Pub Date : 2016-07-10DOI: 10.1109/ISIT.2016.7541411
Christopher G. Blake, F. Kschischang
Sequences of VLSI circuits implemented according to the Thompson VLSI model that compute encoding and decoding functions, called coding schemes, are classified according to the rate at which their associated block error probability scales with block length N. It is shown that coding schemes for binary symmetric channels with probability of error that scales as O(f(N)) must have encoding and decoding energy that scales at least as Ω(N√(-ln f (N))). Polar coding schemes of rate greater than 1/2 are shown to have encoding and decoding energy that scales at least as Ω(N3/2). This lower bound is achievable up to polylogarithmic factors on a mesh-network.
{"title":"Energy complexity of polar codes","authors":"Christopher G. Blake, F. Kschischang","doi":"10.1109/ISIT.2016.7541411","DOIUrl":"https://doi.org/10.1109/ISIT.2016.7541411","url":null,"abstract":"Sequences of VLSI circuits implemented according to the Thompson VLSI model that compute encoding and decoding functions, called coding schemes, are classified according to the rate at which their associated block error probability scales with block length N. It is shown that coding schemes for binary symmetric channels with probability of error that scales as O(f(N)) must have encoding and decoding energy that scales at least as Ω(N√(-ln f (N))). Polar coding schemes of rate greater than 1/2 are shown to have encoding and decoding energy that scales at least as Ω(N3/2). This lower bound is achievable up to polylogarithmic factors on a mesh-network.","PeriodicalId":198767,"journal":{"name":"2016 IEEE International Symposium on Information Theory (ISIT)","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115816629","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 : 2016-07-10DOI: 10.1109/ISIT.2016.7541636
Yaoqing Yang, P. Grover, S. Kar
We consider the problem of computing a binary linear transform when all circuit components are unreliable. We propose a novel “ENCODED” technique that uses LDPC (low-density parity-check) codes and embedded noisy decoders to keep the error probability of the computation below a small constant independent of the size of the linear transform, even when all logic gates in the computation are prone to probabilistic errors. Unlike existing works on applying coding to computing with unreliable components, the “ENCODED” technique explicitly considers the errors that happen during both the encoding and the decoding phases. Further, we show that ENCODED requires fewer operations (in order sense) than repetition techniques.
{"title":"Computing linear transforms with unreliable components","authors":"Yaoqing Yang, P. Grover, S. Kar","doi":"10.1109/ISIT.2016.7541636","DOIUrl":"https://doi.org/10.1109/ISIT.2016.7541636","url":null,"abstract":"We consider the problem of computing a binary linear transform when all circuit components are unreliable. We propose a novel “ENCODED” technique that uses LDPC (low-density parity-check) codes and embedded noisy decoders to keep the error probability of the computation below a small constant independent of the size of the linear transform, even when all logic gates in the computation are prone to probabilistic errors. Unlike existing works on applying coding to computing with unreliable components, the “ENCODED” technique explicitly considers the errors that happen during both the encoding and the decoding phases. Further, we show that ENCODED requires fewer operations (in order sense) than repetition techniques.","PeriodicalId":198767,"journal":{"name":"2016 IEEE International Symposium on Information Theory (ISIT)","volume":"96 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115931777","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 : 2016-07-10DOI: 10.1109/ISIT.2016.7541318
Austin Taghavi, Avinash Vem, J. Chamberland, K. Narayanan
Future wireless access points may have to support sporadic transmissions from a massive number of unattended machines. Recently, there has been a lot of interest in the design of massive uncoordinated multiple access schemes for such systems based on clever enhancements to slotted ALOHA. A close connection has been established between the design of the multiple access scheme and the design of low density generator matrix codes. Based on this connection, optimal multiple access schemes have been designed based on slotted ALOHA and successive interference cancellation, assuming that the number of users in the network is known at the transmitters. In this paper, we extend this work and consider the design of universal uncoordinated multiple access schemes that are agnostic to the number of users in the network. We design Markov chain based transmission policies and numerical results show that substantial improvement to slotted ALOHA is possible.
