Pub Date : 2015-06-14DOI: 10.1109/ISIT.2015.7282440
Yu Zhang, Zhaoyang Zhang, L. Ping, Xiaoming Chen, C. Zhong
This paper studies the capacity scaling law of the multi-pair relay network with K source-destination pairs and M relays, where each node is equipped with a single antenna and works in half duplex mode. With the conventional two-slot relaying, the capacity was found to scale as K/2 log (M)+O(1) for fixed K and M → ∞. This paper shows that the capacity scaling law can be further improved to K log (M)+O(1) with successive relaying, as if the relays were full duplex. This scaling law can be achieved by a distributed coherent amplify-and-forward scheme, which only requires local channel state information (CSI) at each relay and statistical CSI at the sources and destinations.
{"title":"Capacity scaling of relay networks with successive relaying","authors":"Yu Zhang, Zhaoyang Zhang, L. Ping, Xiaoming Chen, C. Zhong","doi":"10.1109/ISIT.2015.7282440","DOIUrl":"https://doi.org/10.1109/ISIT.2015.7282440","url":null,"abstract":"This paper studies the capacity scaling law of the multi-pair relay network with K source-destination pairs and M relays, where each node is equipped with a single antenna and works in half duplex mode. With the conventional two-slot relaying, the capacity was found to scale as K/2 log (M)+O(1) for fixed K and M → ∞. This paper shows that the capacity scaling law can be further improved to K log (M)+O(1) with successive relaying, as if the relays were full duplex. This scaling law can be achieved by a distributed coherent amplify-and-forward scheme, which only requires local channel state information (CSI) at each relay and statistical CSI at the sources and destinations.","PeriodicalId":272313,"journal":{"name":"2015 IEEE International Symposium on Information Theory (ISIT)","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115207109","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 : 2015-06-14DOI: 10.1109/ISIT.2015.7282804
Ayush Jain, R. Bansal
We use the machinery developed by Wyner [1], for the sources satisfying Markov condition, to obtain an upper bound on the contribution of pointer bits to the compression ratio for fixed database Lempel-Ziv (FDLZ) algorithm to be H + O(1/ log2n) which is an improvement from the previous bound of H + H(1 + o(1))log2 log2n/ log2n . We use the definition of compression ratio as in Yang and Kieffer [2]. Here H is the entropy rate of the source and n is the size of the database. Then using the same definition of compression ratio we obtain an upper bound on the contribution of phrase length bits for the variant of FDLZ suggested in [3] to be O(1/ log2n), which gives an upper bound of O(1/ log2n) on the redundancy rate itself for this version of FDLZ.
{"title":"On redundancy rate of FDLZ algorithm and its variants","authors":"Ayush Jain, R. Bansal","doi":"10.1109/ISIT.2015.7282804","DOIUrl":"https://doi.org/10.1109/ISIT.2015.7282804","url":null,"abstract":"We use the machinery developed by Wyner [1], for the sources satisfying Markov condition, to obtain an upper bound on the contribution of pointer bits to the compression ratio for fixed database Lempel-Ziv (FDLZ) algorithm to be H + O(1/ log2n) which is an improvement from the previous bound of H + H(1 + o(1))log2 log2n/ log2n . We use the definition of compression ratio as in Yang and Kieffer [2]. Here H is the entropy rate of the source and n is the size of the database. Then using the same definition of compression ratio we obtain an upper bound on the contribution of phrase length bits for the variant of FDLZ suggested in [3] to be O(1/ log2n), which gives an upper bound of O(1/ log2n) on the redundancy rate itself for this version of FDLZ.","PeriodicalId":272313,"journal":{"name":"2015 IEEE International Symposium on Information Theory (ISIT)","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124261736","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 : 2015-06-14DOI: 10.1109/ISIT.2015.7282618
Yao-Shian Wang, M. Varanasi
We establish the degrees of freedom (DoF) region for the multiple-input multiple-output (MIMO) two-transmit, two-receive network which has an arbitrary number of antennas at each of its four terminals. General message sets are considered, from which all possible communication scenarios based on two-transmit, two-receive network can be regarded as special cases. An outer bound is given first and then it is shown to be tight. In particular, we propose a linear precoding scheme that can achieve all the DoF tuples in the region. Time extension and asymmetric complex signaling are utilized when necessary. The scheme works for both constant channel as well as time/frequency varying channel scenarios. From our general result, one can obtain the degrees of freedom region and the corresponding DoF-optimal precoding scheme for the two-transmit, two-receive network with any subset of all possible messages. Some of these DoF regions have been found before, but many are new. Our work sheds light on the optimal message sets design that could take the most advantage of channel resources in a flexible and efficient manner.
