Pub Date : 2020-09-21DOI: 10.1109/TIT.2020.3015638
Hamdi Joudeh, B. Clerckx
In [1] , reference [26] was incorrect. Reference [26] should be as follows: E. Piovano and B. Clerckx, “Optimal DoF region of the K-user MISO BC with partial CSIT,” IEEE Commun. Lett ., vol. 21, no. 11, pp. 2368–2371, Nov. 2017.
{"title":"Corrections to \"On the Separability of Parallel MISO Broadcast Channels Under Partial CSIT: A Degrees of Freedom Region Perspective\"","authors":"Hamdi Joudeh, B. Clerckx","doi":"10.1109/TIT.2020.3015638","DOIUrl":"https://doi.org/10.1109/TIT.2020.3015638","url":null,"abstract":"In [1] , reference [26] was incorrect. Reference [26] should be as follows: E. Piovano and B. Clerckx, “Optimal DoF region of the K-user MISO BC with partial CSIT,” IEEE Commun. Lett ., vol. 21, no. 11, pp. 2368–2371, Nov. 2017.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"29 1","pages":"6605"},"PeriodicalIF":0.0,"publicationDate":"2020-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88561488","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 : 2017-04-01DOI: 10.1109/TIT.2017.2671410
Ramprasad Saptharishi, Amir Shpilka, Ben lee Volk
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.
{"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}
Pub Date : 2016-02-20DOI: 10.1109/TIT.2016.2573312
Junhong Lin, Song Li
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
本文通过$0
{"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}
Pub Date : 2016-01-01DOI: 10.1109/TIT.2015.2485271
A. Kipnis, A. Goldsmith, Yonina C. Eldar, T. Weissman
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.
{"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}
Pub Date : 2016-01-01DOI: 10.1109/TIT.2015.2501362
Masahiro Yukawa, S. Amari
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.
本文讨论了$ well _{p}$ -正则化最小二乘问题在$0非凸情况下的基本结构。突出显示了两个公式之间的区别(这在$p=1$的凸情况下不会出现):1)$ well _{p}$约束优化($mathcal {p} _{c}^{p}$)和2)$ well _{p}$惩罚(无约束)优化$ (mathcal {L}_{lambda}^{p})$。证明了$ (mathcal {L}_{lambda}^{p})$的解路径是不连续的，也是$mathcal {p} _{c}^{p}$的解路径的一部分。作为解路径的备选，我们考虑了一条关键路径，它是由临界点组成的最大连续曲线。从变分方法的角度来看，关键路径是分段光滑的，通常包含非最优点，如鞍点和局部最大值以及全局/局部最小值。我们的研究揭示了$ (mathcal {P}_{c}^{P})$和$ (mathcal {L}_{lambda}^{P})$正则化参数之间对应关系的多重性(非单调性)。进一步研究了连接原点的两个临界点的特殊路径和一个普通最小二乘解。一条是从OLS解开始的主路径，另一条是从原点开始的贪心路径。部分贪心路径可以用广义闵可夫斯基梯度来构造。本文的贪心路径将正则化最小二乘优化问题与正交匹配寻优的贪心方法联系在了一起。
{"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 ℓ<sub>p</sub>-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 ℓ<sub>p</sub>-constrained optimization (P<sub>c</sub><sup>p</sup>) and 2) an ℓ<sub>p</sub>-penalized (unconstrained) optimization (L<sub>λ</sub><sup>p</sup>). It is shown that the solution path of (L<sub>λ</sub><sup>p</sup>) is discontinuous and also a part of the solution path of (P<sub>c</sub><sup>p</sup>). 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 (P<sub>c</sub><sup>p</sup>) and (L<sub>λ</sub><sup>p</sup> ). 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 ℓ<sub>p</sub>-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}
Pub Date : 2015-12-22DOI: 10.1109/TIT.2017.2738011
Mohamed S. Nafea, A. Yener
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.
{"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}
Pub Date : 2015-11-09DOI: 10.1109/ICC.2015.7249398
Sang-Woon Jeon, Songnam Hong, Mingyue Ji, G. Caire, A. Molisch
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.
{"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}
Pub Date : 2015-01-01DOI: 10.1109/TIT.2014.2372014
Ying Cui, V. Lau, E. Yeh
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.
{"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}
Pub Date : 2013-11-25DOI: 10.1109/TIT.2015.2403302
Dennis L. Wei, A. Hero
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.
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Pub Date : 2013-02-01DOI: 10.1109/TIT.2012.2219035
Woomyoung Park, A. Barg
We study polarization for nonbinary channels with input alphabet of size q=2r, r=2,3,.... Using Arikan's polarizing kernel H2, we prove that the virtual channels that arise in the process of channel evolution converge to q-ary channels with capacity 0,1,2,..., r bits. As a result of this analysis, we show that polar codes support reliable transmission over discrete memoryless channels with q-ary input for all rates below the symmetric capacity of the channel. This leads to an explicit transmission scheme for q-ary channels. The block error probability of decoding using successive cancellation behaves as exp(-Nα), where N is the code length and α is any constant less than 0.5.
{"title":"Polar Codes for $q$-Ary Channels, $q=2^{r}$","authors":"Woomyoung Park, A. Barg","doi":"10.1109/TIT.2012.2219035","DOIUrl":"https://doi.org/10.1109/TIT.2012.2219035","url":null,"abstract":"We study polarization for nonbinary channels with input alphabet of size q=2r, r=2,3,.... Using Arikan's polarizing kernel H2, we prove that the virtual channels that arise in the process of channel evolution converge to q-ary channels with capacity 0,1,2,..., r bits. As a result of this analysis, we show that polar codes support reliable transmission over discrete memoryless channels with q-ary input for all rates below the symmetric capacity of the channel. This leads to an explicit transmission scheme for q-ary channels. The block error probability of decoding using successive cancellation behaves as exp(-Nα), where N is the code length and α is any constant less than 0.5.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"16 1","pages":"955-969"},"PeriodicalIF":0.0,"publicationDate":"2013-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73698643","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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