{"title":"On the design of universal schemes for massive uncoordinated multiple access","authors":"Austin Taghavi, Avinash Vem, J. Chamberland, K. Narayanan","doi":"10.1109/ISIT.2016.7541318","DOIUrl":"https://doi.org/10.1109/ISIT.2016.7541318","url":null,"abstract":"Future wireless access points may have to support sporadic transmissions from a massive number of unattended machines. Recently, there has been a lot of interest in the design of massive uncoordinated multiple access schemes for such systems based on clever enhancements to slotted ALOHA. A close connection has been established between the design of the multiple access scheme and the design of low density generator matrix codes. Based on this connection, optimal multiple access schemes have been designed based on slotted ALOHA and successive interference cancellation, assuming that the number of users in the network is known at the transmitters. In this paper, we extend this work and consider the design of universal uncoordinated multiple access schemes that are agnostic to the number of users in the network. We design Markov chain based transmission policies and numerical results show that substantial improvement to slotted ALOHA is possible.","PeriodicalId":198767,"journal":{"name":"2016 IEEE International Symposium on Information Theory (ISIT)","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134431143","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 : 2016-07-10DOI: 10.1109/ISIT.2016.7541830
Chih-Chun Wang
Supporting delay-sensitive traffic is critical to the next-generation communication network. This work studies the 1-to-2 broadcast packet erasure channels with causal ACKnowledgement (ACK), which is motivated by practical downlink access point networks. While the corresponding delay-constrained Shannon capacity remains an open problem (no existing analysis tools can be directly applied), this work focuses on linear codes and proposes three new definitions of delay-constrained throughput based on different outage metrics: the file-based, the rank-based, and the packet-based ones. It then fully characterizes the corresponding linear coding capacity regions for relatively-short-delay flows - flows for which the delay requirement is no larger than the interval of file arrivals.
{"title":"Delay-constrained capacity for broadcast erasure channels: A linear-coding-based study","authors":"Chih-Chun Wang","doi":"10.1109/ISIT.2016.7541830","DOIUrl":"https://doi.org/10.1109/ISIT.2016.7541830","url":null,"abstract":"Supporting delay-sensitive traffic is critical to the next-generation communication network. This work studies the 1-to-2 broadcast packet erasure channels with causal ACKnowledgement (ACK), which is motivated by practical downlink access point networks. While the corresponding delay-constrained Shannon capacity remains an open problem (no existing analysis tools can be directly applied), this work focuses on linear codes and proposes three new definitions of delay-constrained throughput based on different outage metrics: the file-based, the rank-based, and the packet-based ones. It then fully characterizes the corresponding linear coding capacity regions for relatively-short-delay flows - flows for which the delay requirement is no larger than the interval of file arrivals.","PeriodicalId":198767,"journal":{"name":"2016 IEEE International Symposium on Information Theory (ISIT)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134444505","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 : 2016-07-10DOI: 10.1109/ISIT.2016.7541857
C. Pacher, Philipp Grabenweger, D. Simos
The expectation and the variance of the syndrome weight distribution of linear codes after transmission of codewords through a binary symmetric channel are derived exactly in closed form as functions of the code's parity-check matrix and of the degree distributions of the associated Tanner graph. The influence of (check) regularity of the Tanner graph is studied. Special attention is payed to Tanner graphs that have no cycles of length four. We further study the equivalence of some classes of combinatorial designs and important classes of LDPC codes and apply our general results to those more specific structures. Simulations validate the analytical results and show that the actual cumulative distribution function of the syndrome weight is close to that of a normal distribution.
{"title":"Weight distribution of the syndrome of linear codes and connections to combinatorial designs","authors":"C. Pacher, Philipp Grabenweger, D. Simos","doi":"10.1109/ISIT.2016.7541857","DOIUrl":"https://doi.org/10.1109/ISIT.2016.7541857","url":null,"abstract":"The expectation and the variance of the syndrome weight distribution of linear codes after transmission of codewords through a binary symmetric channel are derived exactly in closed form as functions of the code's parity-check matrix and of the degree distributions of the associated Tanner graph. The influence of (check) regularity of the Tanner graph is studied. Special attention is payed to Tanner graphs that have no cycles of length four. We further study the equivalence of some classes of combinatorial designs and important classes of LDPC codes and apply our general results to those more specific structures. Simulations validate the analytical results and show that the actual cumulative distribution function of the syndrome weight is close to that of a normal distribution.","PeriodicalId":198767,"journal":{"name":"2016 IEEE International Symposium on Information Theory (ISIT)","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134000529","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 : 2016-07-10DOI: 10.1109/ISIT.2016.7541717
G. Spini, G. Zémor
In the model of Secure Network Coding, a sender is connected to several receivers by a network, i.e. a directed graph with a single source node and several destination nodes, where each node can perform operations on the values received via the incoming edges and sends the results via the outbound edges. An active adversary controls some of the edges; this means that he can read every symbol transmitted over the edges under his control and replace them with symbols of his choice. The goal of Secure Network Coding is to design protocols that allow transmission of a secret message from the sender to all receivers in a private and reliable way. Classically, only one-way communication (from sender to receivers) has been studied; in this setting, security can be guaranteed as long as the number of edges controlled by the adversary is less than one third of the network connectivity. In this paper, we present a procedure where receivers are allowed to send feedback to the sender; with this feature, security is guaranteed against a stronger adversary: namely, the number of corrupted edges only needs to be smaller than one half of the connectivity. Furthermore, like previous state-of-the-art work on the single-round scenario, our scheme is universal, i.e. it does not require knowledge of the network code.
