Pub Date : 2008-03-31DOI: 10.1109/NETCOD.2008.4476186
Zhen Zhang
In this talk, we summarize some of our recent works on network error correction coding theory. Our works mainly focus on issues related to the goal of pushing the theory of network error correction coding to applications. In (Zhen Zhang, 2006), we define the minimum distance of a linear network error correction code and prove that it plays the same role as it does in classical coding theory, we propose the concept of statistical decoding and develop a statistical algorithm for decoding packet network error correction codes. In (S. Yang et al.), we study the characterization of network error correction capabilities in the general case which includes nonlinear codes. In (H. Bali et al., 2007), we propose an improved upper bound for the failure probability of random network code and use it to analyze the performance of randomized network error correction codes. In (X. Yan et al.), we study the possibility of decoding network error correction codes beyond its error correction capability, and analyze the decoding complexity of statistical decoding algorithms. In (H. Bali and Z. Zhang), we propose some techniques for reducing overhead of network error correction coding. This is a key issue for pushing network error correction codes to applications. In (Zhen Zhang), we propose a hybrid network error correction coding systems combining both the network error correction codes in the space domain and the classical error correction codes in the time domain and analyze its performance.
在这次演讲中，我们总结了我们最近在网络纠错编码理论方面的一些工作。我们的工作主要集中在将网络纠错编码理论推向应用的相关问题上。在(Zhen Zhang, 2006)中，我们定义了线性网络纠错码的最小距离，并证明了其在经典编码理论中的作用，我们提出了统计译码的概念，并开发了分组网络纠错码译码的统计算法。在(S. Yang等)中，我们研究了包含非线性码的一般情况下网络纠错能力的表征。在(H. Bali et al.， 2007)中，我们提出了一个改进的随机网络码失效概率上界，并用它来分析随机网络纠错码的性能。在(X. Yan等)中，我们研究了网络纠错码超出其纠错能力的译码可能性，并分析了统计译码算法的译码复杂度。在(H. Bali和Z. Zhang)中，我们提出了一些减少网络纠错编码开销的技术。这是向应用程序推送网络纠错码的关键问题。在张震(Zhen Zhang)中，我们提出了一种将空间域的网络纠错码与时域的经典纠错码相结合的混合网络纠错编码系统，并对其性能进行了分析。
{"title":"Some Recent Progresses in Network Error Correction Coding Theory","authors":"Zhen Zhang","doi":"10.1109/NETCOD.2008.4476186","DOIUrl":"https://doi.org/10.1109/NETCOD.2008.4476186","url":null,"abstract":"In this talk, we summarize some of our recent works on network error correction coding theory. Our works mainly focus on issues related to the goal of pushing the theory of network error correction coding to applications. In (Zhen Zhang, 2006), we define the minimum distance of a linear network error correction code and prove that it plays the same role as it does in classical coding theory, we propose the concept of statistical decoding and develop a statistical algorithm for decoding packet network error correction codes. In (S. Yang et al.), we study the characterization of network error correction capabilities in the general case which includes nonlinear codes. In (H. Bali et al., 2007), we propose an improved upper bound for the failure probability of random network code and use it to analyze the performance of randomized network error correction codes. In (X. Yan et al.), we study the possibility of decoding network error correction codes beyond its error correction capability, and analyze the decoding complexity of statistical decoding algorithms. In (H. Bali and Z. Zhang), we propose some techniques for reducing overhead of network error correction coding. This is a key issue for pushing network error correction codes to applications. In (Zhen Zhang), we propose a hybrid network error correction coding systems combining both the network error correction codes in the space domain and the classical error correction codes in the time domain and analyze its performance.","PeriodicalId":186056,"journal":{"name":"2008 Fourth Workshop on Network Coding, Theory and Applications","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114890524","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 : 2008-03-31DOI: 10.1109/NETCOD.2008.4476183
L. Keller, Eleni Drinea, C. Fragouli
Consider a source broadcasting M packets to N receivers over independent erasure channels, where perfect feedback is available from the receivers to the source, and the source is allowed to use coding. We investigate offline and online algorithms that optimize delay, both through theoretical analysis as well as simulation results.
