Beongjun Choi, Jy-yong Sohn, Dong-Jun Han, J. Moon
{"title":"Scalable Network-Coded PBFT Consensus Algorithm","authors":"Beongjun Choi, Jy-yong Sohn, Dong-Jun Han, J. Moon","doi":"10.1109/ISIT.2019.8849573","DOIUrl":"https://doi.org/10.1109/ISIT.2019.8849573","url":null,"abstract":"We suggest a general framework for network-coded Practical Byzantine Fault Tolerant (PBFT) consensus for enabling agreement among distributed nodes under Byzantine attacks. The suggested protocol generalizes existing replication and sharding schemes which are frequently used for consensus in current blockchain systems. Using the proposed algorithm, it is possible to reach a consensus when the available bandwidth is considerably smaller on individual links compared to that required for conventional schemes. It is shown that there exists an upper bound on the number of nodes that can participate in the protocol, given a maximum bandwidth constraint across all pairwise links. Furthermore, the protocol that achieves the upper bound is provided by using a set of constant weight codes.","PeriodicalId":6708,"journal":{"name":"2019 IEEE International Symposium on Information Theory (ISIT)","volume":"2007 1","pages":"857-861"},"PeriodicalIF":0.0,"publicationDate":"2019-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82493282","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}
{"title":"On the Analysis of Energy-Distortion Tradeoff for Zero-Delay Transmission over Gaussian Broadcast Channels","authors":"Ceren Sevinç, E. Tuncel","doi":"10.1109/ISIT.2019.8849627","DOIUrl":"https://doi.org/10.1109/ISIT.2019.8849627","url":null,"abstract":"Asymptotic energy-distortion performance of zero-delay communication under Gaussian broadcasting is investigated. The analysis can be motivated by the scenario where the same internet of things (IoT) device is transmitting its measurements to multiple control units that are experiencing varying noise levels. Using high-resolution analysis for quantizer design coupled with orthogonal signaling, the higher-order term in the negative logarithm of the distortion, termed the energy-distortion dispersion, is optimized while keeping the leading term, the energy-distortion exponent, at its optimal value for the zero-delay regime.","PeriodicalId":6708,"journal":{"name":"2019 IEEE International Symposium on Information Theory (ISIT)","volume":"22 1","pages":"2758-2762"},"PeriodicalIF":0.0,"publicationDate":"2019-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90973787","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}
{"title":"Construction of Partial Geometries and LDPC codes based on Reed-Solomon Codes","authors":"Juane Li, Keke Liu, Shu Lin, K. Abdel-Ghaffar","doi":"10.1109/ISIT.2019.8849677","DOIUrl":"https://doi.org/10.1109/ISIT.2019.8849677","url":null,"abstract":"This paper presents a construction of a class of partial geometries based on RS codes of prime lengths and shows that LDPC codes constructed based on Reed-Solomon codes of prime lengths are finite geometry LDPC codes. Furthermore, a new method for design and construction of nonbinary quasi-cyclic LDPC codes based on the conventional parity-check matrices of Reed-Solomon codes is presented. Simulation results show that the constructed nonbinary LDPC codes perform well over the additive white Gaussian channel.","PeriodicalId":6708,"journal":{"name":"2019 IEEE International Symposium on Information Theory (ISIT)","volume":"1 1","pages":"61-65"},"PeriodicalIF":0.0,"publicationDate":"2019-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88655427","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}
Xishi Wang, Amitalok J. Budkuley, Andrej Bogdanov, S. Jaggi
{"title":"When are large codes possible for AVCs?","authors":"Xishi Wang, Amitalok J. Budkuley, Andrej Bogdanov, S. Jaggi","doi":"10.1109/ISIT.2019.8849324","DOIUrl":"https://doi.org/10.1109/ISIT.2019.8849324","url":null,"abstract":"We study a general Omniscient Arbitrarily Varying Channel (AVC) problem where Alice wishes to communicate a message to receiver Bob by inputting a length-n vector x to a channel. Jammer James observes x, and as a function of x chooses a state sequence s. Bob observes y (such that channel inputs and outputs are related component-wise as yi = w(xi,si) for some deterministic function w(.,.)) from which he must estimate m with no error. Input and state constraints determine feasible inputs x and s for Alice and James respectively. In this work we characterize when a positive communication rate is possible.We first show that the capacity of any such AVC completely depends upon the relationship between a confusability set, and the set of completely-positive-self-couplings (both are convex sets of certain single-letter probability distributions). Our main result provides essentially matching necessary and sufficient conditions for capacity positivity; we show that the zero-error capacity of an AVC is positive if there are completely-positive-self-couplings outside the confusability set of the given AVC; and that the AVC capacity is zero if all completely-positive-self couplings are in the interior of this confusability set. Our achievability uses a novel code construction based on completely-positive-self-couplings called cloud codes which are strict generalizations of all known Gilbert-Varshamov (GV) type codes. Our converse is based upon Ramsey-theoretic ideas, a generalization of the Plotkin bound leveraging a known result on the duality of completely positive matrices and copositive matrices, and a Fourier-analytic proof of the non-existence of certain sequences of random variables.","PeriodicalId":6708,"journal":{"name":"2019 IEEE International Symposium on Information Theory (ISIT)","volume":"96 1","pages":"632-636"},"PeriodicalIF":0.0,"publicationDate":"2019-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80108087","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}
Sagnik Bhattacharya, Amitalok J. Budkuley, S. Jaggi
