Pub Date : 2006-03-13DOI: 10.1109/ITW.2006.1633826
L. Tallini, S. Elmougy, B. Bose
In the ARQ (Automatic Retransmission Request) protocol, the sender keeps retransmitting a codeword until it receives a positive acknowledgment from the receiver sent through the feedback channel. This paper proposes Plain and Diversity Combining ARQ Hybrid protocol communication schemes suitable for the m(≥ 2)-ary asymmetric channel using t-Asymmetric Error Correcting/All Asymmetric Error Detecting (t-AEC/AAED) codes. The analysis shows that error correction definitely improves the throughput of the system compared to the ARQ protocol which uses only error detecting codes. The paper provides simple analytic expressions and bounds for the average number of retransmissions in both Plain and Diversity Combining t-AEC/AAED ARQ (t ≥ 0) protocol systems over the m-ary asymmetric channel, m ≥ 2. These can be applied into the design and analysis of error controlling schemes in practical systems such as VLSI and optical communications.
{"title":"On Hybrid ARQ Protocol schemes over the m(≥ 2)-ary Asymmetric Channel","authors":"L. Tallini, S. Elmougy, B. Bose","doi":"10.1109/ITW.2006.1633826","DOIUrl":"https://doi.org/10.1109/ITW.2006.1633826","url":null,"abstract":"In the ARQ (Automatic Retransmission Request) protocol, the sender keeps retransmitting a codeword until it receives a positive acknowledgment from the receiver sent through the feedback channel. This paper proposes Plain and Diversity Combining ARQ Hybrid protocol communication schemes suitable for the m(≥ 2)-ary asymmetric channel using t-Asymmetric Error Correcting/All Asymmetric Error Detecting (t-AEC/AAED) codes. The analysis shows that error correction definitely improves the throughput of the system compared to the ARQ protocol which uses only error detecting codes. The paper provides simple analytic expressions and bounds for the average number of retransmissions in both Plain and Diversity Combining t-AEC/AAED ARQ (t ≥ 0) protocol systems over the m-ary asymmetric channel, m ≥ 2. These can be applied into the design and analysis of error controlling schemes in practical systems such as VLSI and optical communications.","PeriodicalId":293144,"journal":{"name":"2006 IEEE Information Theory Workshop - ITW '06 Punta del Este","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132503227","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 : 2006-03-13DOI: 10.1109/ITW.2006.1633799
J. Wolf
In this paper we compare some aspects of the design and analysis of one-dimensional (1-D) and two-dimensional (2-D) storage systems. We show that for modulation codes and for the detection of signals corrupted by intersymbol interference and additive white Gaussian noise, the design and analysis is much more complicated in the 2-D case as compared with the 1-D case. However, we show that the reverse is true for the design of burst error correcting cyclic codes. That is, we show that one must carefully choose the generator polynomial to obtain a good 1-D burst error correcting code but using a cyclic product code, any arbitrary generator polynomials for the row code and for the column code can produce a good 2-D burst error correcting code.
{"title":"On Coding for 2-D Storage Systems","authors":"J. Wolf","doi":"10.1109/ITW.2006.1633799","DOIUrl":"https://doi.org/10.1109/ITW.2006.1633799","url":null,"abstract":"In this paper we compare some aspects of the design and analysis of one-dimensional (1-D) and two-dimensional (2-D) storage systems. We show that for modulation codes and for the detection of signals corrupted by intersymbol interference and additive white Gaussian noise, the design and analysis is much more complicated in the 2-D case as compared with the 1-D case. However, we show that the reverse is true for the design of burst error correcting cyclic codes. That is, we show that one must carefully choose the generator polynomial to obtain a good 1-D burst error correcting code but using a cyclic product code, any arbitrary generator polynomials for the row code and for the column code can produce a good 2-D burst error correcting code.","PeriodicalId":293144,"journal":{"name":"2006 IEEE Information Theory Workshop - ITW '06 Punta del Este","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129324155","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 : 2006-03-13DOI: 10.1109/ITW.2006.1633807
Hui Jin, T. Richardson
Density evolution for LDPC codes predicts asymptotic performance and serves as a practical design tool for designing top performing structures [1]. Many papers advocate the use of exit chart methods and other approximations, proclaiming that density evolution is computationally too intensive. In this paper we show that this is not the case: we present a highly efficient and accurate implementation of density evolution for LDPC codes.
