_c$ are derived, and are shown to be tight. The achievability techniques developed rely on a variety of signaling, beamforming, and alignment techniques which vary according to the (relative) number of antennas at each terminal and whether the s.d.o.f. is integer valued. Specifically, it is shown that, whenever the s.d.o.f. is integer valued, Gaussian signaling for both transmission and cooperative jamming, linear precoding at the transmitter and the cooperative jammer, and linear processing at the legitimate receiver, are sufficient for achieving the s.d.o.f. of the channel. By contrast, when the s.d.o.f. is not an integer, the achievable schemes need to rely on structured signaling at the transmitter and the cooperative jammer, and joint signal space and signal scale alignment. The converse is established by combining an upper bound which allows for full cooperation between the transmitter and the cooperative jammer, with another upper bound which exploits the secrecy and reliability constraints.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"10 1","pages":"7420-7441"},"PeriodicalIF":0.0,"publicationDate":"2015-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90191032","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}

引用次数: 24

Wireless Multihop Device-to-Device Caching Networks 无线多跳设备到设备缓存网络

IEEE Trans. Inf. Theory Pub Date : 2015-11-09 DOI: 10.1109/ICC.2015.7249398

Sang-Woon Jeon, Songnam Hong, Mingyue Ji, G. Caire, A. Molisch

{"title":"Wireless Multihop Device-to-Device Caching Networks","authors":"Sang-Woon Jeon, Songnam Hong, Mingyue Ji, G. Caire, A. Molisch","doi":"10.1109/ICC.2015.7249398","DOIUrl":"https://doi.org/10.1109/ICC.2015.7249398","url":null,"abstract":"We consider a wireless device-to-device network, where $n$ nodes are uniformly distributed at random over the network area. We let each node caches $M$ files from a library of size $mgeq M$ . Each node in the network requests a file from the library independently at random, according to a popularity distribution, and is served by other nodes having the requested file in their local cache via (possibly) multihop transmissions. Under the classical “protocol model” of wireless networks, we characterize the optimal per-node capacity scaling law for a broad class of heavy-tailed popularity distributions, including Zipf distributions with exponent less than one. In the parameter regime of interest, i.e., $m=o(nM)$ , we show that a decentralized random caching strategy with uniform probability over the library yields the optimal per-node capacity scaling of $Theta (sqrt {M/m})$ for heavy-tailed popularity distributions. This scaling is constant with $n$ , thus yielding throughput scalability with the network size. Furthermore, the multihop capacity scaling can be significantly better than for the case of single-hop caching networks, for which the per-node capacity is $Theta (M/m)$ . The multihop capacity scaling law can be further improved for a Zipf distribution with exponent larger than some threshold > 1, by using a decentralized random caching uniformly across a subset of most popular files in the library. Namely, ignoring a subset of less popular files (i.e., effectively reducing the size of the library) can significantly improve the throughput scaling while guaranteeing that all nodes will be served with high probability as $n$ increases.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"14 1","pages":"1662-1676"},"PeriodicalIF":0.0,"publicationDate":"2015-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78323176","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}

引用次数: 41

Delay Optimal Buffered Decode-and-Forward for Two-Hop Networks With Random Link Connectivity 具有随机链路连接的两跳网络的延迟最优缓冲译码转发

IEEE Trans. Inf. Theory Pub Date : 2015-01-01 DOI: 10.1109/TIT.2014.2372014

Ying Cui, V. Lau, E. Yeh

{"title":"Delay Optimal Buffered Decode-and-Forward for Two-Hop Networks With Random Link Connectivity","authors":"Ying Cui, V. Lau, E. Yeh","doi":"10.1109/TIT.2014.2372014","DOIUrl":"https://doi.org/10.1109/TIT.2014.2372014","url":null,"abstract":"Delay optimal control of multi-hop networks remains a challenging problem even in the simplest scenarios. In this paper, we consider delay optimal control of a two-hop half-duplex network with independent identically distributed ON-OFF fading. Both the source node and the relay node are equipped with infinite buffers and have exogenous bit arrivals. We focus on delay optimal link selection to minimize the average sum queue length over a finite horizon subject to a half-duplex constraint. To solve the problem, we introduce a new approach, whereby an actual discrete time system (ADTS) is approximated using a virtual continuous time system (VCTS). We obtain an asymptotically delay optimal policy in the VCTS. Using the relationship between the VCTS and the ADTS, we obtain an asymptotically delay optimal policy in the ADTS. The obtained policy has both a priority feature and a safety stock feature. It offers good design insights for wireless relay networks. In addition, the obtained policy has a closed-form expression, does not require knowledge of arrival statistics, and can be implemented online. Finally, using renewal theory and the theory of random walks, we analyze the average delay resulting from the asymptotically delay optimal policy.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"1 1","pages":"404-425"},"PeriodicalIF":0.0,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75744844","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}

引用次数: 2

Performance Guarantees for Adaptive Estimation of Sparse Signals 稀疏信号自适应估计的性能保证

IEEE Trans. Inf. Theory Pub Date : 2013-11-25 DOI: 10.1109/TIT.2015.2403302

Dennis L. Wei, A. Hero

{"title":"Performance Guarantees for Adaptive Estimation of Sparse Signals","authors":"Dennis L. Wei, A. Hero","doi":"10.1109/TIT.2015.2403302","DOIUrl":"https://doi.org/10.1109/TIT.2015.2403302","url":null,"abstract":"This paper studies adaptive sensing for estimating the nonzero amplitudes of a sparse signal with the aim of providing analytical guarantees on the performance gain due to adaptive resource allocation. We consider a previously proposed optimal two-stage policy for allocating sensing resources. For positive powers $q$ , we derive tight upper bounds on the mean $q$ th-power error resulting from the optimal two-stage policy and corresponding lower bounds on the improvement over nonadaptive uniform sensing. It is shown that the adaptation gain is related to the detectability of nonzero signal components as characterized by Chernoff coefficients, thus quantifying analytically the dependence on the sparsity level of the signal, the signal-to-noise ratio (SNR), and the sensing resource budget. For fixed sparsity levels and increasing SNR or sensing budget, we obtain the rate of convergence to oracle performance and the rate at which the fraction of resources spent on the first exploratory stage decreases to zero. For a vanishing fraction of nonzero components, the gain increases without bound as a function of SNR and sensing budget. Numerical simulations demonstrate that the bounds on adaptation gain are quite tight in nonasymptotic regimes as well.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"270 1","pages":"2043-2059"},"PeriodicalIF":0.0,"publicationDate":"2013-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72924956","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}

引用次数: 14

Polar Codes for $q$-Ary Channels, $q=2^{r}$ $q$-任意信道的极性码，$q=2^{r}$

IEEE Trans. Inf. Theory Pub Date : 2013-02-01 DOI: 10.1109/TIT.2012.2219035

Woomyoung Park, A. Barg

引用次数: 9