{"title":"Degrees of freedom region of the MIMO two-transmit, two-receive network with General message sets","authors":"Yao-Shian Wang, M. Varanasi","doi":"10.1109/ISIT.2015.7282618","DOIUrl":"https://doi.org/10.1109/ISIT.2015.7282618","url":null,"abstract":"We establish the degrees of freedom (DoF) region for the multiple-input multiple-output (MIMO) two-transmit, two-receive network which has an arbitrary number of antennas at each of its four terminals. General message sets are considered, from which all possible communication scenarios based on two-transmit, two-receive network can be regarded as special cases. An outer bound is given first and then it is shown to be tight. In particular, we propose a linear precoding scheme that can achieve all the DoF tuples in the region. Time extension and asymmetric complex signaling are utilized when necessary. The scheme works for both constant channel as well as time/frequency varying channel scenarios. From our general result, one can obtain the degrees of freedom region and the corresponding DoF-optimal precoding scheme for the two-transmit, two-receive network with any subset of all possible messages. Some of these DoF regions have been found before, but many are new. Our work sheds light on the optimal message sets design that could take the most advantage of channel resources in a flexible and efficient manner.","PeriodicalId":272313,"journal":{"name":"2015 IEEE International Symposium on Information Theory (ISIT)","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114730895","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 : 2015-06-14DOI: 10.1109/ISIT.2015.7282936
Jaemin Han, Chih-Chun Wang
This work considers the fully-connected 3-node packet erasure network: For each time slot, with some probabilities a packet sent by any node i may be received by both of the other nodes j and k; received only by node j (or node k); or received by neither nodes. Interference is avoided by enforcing that at most one node can transmit in each time slot. We assume that node i can always reach node j, possibly with the help of the third node k, for any i ≠ j pairs (thus the term fully-connected). One example of this model is any Wi-Fi network with 3 nodes within the hearing range of each other. We consider the most general traffic demands. Namely, there are six private-information flows with rates (R1→2,R1→3,R2→1, R2→3,R3→1,R3→2), respectively, and three common-information flows with rates (R1→23,R2→31,R3→12), respectively. We characterize the 9-dimensional Shannon capacity region within a gap that is inversely proportional to the packet size (bits). The gap can be attributed to exchanging reception status (ACK) and can be further reduced to 0 if we allow ACK to be transmitted via a separate control channel. For normal-sized packets, say 12000 bits, our results have thus effectively characterized the capacity region. Technical contributions of this work include a new converse for many-to-many network communications and a new capacity-approaching simple linear network coding scheme.