{"title":"A New Fast Density Evolution","authors":"Hui Jin, T. Richardson","doi":"10.1109/ITW.2006.1633807","DOIUrl":"https://doi.org/10.1109/ITW.2006.1633807","url":null,"abstract":"Density evolution for LDPC codes predicts asymptotic performance and serves as a practical design tool for designing top performing structures [1]. Many papers advocate the use of exit chart methods and other approximations, proclaiming that density evolution is computationally too intensive. In this paper we show that this is not the case: we present a highly efficient and accurate implementation of density evolution for LDPC codes.","PeriodicalId":293144,"journal":{"name":"2006 IEEE Information Theory Workshop - ITW '06 Punta del Este","volume":"200 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123017292","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 : 2006-03-13DOI: 10.1109/ITW.2006.1633809
Chris T. K. Ng, I. Marić, A. Goldsmith, S. Shamai, R. Yates
We compare the rates of one-shot and iterative conferencing in a cooperative Gaussian relay channel. The relay and receiver cooperate via a conference, as introduced by Willems, in which they exchange a series of communications over orthogonal links. Under one-shot conferencing, decode-and-forward (DF) is capacity-achieving when the relay has a strong channel. On the other hand, Wyner-Ziv compress-and-forward (CF) approaches the cut-set bound when the conference link capacity is large. To contrast with one-shot conferencing, we consider a two-round iterative conference scheme; it comprises CF in the first round, and DF in the second. When the relay has a weak channel, the iterative scheme is disadvantageous. However, when the relay channel is strong, iterative cooperation, with optimal allocation of conferencing resources, outperforms one-shot cooperation provided that the conference link capacity is large. When precise allocation of conferencing resources is not possible, we consider iterative cooperation with symmetric conference links, and show that the iterative scheme still surpasses one-shot cooperation, albeit under more restricted conditions.
{"title":"Iterative and One-shot Conferencing in Relay Channels","authors":"Chris T. K. Ng, I. Marić, A. Goldsmith, S. Shamai, R. Yates","doi":"10.1109/ITW.2006.1633809","DOIUrl":"https://doi.org/10.1109/ITW.2006.1633809","url":null,"abstract":"We compare the rates of one-shot and iterative conferencing in a cooperative Gaussian relay channel. The relay and receiver cooperate via a conference, as introduced by Willems, in which they exchange a series of communications over orthogonal links. Under one-shot conferencing, decode-and-forward (DF) is capacity-achieving when the relay has a strong channel. On the other hand, Wyner-Ziv compress-and-forward (CF) approaches the cut-set bound when the conference link capacity is large. To contrast with one-shot conferencing, we consider a two-round iterative conference scheme; it comprises CF in the first round, and DF in the second. When the relay has a weak channel, the iterative scheme is disadvantageous. However, when the relay channel is strong, iterative cooperation, with optimal allocation of conferencing resources, outperforms one-shot cooperation provided that the conference link capacity is large. When precise allocation of conferencing resources is not possible, we consider iterative cooperation with symmetric conference links, and show that the iterative scheme still surpasses one-shot cooperation, albeit under more restricted conditions.","PeriodicalId":293144,"journal":{"name":"2006 IEEE Information Theory Workshop - ITW '06 Punta del Este","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123663024","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 : 2006-03-13DOI: 10.1109/ITW.2006.1633822
Cheng Chang, A. Sahai
In channel coding, reliable communication takes place at rates below capacity at the fundamental cost of end-to-end delay. Error exponents tell us how much faster convergence is when we settle for less rate. For lossless source coding, entropy takes the place of capacity and error exponents tell us how much faster convergence is when we use more rate. While in channel coding without feedback the block error exponent is a good proxy for studying the more fundamental tradeoff with fixed end-to-end delay, it is not so in source coding. Block-coding error exponents are quite conservative (despite being tight!) when it comes to the tradeoff with delay. Nonblock codes can achieve much better performance with fixed delay and we present both the fundamental bound and how to achieve it in a delay-universal manner. The proof gives substance to Shannon's cryptic statement about how the duality between source and channel coding is like the duality between the past and the future.