{"title":"Online Broadcasting with Network Coding","authors":"L. Keller, Eleni Drinea, C. Fragouli","doi":"10.1109/NETCOD.2008.4476183","DOIUrl":"https://doi.org/10.1109/NETCOD.2008.4476183","url":null,"abstract":"Consider a source broadcasting M packets to N receivers over independent erasure channels, where perfect feedback is available from the receivers to the source, and the source is allowed to use coding. We investigate offline and online algorithms that optimize delay, both through theoretical analysis as well as simulation results.","PeriodicalId":186056,"journal":{"name":"2008 Fourth Workshop on Network Coding, Theory and Applications","volume":"258 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132126863","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 : 2008-03-31DOI: 10.1109/NETCOD.2008.4476170
H. Bahramgiri, F. Lahouti
We introduce algorithms to design robust network codes in the presence of link failures for multicast in a directed acyclic network. Robustness is achieved through diversity provided by the network links and flows, while the maximum multicast rate due to max-flow min-cut bound is maintained. The proposed scheme is a receiver-based robust network coding, which exploits the diversity due to the possible gap of the specific receivers min-cut with respect to the network multicast capacity. An improved version of this scheme guarantees multicast capacity for a certain level of failures. In a multicast session, failure of a flow may not necessarily reduce the capacity of the network as other useful branches within the network could still facilitate back up routes (flows) from the source to the sinks. We introduce a scheme to employ backup flows in addition to the main flows to multicast data at maximum rate h, when possible. In a limiting case, the scheme guarantees the rate h, for all link failure patterns, which do not decrease the maximum rate below h. Here, the number of link failures may in general exceed the refined singleton bound.
{"title":"Robust Network Coding Using Diversity through Backup Flows","authors":"H. Bahramgiri, F. Lahouti","doi":"10.1109/NETCOD.2008.4476170","DOIUrl":"https://doi.org/10.1109/NETCOD.2008.4476170","url":null,"abstract":"We introduce algorithms to design robust network codes in the presence of link failures for multicast in a directed acyclic network. Robustness is achieved through diversity provided by the network links and flows, while the maximum multicast rate due to max-flow min-cut bound is maintained. The proposed scheme is a receiver-based robust network coding, which exploits the diversity due to the possible gap of the specific receivers min-cut with respect to the network multicast capacity. An improved version of this scheme guarantees multicast capacity for a certain level of failures. In a multicast session, failure of a flow may not necessarily reduce the capacity of the network as other useful branches within the network could still facilitate back up routes (flows) from the source to the sinks. We introduce a scheme to employ backup flows in addition to the main flows to multicast data at maximum rate h, when possible. In a limiting case, the scheme guarantees the rate h, for all link failure patterns, which do not decrease the maximum rate below h. Here, the number of link failures may in general exceed the refined singleton bound.","PeriodicalId":186056,"journal":{"name":"2008 Fourth Workshop on Network Coding, Theory and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131153321","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 : 2008-03-31DOI: 10.1109/NETCOD.2008.4476180
K. Shum, C. Sung
The collision channel without feedback is a system with multiple source nodes and a single destination node, where coordination among the source nodes and feedback from the destination node are not available. Its capacity region was first derived by Massey and Mathys. We generalize their model by introducing multiple destination nodes and relay nodes. In this paper, we consider linear collision networks in which the nodes lie on a straight line. The two nodes at the ends want to exchange data through the relay nodes in the middle. An outer bound on achievable rates is derived. By using a simple network code, we can show that all points within the outer bound are indeed achievable, and thus obtain the capacity region.
{"title":"The Capacity Region of Two-way Collision Networks","authors":"K. Shum, C. Sung","doi":"10.1109/NETCOD.2008.4476180","DOIUrl":"https://doi.org/10.1109/NETCOD.2008.4476180","url":null,"abstract":"The collision channel without feedback is a system with multiple source nodes and a single destination node, where coordination among the source nodes and feedback from the destination node are not available. Its capacity region was first derived by Massey and Mathys. We generalize their model by introducing multiple destination nodes and relay nodes. In this paper, we consider linear collision networks in which the nodes lie on a straight line. The two nodes at the ends want to exchange data through the relay nodes in the middle. An outer bound on achievable rates is derived. By using a simple network code, we can show that all points within the outer bound are indeed achievable, and thus obtain the capacity region.","PeriodicalId":186056,"journal":{"name":"2008 Fourth Workshop on Network Coding, Theory and Applications","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124418124","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 : 2008-03-31DOI: 10.1109/NETCOD.2008.4476184
I. Grivell, A. Grant, T. Chan
The entropy space for n random variables has dimension 2n -1, one dimension for each joint entropy. When the random variables are known to satisfy given functional dependence relationships, the dimension may be smaller. In this paper, we identify a basis for the restriction of the entropy space to distributions satisfying functional dependence relations specified by an acyclic graph. We provide an efficient algorithm for determination of this basis. One application is a reduction in the computational effort required to compute the linear programming bound for multi-source network coding.