{"title":"General capacity region for the fully-connected 3-node packet erasure network","authors":"Jaemin Han, Chih-Chun Wang","doi":"10.1109/ISIT.2015.7282936","DOIUrl":"https://doi.org/10.1109/ISIT.2015.7282936","url":null,"abstract":"This work considers the fully-connected 3-node packet erasure network: For each time slot, with some probabilities a packet sent by any node i may be received by both of the other nodes j and k; received only by node j (or node k); or received by neither nodes. Interference is avoided by enforcing that at most one node can transmit in each time slot. We assume that node i can always reach node j, possibly with the help of the third node k, for any i ≠ j pairs (thus the term fully-connected). One example of this model is any Wi-Fi network with 3 nodes within the hearing range of each other. We consider the most general traffic demands. Namely, there are six private-information flows with rates (R<sub>1→2</sub>,R<sub>1→3</sub>,R<sub>2→1</sub>, R<sub>2→3</sub>,R<sub>3→1</sub>,R<sub>3→2</sub>), respectively, and three common-information flows with rates (R<sub>1→23</sub>,R<sub>2→31</sub>,R<sub>3→12</sub>), respectively. We characterize the 9-dimensional Shannon capacity region within a gap that is inversely proportional to the packet size (bits). The gap can be attributed to exchanging reception status (ACK) and can be further reduced to 0 if we allow ACK to be transmitted via a separate control channel. For normal-sized packets, say 12000 bits, our results have thus effectively characterized the capacity region. Technical contributions of this work include a new converse for many-to-many network communications and a new capacity-approaching simple linear network coding scheme.","PeriodicalId":272313,"journal":{"name":"2015 IEEE International Symposium on Information Theory (ISIT)","volume":"266 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116396894","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 : 2015-06-14DOI: 10.1109/ISIT.2015.7282756
Po-Ning Chen, Hsuan-Yin Lin, S. M. Moser
The exact value of the average error probability of an arbitrary code (linear or nonlinear) using maximum likelihood decoding is studied on binary erasure channels (BECs) with arbitrary erasure probability 0 <; δ <; 1. The family of the fair linear codes, which are equivalent to a concatenation of several Hadamard linear codes, is proven to perform better (in the sense of average error probability with respect to maximum-likelihood decoding) than all other linear codes for many values of the blocklength n and for a dimension k = 3. It is then noted that the family of fair linear codes and the family of fair nonlinear weak flip codes both maximize the minimum Hamming distance under certain blocklengths. However, the fair nonlinear weak flip codes actually outperform the fair linear codes, i.e., linearity and global optimality cannot be simultaneously achieved for the number of codewords being M = 23.
{"title":"Nonlinear codes outperform the best linear codes on the binary erasure channel","authors":"Po-Ning Chen, Hsuan-Yin Lin, S. M. Moser","doi":"10.1109/ISIT.2015.7282756","DOIUrl":"https://doi.org/10.1109/ISIT.2015.7282756","url":null,"abstract":"The exact value of the average error probability of an arbitrary code (linear or nonlinear) using maximum likelihood decoding is studied on binary erasure channels (BECs) with arbitrary erasure probability 0 <; δ <; 1. The family of the fair linear codes, which are equivalent to a concatenation of several Hadamard linear codes, is proven to perform better (in the sense of average error probability with respect to maximum-likelihood decoding) than all other linear codes for many values of the blocklength n and for a dimension k = 3. It is then noted that the family of fair linear codes and the family of fair nonlinear weak flip codes both maximize the minimum Hamming distance under certain blocklengths. However, the fair nonlinear weak flip codes actually outperform the fair linear codes, i.e., linearity and global optimality cannot be simultaneously achieved for the number of codewords being M = 23.","PeriodicalId":272313,"journal":{"name":"2015 IEEE International Symposium on Information Theory (ISIT)","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123452354","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 : 2015-06-14DOI: 10.1109/ISIT.2015.7282463
Huishuai Zhang, Yingbin Liang, L. Lai
The problem of when all terminals must talk to achieve the secrecy capacity in the multiterminal source model is investigated. Two conditions under which respectively a given terminal does not need to and must talk to achieve the secrecy capacity are characterized. The cases when all terminals must talk to achieve secrecy capacity are shown to be many more than those conjectured in [1] for systems with four or more terminals. There is a gap between the above two conditions, in which whether a given terminal need to talk is not clear. A conjecture is further made in order to narrow down the gap.