{"title":"The error exponent with delay for lossless source coding","authors":"Cheng Chang, A. Sahai","doi":"10.1109/ITW.2006.1633822","DOIUrl":"https://doi.org/10.1109/ITW.2006.1633822","url":null,"abstract":"In channel coding, reliable communication takes place at rates below capacity at the fundamental cost of end-to-end delay. Error exponents tell us how much faster convergence is when we settle for less rate. For lossless source coding, entropy takes the place of capacity and error exponents tell us how much faster convergence is when we use more rate. While in channel coding without feedback the block error exponent is a good proxy for studying the more fundamental tradeoff with fixed end-to-end delay, it is not so in source coding. Block-coding error exponents are quite conservative (despite being tight!) when it comes to the tradeoff with delay. Nonblock codes can achieve much better performance with fixed delay and we present both the fundamental bound and how to achieve it in a delay-universal manner. The proof gives substance to Shannon's cryptic statement about how the duality between source and channel coding is like the duality between the past and the future.","PeriodicalId":293144,"journal":{"name":"2006 IEEE Information Theory Workshop - ITW '06 Punta del Este","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121572403","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 : 2006-03-13DOI: 10.1109/ITW.2006.1633778
A. Ashikhmin
We consider a generalization of a classical ARQ protocol for the case of quantum error correcting codes and the quantum depolarizing channel. We define the fidelity of the ARQ protocol as the probability that the outcome of a measurement of the received quantum state is collinear to the transmitted quantum state, under the condition that the measurement outcome belongs to the code space. Further, we derive tight upper and lower bounds on the exponent of the fidelity of the ARQ protocol. The obtained bounds show a threshold behavior of the fidelity. Namely, in asymptotics, as the code length tends to infinity, the fidelity tends to either 1 or 0 depending on the code rate and the probability of error of the quantum depolarizing channel.
{"title":"Fidelity of a Quantum ARQ Protocol","authors":"A. Ashikhmin","doi":"10.1109/ITW.2006.1633778","DOIUrl":"https://doi.org/10.1109/ITW.2006.1633778","url":null,"abstract":"We consider a generalization of a classical ARQ protocol for the case of quantum error correcting codes and the quantum depolarizing channel. We define the fidelity of the ARQ protocol as the probability that the outcome of a measurement of the received quantum state is collinear to the transmitted quantum state, under the condition that the measurement outcome belongs to the code space. Further, we derive tight upper and lower bounds on the exponent of the fidelity of the ARQ protocol. The obtained bounds show a threshold behavior of the fidelity. Namely, in asymptotics, as the code length tends to infinity, the fidelity tends to either 1 or 0 depending on the code rate and the probability of error of the quantum depolarizing channel.","PeriodicalId":293144,"journal":{"name":"2006 IEEE Information Theory Workshop - ITW '06 Punta del Este","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125242153","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 : 2006-03-13DOI: 10.1109/ITW.2006.1633776
V. Guruswami
This is a brief survey into the applications of list decoding in complexity theory, specifically in relating the worst-case and average-case complexity of computational problems, and in construction of pseudorandom generators. Since we do not have space for full proofs, the aim is to give a flavor of the utility of list decoding in these settings together with pointers to where further details can be found.
{"title":"List Decoding in Average-Case Complexity and Pseudorandomness","authors":"V. Guruswami","doi":"10.1109/ITW.2006.1633776","DOIUrl":"https://doi.org/10.1109/ITW.2006.1633776","url":null,"abstract":"This is a brief survey into the applications of list decoding in complexity theory, specifically in relating the worst-case and average-case complexity of computational problems, and in construction of pseudorandom generators. Since we do not have space for full proofs, the aim is to give a flavor of the utility of list decoding in these settings together with pointers to where further details can be found.","PeriodicalId":293144,"journal":{"name":"2006 IEEE Information Theory Workshop - ITW '06 Punta del Este","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126081439","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 : 2006-03-13DOI: 10.1109/ITW.2006.1633787
A. György, T. Linder, G. Lugosi
The on-line shortest path problem is considered in the bandit setting. Given a weighted directed acyclic graph whose edge weights can change in an arbitrary way, a decision maker has to pick in each round a path between two distinguished vertices, such that the weight of this path, given as the sum of the weights of its composing edges, be as small as possible. The decision maker has only limited information on how the weights of the edges are generated. In particular, the edge weights in the current round are unknown to the decision maker when it chooses a path, and after choosing a path, it learns only the weights of those edges that belong to the chosen path. An algorithm is given whose average cumulative loss in n rounds exceeds that of the best path, matched off-line to the entire sequence of the edge weights, by a quantity that is proportional to 1/√n and depends only polynomially on the number of edges of the graph. The algorithm can be implemented with linear complexity in the number of rounds n and in the number of edges. This result improves earlier algorithms which have performance bounds that either depend exponentially on the number of edges or converge to zero at a slower rate than O(1/√n).