{"title":"Universally Secure Network Coding with feedback","authors":"G. Spini, G. Zémor","doi":"10.1109/ISIT.2016.7541717","DOIUrl":"https://doi.org/10.1109/ISIT.2016.7541717","url":null,"abstract":"In the model of Secure Network Coding, a sender is connected to several receivers by a network, i.e. a directed graph with a single source node and several destination nodes, where each node can perform operations on the values received via the incoming edges and sends the results via the outbound edges. An active adversary controls some of the edges; this means that he can read every symbol transmitted over the edges under his control and replace them with symbols of his choice. The goal of Secure Network Coding is to design protocols that allow transmission of a secret message from the sender to all receivers in a private and reliable way. Classically, only one-way communication (from sender to receivers) has been studied; in this setting, security can be guaranteed as long as the number of edges controlled by the adversary is less than one third of the network connectivity. In this paper, we present a procedure where receivers are allowed to send feedback to the sender; with this feature, security is guaranteed against a stronger adversary: namely, the number of corrupted edges only needs to be smaller than one half of the connectivity. Furthermore, like previous state-of-the-art work on the single-round scenario, our scheme is universal, i.e. it does not require knowledge of the network code.","PeriodicalId":198767,"journal":{"name":"2016 IEEE International Symposium on Information Theory (ISIT)","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134315351","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 : 2016-07-10DOI: 10.1109/ISIT.2016.7541797
Abdulrahman Baknina, S. Ulukus
We consider online transmission policies for the two-user multiple access channel, where both users harvest energy from a common source. The transmitters are equipped with arbitrary but finite-sized batteries. The energy harvests are independent and identically distributed (i.i.d.) over time, and synchronized at the two users due to their common source. The transmitters know the energy arrivals only causally. We first consider the special case of Bernoulli energy arrivals. For this case, we determine the optimal policies that achieve the boundary of the capacity region. We show that the optimal power allocation decreases in time, and that the capacity region is a pentagon. We then consider general i.i.d. energy arrivals, and propose a distributed fractional power (DFP) policy. We develop lower and upper bounds on the performance of the proposed DFP policy for general i.i.d. energy arrivals, and show that the proposed DFP is near-optimal in that it yields rates which are within a constant gap of the derived lower and upper bounds.
{"title":"Online policies for multiple access channel with common energy harvesting source","authors":"Abdulrahman Baknina, S. Ulukus","doi":"10.1109/ISIT.2016.7541797","DOIUrl":"https://doi.org/10.1109/ISIT.2016.7541797","url":null,"abstract":"We consider online transmission policies for the two-user multiple access channel, where both users harvest energy from a common source. The transmitters are equipped with arbitrary but finite-sized batteries. The energy harvests are independent and identically distributed (i.i.d.) over time, and synchronized at the two users due to their common source. The transmitters know the energy arrivals only causally. We first consider the special case of Bernoulli energy arrivals. For this case, we determine the optimal policies that achieve the boundary of the capacity region. We show that the optimal power allocation decreases in time, and that the capacity region is a pentagon. We then consider general i.i.d. energy arrivals, and propose a distributed fractional power (DFP) policy. We develop lower and upper bounds on the performance of the proposed DFP policy for general i.i.d. energy arrivals, and show that the proposed DFP is near-optimal in that it yields rates which are within a constant gap of the derived lower and upper bounds.","PeriodicalId":198767,"journal":{"name":"2016 IEEE International Symposium on Information Theory (ISIT)","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131472263","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 : 2016-07-10DOI: 10.1109/ISIT.2016.7541818
M. Berta, Omar Fawzi, M. Tomamichel
The relative entropy is the basic concept underlying various information measures like entropy, conditional entropy and mutual information. Here, we discuss how to make use of variational formulas for measured relative entropy and quantum relative entropy for understanding the additivity properties of various entropic quantities that appear in quantum information theory. In particular, we show that certain lower bounds on quantum conditional mutual information are superadditive.