{"title":"Basic Entropy Sets","authors":"I. Grivell, A. Grant, T. Chan","doi":"10.1109/NETCOD.2008.4476184","DOIUrl":"https://doi.org/10.1109/NETCOD.2008.4476184","url":null,"abstract":"The entropy space for n random variables has dimension 2n -1, one dimension for each joint entropy. When the random variables are known to satisfy given functional dependence relationships, the dimension may be smaller. In this paper, we identify a basis for the restriction of the entropy space to distributions satisfying functional dependence relations specified by an acyclic graph. We provide an efficient algorithm for determination of this basis. One application is a reduction in the computational effort required to compute the linear programming bound for multi-source network coding.","PeriodicalId":186056,"journal":{"name":"2008 Fourth Workshop on Network Coding, Theory and Applications","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126709312","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 : 2008-03-31DOI: 10.1109/NETCOD.2008.4476188
L. Loyola, T. D. de Souza, J. Widmer, C. Fragouli
We consider the problem of finding the minimum number of transmissions in an ad-hoc network for all-to-all broadcasting using network coding. This work generalizes previous results for canonical topologies such as the circle and the wrap around grid to the finite-sized line, and non-wrap-around grid. The latter topologies better reflect network coding in random topologies, since the dissemination of information is "directional", in a sense that information usually arrives via the neighbors on the path to its originator instead of from all possible directions. We find that while the line topology requires a higher number of transmissions compared to the circle, this is interestingly not the case for the grid. We further present simulation results on a heuristic that estimates the required minimum number of transmissions in random wireless topologies and compare it to the optimum solution, as well as previously proposed heuristics.
{"title":"Network-Coded Broadcast: from Canonical Networks to Random Topologies","authors":"L. Loyola, T. D. de Souza, J. Widmer, C. Fragouli","doi":"10.1109/NETCOD.2008.4476188","DOIUrl":"https://doi.org/10.1109/NETCOD.2008.4476188","url":null,"abstract":"We consider the problem of finding the minimum number of transmissions in an ad-hoc network for all-to-all broadcasting using network coding. This work generalizes previous results for canonical topologies such as the circle and the wrap around grid to the finite-sized line, and non-wrap-around grid. The latter topologies better reflect network coding in random topologies, since the dissemination of information is \"directional\", in a sense that information usually arrives via the neighbors on the path to its originator instead of from all possible directions. We find that while the line topology requires a higher number of transmissions compared to the circle, this is interestingly not the case for the grid. We further present simulation results on a heuristic that estimates the required minimum number of transmissions in random wireless topologies and compare it to the optimum solution, as well as previously proposed heuristics.","PeriodicalId":186056,"journal":{"name":"2008 Fourth Workshop on Network Coding, Theory and Applications","volume":"243 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134304323","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 : 2008-03-31DOI: 10.1109/NETCOD.2008.4476179
S.-Y.R. Li, S. Ho
Convolutional network coding deals with the propagation of symbol streams through a network with a linear time-invariant encoder at every node. When the symbol alphabet is a field F, a symbol stream becomes a power series over F. Physical implementation requires the coding/decoding kernels be restricted to finite objects. A proper domain for convolutional network coding consists of rational power series rather than polynomials, because polynomial coding kernels do not necessarily correspond to polynomial decoding kernels when the network includes a cycle. One naturally wonders what algebraic structure makes rational power series a suitable domain for coding/decoding kernels. The proposed answer by this paper is discrete valuation ring (DVR). A general abstract theory of convolutional network coding is formulated over a generic DVR and does not confine convolutional network coding to the combined space-time domain. Abstract generality enhances mathematical elegance, depth of understanding, and adaptability to practical applications. Optimal convolutional network codes at various levels of strength are introduced and constructed for delivering highest possible data rates.
{"title":"Ring-theoretic foundation of convolutional network coding","authors":"S.-Y.R. Li, S. Ho","doi":"10.1109/NETCOD.2008.4476179","DOIUrl":"https://doi.org/10.1109/NETCOD.2008.4476179","url":null,"abstract":"Convolutional network coding deals with the propagation of symbol streams through a network with a linear time-invariant encoder at every node. When the symbol alphabet is a field F, a symbol stream becomes a power series over F. Physical implementation requires the coding/decoding kernels be restricted to finite objects. A proper domain for convolutional network coding consists of rational power series rather than polynomials, because polynomial coding kernels do not necessarily correspond to polynomial decoding kernels when the network includes a cycle. One naturally wonders what algebraic structure makes rational power series a suitable domain for coding/decoding kernels. The proposed answer by this paper is discrete valuation ring (DVR). A general abstract theory of convolutional network coding is formulated over a generic DVR and does not confine convolutional network coding to the combined space-time domain. Abstract generality enhances mathematical elegance, depth of understanding, and adaptability to practical applications. Optimal convolutional network codes at various levels of strength are introduced and constructed for delivering highest possible data rates.","PeriodicalId":186056,"journal":{"name":"2008 Fourth Workshop on Network Coding, Theory and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131360587","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 : 2008-03-31DOI: 10.1109/NETCOD.2008.4476176
Ling Lv, Hongyi Yu, Jianzu Yang
In multi-hop wireless networks, network coding can take advantage of the bi-directional traffic flows to increase the achievable throughput. To combat fading in wireless channel, cooperative diversity is integrated into the network-coding schemes. In this paper, we propose an opportunistic cooperative network-coding scheme based on space-time coding (OCNC), which combats channel fading and improves resource efficiency and network throughput. Focusing on the bi-directional traffic flows in wireless cooperative relaying networks, we develop and analyze the outage probabilities and the network-coding gain of different bi-directional relaying schemes. The numerical results show that in contrast to traditional scheme both full diversity (i.e. K-order diversity in case of K relay nodes) and asymptotical 4/3 times of network-coding gain are achieved by OCNC. In addition, because of opportunistic relaying of multiple nodes, the network-coding gain is more considerable in the low and middle SNR regimes.