{"title":"Secret key capacity: Talk or keep silent?","authors":"Huishuai Zhang, Yingbin Liang, L. Lai","doi":"10.1109/ISIT.2015.7282463","DOIUrl":"https://doi.org/10.1109/ISIT.2015.7282463","url":null,"abstract":"The problem of when all terminals must talk to achieve the secrecy capacity in the multiterminal source model is investigated. Two conditions under which respectively a given terminal does not need to and must talk to achieve the secrecy capacity are characterized. The cases when all terminals must talk to achieve secrecy capacity are shown to be many more than those conjectured in [1] for systems with four or more terminals. There is a gap between the above two conditions, in which whether a given terminal need to talk is not clear. A conjecture is further made in order to narrow down the gap.","PeriodicalId":272313,"journal":{"name":"2015 IEEE International Symposium on Information Theory (ISIT)","volume":"84 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123978351","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 : 2015-06-14DOI: 10.1109/ISIT.2015.7282878
A. Hari, Urs Niesen, G. Wilfong
Packet networks need to maintain state in the form of forwarding tables at each switch. The cost of this state increases as networks support ever more sophisticated per-flow routing, traffic engineering, and service chaining. Per-flow or per-path state at the switches can be eliminated by encoding each packet's desired path in its header. A key component of such a method is an efficient encoding of paths through the network. We introduce a mathematical formulation of this optimal path-encoding problem. We prove that the problem is APX-hard, by showing that approximating it to within a factor less than 8/7 is NP-hard. Thus, at best we can hope for a constant-factor approximation algorithm. We then present such an algorithm, approximating the optimal path-encoding problem to within a factor 2. Finally, we provide empirical results illustrating the effectiveness of the proposed algorithm.
{"title":"Optimal path encoding for software-defined networks","authors":"A. Hari, Urs Niesen, G. Wilfong","doi":"10.1109/ISIT.2015.7282878","DOIUrl":"https://doi.org/10.1109/ISIT.2015.7282878","url":null,"abstract":"Packet networks need to maintain state in the form of forwarding tables at each switch. The cost of this state increases as networks support ever more sophisticated per-flow routing, traffic engineering, and service chaining. Per-flow or per-path state at the switches can be eliminated by encoding each packet's desired path in its header. A key component of such a method is an efficient encoding of paths through the network. We introduce a mathematical formulation of this optimal path-encoding problem. We prove that the problem is APX-hard, by showing that approximating it to within a factor less than 8/7 is NP-hard. Thus, at best we can hope for a constant-factor approximation algorithm. We then present such an algorithm, approximating the optimal path-encoding problem to within a factor 2. Finally, we provide empirical results illustrating the effectiveness of the proposed algorithm.","PeriodicalId":272313,"journal":{"name":"2015 IEEE International Symposium on Information Theory (ISIT)","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129393845","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 : 2015-06-14DOI: 10.1109/ISIT.2015.7282525
Bin Wang, Haibin Kan, K. Shum
Maximum distance separable (MDS) erasure codes are widely used in distributed storage systems (DSS) for better storage efficiency and protection against Byzantine attacks. In this paper, we aim at enhancing the error-correction capacity of DSS in a hostile network. Firstly, we apply Hermitian code in DSS and presented a special placing mode for the encoded symbols. A reconstruction algorithm in error-free network is given. Next we show that the burst-error-correcting algorithm by Ren can correct more errors than Reed-Solomon code. We proposed an erasure rollback strategy in decoding. The new reconstructing algorithm improves both the lower and upper bound of error-correcting capacity. It has better computing complexity than Reed-Solomon code with the same storage efficiency.