{"title":"The Shortest Path Problem in the Bandit Setting","authors":"A. György, T. Linder, G. Lugosi","doi":"10.1109/ITW.2006.1633787","DOIUrl":"https://doi.org/10.1109/ITW.2006.1633787","url":null,"abstract":"The on-line shortest path problem is considered in the bandit setting. Given a weighted directed acyclic graph whose edge weights can change in an arbitrary way, a decision maker has to pick in each round a path between two distinguished vertices, such that the weight of this path, given as the sum of the weights of its composing edges, be as small as possible. The decision maker has only limited information on how the weights of the edges are generated. In particular, the edge weights in the current round are unknown to the decision maker when it chooses a path, and after choosing a path, it learns only the weights of those edges that belong to the chosen path. An algorithm is given whose average cumulative loss in n rounds exceeds that of the best path, matched off-line to the entire sequence of the edge weights, by a quantity that is proportional to 1/√n and depends only polynomially on the number of edges of the graph. The algorithm can be implemented with linear complexity in the number of rounds n and in the number of edges. This result improves earlier algorithms which have performance bounds that either depend exponentially on the number of edges or converge to zero at a slower rate than O(1/√n).","PeriodicalId":293144,"journal":{"name":"2006 IEEE Information Theory Workshop - ITW '06 Punta del Este","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130257562","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 : 2006-03-13DOI: 10.1109/ITW.2006.1633813
K. Jain, V. Vazirani, G. Yuval
Li and Li conjectured that in an undirected network with multiple unicast sessions, network coding does not lead to any coding gain. Surprisingly enough, so far this conjecture could not be verified even for the simple network consisting of K3,2with four source-sink pairs. Using entropy calculus, we provide the first verification of the Li-Li conjecture for this network. We extend our bound to the case of an arbitrary directed bipartite network.
{"title":"On the Coding Advantage of Multiple Unicast Sessions in Undirected Graphs","authors":"K. Jain, V. Vazirani, G. Yuval","doi":"10.1109/ITW.2006.1633813","DOIUrl":"https://doi.org/10.1109/ITW.2006.1633813","url":null,"abstract":"Li and Li conjectured that in an undirected network with multiple unicast sessions, network coding does not lead to any coding gain. Surprisingly enough, so far this conjecture could not be verified even for the simple network consisting of K3,2with four source-sink pairs. Using entropy calculus, we provide the first verification of the Li-Li conjecture for this network. We extend our bound to the case of an arbitrary directed bipartite network.","PeriodicalId":293144,"journal":{"name":"2006 IEEE Information Theory Workshop - ITW '06 Punta del Este","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128203874","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 : 2006-03-13DOI: 10.1109/ITW.2006.1633828
R. M. Siqueira, S. Costa
Good spherical codes have large minimum squared distance. An important quota in the theory of spherical codes is the maximum number of points M(n, rho) displayed on the sphere Sn-1, having a minimum squared distance rho. The aim of this work is to study this problem within the class of group codes. We establish a bound for the number of points of a commutative group code in dimension even.
{"title":"Upper bounds for a Commutative Group Code","authors":"R. M. Siqueira, S. Costa","doi":"10.1109/ITW.2006.1633828","DOIUrl":"https://doi.org/10.1109/ITW.2006.1633828","url":null,"abstract":"Good spherical codes have large minimum squared distance. An important quota in the theory of spherical codes is the maximum number of points M(n, rho) displayed on the sphere Sn-1, having a minimum squared distance rho. The aim of this work is to study this problem within the class of group codes. We establish a bound for the number of points of a commutative group code in dimension even.","PeriodicalId":293144,"journal":{"name":"2006 IEEE Information Theory Workshop - ITW '06 Punta del Este","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134408488","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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