{"title":"Opportunistic Cooperative Network-Coding Based on Space-Time Coding for Bi-Directional Traffic Flows","authors":"Ling Lv, Hongyi Yu, Jianzu Yang","doi":"10.1109/NETCOD.2008.4476176","DOIUrl":"https://doi.org/10.1109/NETCOD.2008.4476176","url":null,"abstract":"In multi-hop wireless networks, network coding can take advantage of the bi-directional traffic flows to increase the achievable throughput. To combat fading in wireless channel, cooperative diversity is integrated into the network-coding schemes. In this paper, we propose an opportunistic cooperative network-coding scheme based on space-time coding (OCNC), which combats channel fading and improves resource efficiency and network throughput. Focusing on the bi-directional traffic flows in wireless cooperative relaying networks, we develop and analyze the outage probabilities and the network-coding gain of different bi-directional relaying schemes. The numerical results show that in contrast to traditional scheme both full diversity (i.e. K-order diversity in case of K relay nodes) and asymptotical 4/3 times of network-coding gain are achieved by OCNC. In addition, because of opportunistic relaying of multiple nodes, the network-coding gain is more considerable in the low and middle SNR regimes.","PeriodicalId":186056,"journal":{"name":"2008 Fourth Workshop on Network Coding, Theory and Applications","volume":"83 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126625431","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 : 2008-03-31DOI: 10.1109/NETCOD.2008.4476168
Junghyun Kim, Seon-Yeong Park, Ju Young Kim, Young-Joon Kim, Hong‐Yeop Song
We propose a joint low-density parity-check (LDPC) code scheme for multi-user relay channel. Joint LDPC codes guarantee high level of performance and achieved service quality. In this paper, we describe how to apply proposed model to relay channel and analyze a method of optimization. Additionally, we show how efficient joint LDPC code scheme using intelligent relay is in wireless ad-hoc networks.
{"title":"Joint LDPC Codes for Multi-User Relay Channel","authors":"Junghyun Kim, Seon-Yeong Park, Ju Young Kim, Young-Joon Kim, Hong‐Yeop Song","doi":"10.1109/NETCOD.2008.4476168","DOIUrl":"https://doi.org/10.1109/NETCOD.2008.4476168","url":null,"abstract":"We propose a joint low-density parity-check (LDPC) code scheme for multi-user relay channel. Joint LDPC codes guarantee high level of performance and achieved service quality. In this paper, we describe how to apply proposed model to relay channel and analyze a method of optimization. Additionally, we show how efficient joint LDPC code scheme using intelligent relay is in wireless ad-hoc networks.","PeriodicalId":186056,"journal":{"name":"2008 Fourth Workshop on Network Coding, Theory and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124904229","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 : 2008-03-31DOI: 10.1109/NETCOD.2008.4476190
Shutao Xia
Very recently, an operator channel was defined by Koetter and Kschischang when they studied random network coding. They also introduced constant dimension codes and demonstrated that these codes can be employed to correct errors and/or erasures over the operator channel. In this paper, a Graham-Sloane type construction of constant dimension codes is presented. It is shown that the construction for the case of minimum dimension distance 4 exceeds the Gilbert type lower bound for constant dimension codes.
{"title":"A Graham-Sloane Type Construction of Constant Dimension Codes","authors":"Shutao Xia","doi":"10.1109/NETCOD.2008.4476190","DOIUrl":"https://doi.org/10.1109/NETCOD.2008.4476190","url":null,"abstract":"Very recently, an operator channel was defined by Koetter and Kschischang when they studied random network coding. They also introduced constant dimension codes and demonstrated that these codes can be employed to correct errors and/or erasures over the operator channel. In this paper, a Graham-Sloane type construction of constant dimension codes is presented. It is shown that the construction for the case of minimum dimension distance 4 exceeds the Gilbert type lower bound for constant dimension codes.","PeriodicalId":186056,"journal":{"name":"2008 Fourth Workshop on Network Coding, Theory and Applications","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115443638","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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