{"title":"Hermitian codes in distributed storage systems with optimal error-correcting capacity","authors":"Bin Wang, Haibin Kan, K. Shum","doi":"10.1109/ISIT.2015.7282525","DOIUrl":"https://doi.org/10.1109/ISIT.2015.7282525","url":null,"abstract":"Maximum distance separable (MDS) erasure codes are widely used in distributed storage systems (DSS) for better storage efficiency and protection against Byzantine attacks. In this paper, we aim at enhancing the error-correction capacity of DSS in a hostile network. Firstly, we apply Hermitian code in DSS and presented a special placing mode for the encoded symbols. A reconstruction algorithm in error-free network is given. Next we show that the burst-error-correcting algorithm by Ren can correct more errors than Reed-Solomon code. We proposed an erasure rollback strategy in decoding. The new reconstructing algorithm improves both the lower and upper bound of error-correcting capacity. It has better computing complexity than Reed-Solomon code with the same storage efficiency.","PeriodicalId":272313,"journal":{"name":"2015 IEEE International Symposium on Information Theory (ISIT)","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128357307","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 : 2015-06-14DOI: 10.1109/ISIT.2015.7282422
J. Scarlett, Alfonso Martinez, A. G. Fàbregas
This paper studies likelihood decoding for channel coding over discrete memoryless channels. It is shown that the likelihood decoder recovers the same random-coding error exponents as the maximum-likelihood decoder for i.i.d. and constant-composition random codes. The role of mismatch in likelihood decoding is studied, and the notion of the mismatched likelihood decoder capacity is introduced. It is shown, both in the case of random coding and optimized codebooks, that the mismatched likelihood decoder can lead to strictly worse achievable rates and error exponents compared to the corresponding mismatched maximum-metric decoder.
{"title":"The likelihood decoder: Error exponents and mismatch","authors":"J. Scarlett, Alfonso Martinez, A. G. Fàbregas","doi":"10.1109/ISIT.2015.7282422","DOIUrl":"https://doi.org/10.1109/ISIT.2015.7282422","url":null,"abstract":"This paper studies likelihood decoding for channel coding over discrete memoryless channels. It is shown that the likelihood decoder recovers the same random-coding error exponents as the maximum-likelihood decoder for i.i.d. and constant-composition random codes. The role of mismatch in likelihood decoding is studied, and the notion of the mismatched likelihood decoder capacity is introduced. It is shown, both in the case of random coding and optimized codebooks, that the mismatched likelihood decoder can lead to strictly worse achievable rates and error exponents compared to the corresponding mismatched maximum-metric decoder.","PeriodicalId":272313,"journal":{"name":"2015 IEEE International Symposium on Information Theory (ISIT)","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128472827","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 : 2015-06-14DOI: 10.1109/ISIT.2015.7282777
Sang-Woon Jeon, B. Jung
Function computation over wireless sensor networks is investigated, where K sensors measure their observations and a fusion center wishes to estimate a pre-defined function of the observations via fading multiple access channels (MACs). The arithmetic sum and type functions are considered since they yield various fundamental sample statistics such as mean, variance, maximum, minimum, etc. We propose a novel opportunistic in-network computation (INC) scheme in which a subset of sensors with large channel gains opportunistically participate in the transmission at each time slot, while all sensors in a network simultaneously send their observations or only a single sensor sends its observation in the conventional INC schemes. We analyze the ergodic computation rate of the proposed INC scheme and prove that it achieves a non-vanishing computation rate even when the number of sensors K tends to infinity, which provides a significant rate improvement compared to the conventional INC schemes whose computation rates converge to zero as K increases.
{"title":"Opportunistic in-network computation for wireless sensor networks","authors":"Sang-Woon Jeon, B. Jung","doi":"10.1109/ISIT.2015.7282777","DOIUrl":"https://doi.org/10.1109/ISIT.2015.7282777","url":null,"abstract":"Function computation over wireless sensor networks is investigated, where K sensors measure their observations and a fusion center wishes to estimate a pre-defined function of the observations via fading multiple access channels (MACs). The arithmetic sum and type functions are considered since they yield various fundamental sample statistics such as mean, variance, maximum, minimum, etc. We propose a novel opportunistic in-network computation (INC) scheme in which a subset of sensors with large channel gains opportunistically participate in the transmission at each time slot, while all sensors in a network simultaneously send their observations or only a single sensor sends its observation in the conventional INC schemes. We analyze the ergodic computation rate of the proposed INC scheme and prove that it achieves a non-vanishing computation rate even when the number of sensors K tends to infinity, which provides a significant rate improvement compared to the conventional INC schemes whose computation rates converge to zero as K increases.","PeriodicalId":272313,"journal":{"name":"2015 IEEE International Symposium on Information Theory (ISIT)","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128549519","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：