{"title":"Exploiting variational formulas for quantum relative entropy","authors":"M. Berta, Omar Fawzi, M. Tomamichel","doi":"10.1109/ISIT.2016.7541818","DOIUrl":"https://doi.org/10.1109/ISIT.2016.7541818","url":null,"abstract":"The relative entropy is the basic concept underlying various information measures like entropy, conditional entropy and mutual information. Here, we discuss how to make use of variational formulas for measured relative entropy and quantum relative entropy for understanding the additivity properties of various entropic quantities that appear in quantum information theory. In particular, we show that certain lower bounds on quantum conditional mutual information are superadditive.","PeriodicalId":198767,"journal":{"name":"2016 IEEE International Symposium on Information Theory (ISIT)","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131702810","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 : 2016-07-10DOI: 10.1109/ISIT.2016.7541847
S. R. Aghdam, T. Duman
We propose a low complexity transmit signal design scheme for achieving information-theoretic secrecy over a MIMO wiretap channel driven by finite-alphabet inputs. We assume that the transmitter has perfect channel state information (CSI) of the main channel and also knows the statistics of the eavesdropper's channel. The proposed transmission scheme relies on jointly optimizing the precoder matrix and the artificial noise so as to maximize the achievable secrecy rates. In order to lower the computational complexity associated with the transmit signal design, we employ a design metric using the cut-off rate instead of the mutual information. We formulate a gradient-descent based optimization algorithm and demonstrate via extensive numerical examples that the proposed signal design scheme can yield an enhanced secrecy performance compared with the existing solutions in spite of its relatively lower computational complexity. The impacts of the modulation order as well as the number of antennas at the transmitter and receiver ends on the achievable secrecy rates are also investigated.
{"title":"Low complexity precoding for MIMOME wiretap channels based on cut-off rate","authors":"S. R. Aghdam, T. Duman","doi":"10.1109/ISIT.2016.7541847","DOIUrl":"https://doi.org/10.1109/ISIT.2016.7541847","url":null,"abstract":"We propose a low complexity transmit signal design scheme for achieving information-theoretic secrecy over a MIMO wiretap channel driven by finite-alphabet inputs. We assume that the transmitter has perfect channel state information (CSI) of the main channel and also knows the statistics of the eavesdropper's channel. The proposed transmission scheme relies on jointly optimizing the precoder matrix and the artificial noise so as to maximize the achievable secrecy rates. In order to lower the computational complexity associated with the transmit signal design, we employ a design metric using the cut-off rate instead of the mutual information. We formulate a gradient-descent based optimization algorithm and demonstrate via extensive numerical examples that the proposed signal design scheme can yield an enhanced secrecy performance compared with the existing solutions in spite of its relatively lower computational complexity. The impacts of the modulation order as well as the number of antennas at the transmitter and receiver ends on the achievable secrecy rates are also investigated.","PeriodicalId":198767,"journal":{"name":"2016 IEEE International Symposium on Information Theory (ISIT)","volume":"747 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133554314","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 : 2016-07-10DOI: 10.1109/ISIT.2016.7541520
Qian Guo, T. Johansson
The McEliece public key cryptosystem is an attractive general construction that has received extensive attention over the years. Recently, a very promising version called QC-MDPC, was proposed. By using binary quasi-cyclic codes, the size of the public key can be decreased significantly. The decryption step involves iterative decoding of moderate density parity check codes (MDPC). In this paper we propose a non-binary version of QC-MDPC. The errors in the new scheme are discrete Gaussian and the decryption involves a new type of iterative decoding with a non-binary alphabet. The resulting scheme improves upon the binary QC-MDPC in that the size of the pubic key can be even smaller.
{"title":"A p-ary MDPC scheme","authors":"Qian Guo, T. Johansson","doi":"10.1109/ISIT.2016.7541520","DOIUrl":"https://doi.org/10.1109/ISIT.2016.7541520","url":null,"abstract":"The McEliece public key cryptosystem is an attractive general construction that has received extensive attention over the years. Recently, a very promising version called QC-MDPC, was proposed. By using binary quasi-cyclic codes, the size of the public key can be decreased significantly. The decryption step involves iterative decoding of moderate density parity check codes (MDPC). In this paper we propose a non-binary version of QC-MDPC. The errors in the new scheme are discrete Gaussian and the decryption involves a new type of iterative decoding with a non-binary alphabet. The resulting scheme improves upon the binary QC-MDPC in that the size of the pubic key can be even smaller.","PeriodicalId":198767,"journal":{"name":"2016 IEEE International Symposium on Information Theory (ISIT)","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132140526","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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