{"title":"Shared Randomness in Arbitrarily Varying Channels","authors":"Sagnik Bhattacharya, Amitalok J. Budkuley, S. Jaggi","doi":"10.1109/ISIT.2019.8849801","DOIUrl":"https://doi.org/10.1109/ISIT.2019.8849801","url":null,"abstract":"We study an adversarial communication problem where sender Alice wishes to send a message m to receiver Bob over an arbitrarily varying channel (AVC) controlled by a malicious adversary James. We assume that Alice and Bob share randomness K unknown to James. Using K, Alice first encodes the message m to a codeword X and transmits it over the AVC. James knows the message m, the (randomized) codebook and the codeword X. James then inputs a jamming state S to disrupt communication; we assume a state-deterministic AVC where S completely specifies the channel noise. Bob receives a noisy version Y of codeword X; it outputs a message estimate $mathop {hat m}$ using Y and the shared randomness K. We study AVCs, called ‘adversary-weakened’ AVCs here, where the availability of shared randomness strictly improves the optimum throughput or capacity over it than when it is not available; the randomized coding capacity characterizes the largest rate possible when K is unrestricted. In this work, we characterize the exact threshold for the amount of shared randomness K so as to achieve the randomized coding capacity for ‘adversary-weakened’ AVCs.We show that exactly log(n) equiprobable and independent bits of randomness, shared between Alice and Bob and unknown to adversary James, are both necessary and sufficient for achieving randomized coding capacity for ‘adversary-weakened’ AVCs. For sufficiency, our achievability is based on a randomized code construction which uses deterministic list codes along with a polynomial hashing technique which uses the shared randomness. Our converse, which establishes the necessity of log(n) bits of shared randomness, uses a known approach for binary AVCs, and extends it to general ‘adversary-weakened’ AVCs using a notion of confusable codewords.","PeriodicalId":6708,"journal":{"name":"2019 IEEE International Symposium on Information Theory (ISIT)","volume":"1 1","pages":"627-631"},"PeriodicalIF":0.0,"publicationDate":"2019-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86969597","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}
{"title":"Local Geometry of Cross Entropy Loss in Learning One-Hidden-Layer Neural Networks","authors":"H. Fu, Yuejie Chi, Yingbin Liang","doi":"10.1109/ISIT.2019.8849289","DOIUrl":"https://doi.org/10.1109/ISIT.2019.8849289","url":null,"abstract":"We study model recovery for data classification, where the training labels are generated from a one-hidden-layer neural network with sigmoid activations, and the goal is to recover the weights of the neural network. We consider two network models, the fully-connected network (FCN) and the non-overlapping convolutional neural network (CNN). We prove that with Gaussian inputs, the empirical risk based on cross entropy exhibits strong convexity and smoothness uniformly in a local neighborhood of the ground truth, as soon as the sample complexity is sufficiently large. Hence, if initialized in this neighborhood, it establishes the local convergence guarantee for empirical risk minimization using cross entropy via gradient descent for learning one-hidden-layer neural networks, at the near-optimal sample and computational complexity with respect to the network input dimension without unrealistic assumptions such as requiring a fresh set of samples at each iteration.","PeriodicalId":6708,"journal":{"name":"2019 IEEE International Symposium on Information Theory (ISIT)","volume":"187 1","pages":"1972-1976"},"PeriodicalIF":0.0,"publicationDate":"2019-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87622217","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}
{"title":"Context Block Estimation for Random Fields","authors":"Zsolt Talata","doi":"10.1109/ISIT.2019.8849574","DOIUrl":"https://doi.org/10.1109/ISIT.2019.8849574","url":null,"abstract":"For random fields on the d-dimensional integer lattice with finite state space, the basic neighborhood is the smallest region around a site that determines the conditional distribution at the site given the values at all other sites. For variable basic neighborhood random fields the basic neighborhood may vary with the values at the surrounding sites, and the sets of the values in these basic neighborhoods are called context blocks. The context blocks may be infinite. Statistical estimation of the context block system of a random field from a sample, a single realization of the random field observed in a finite region, is addressed. The Optimal Likelihood Ratio (OLR) estimator is introduced. Its nearly linear computation complexity is shown and a bound on the probability of the estimation error is proved that implies strong consistency of the estimator.","PeriodicalId":6708,"journal":{"name":"2019 IEEE International Symposium on Information Theory (ISIT)","volume":"6 1","pages":"51-55"},"PeriodicalIF":0.0,"publicationDate":"2019-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89315660","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}
{"title":"How to Modify Polar Codes for List Decoding","authors":"M. Rowshan, E. Viterbo","doi":"10.1109/ISIT.2019.8849539","DOIUrl":"https://doi.org/10.1109/ISIT.2019.8849539","url":null,"abstract":"Polar codes are constructed based on the reliability of bit-channels. This construction suits the successive cancellation (SC) decoding, where one error in the successive estimation of the bits fails the decoding. However, in SC list (SCL) decoding, the correct path may remain in the list by tolerating multiple penalties. This characteristic of list decoding demands a different approach in code construction.In this work, we modify the conventional construction by a greedy search algorithm in which a bit-swapping approach is employed to re-distribute the low-reliability bits in the subblocks aiming for a reduction in the probability of correct path elimination. The numerical results for polar codes of length 1 kb under CRC-aided SCL decoding show improvements of about 0.4 dB for R=0.8 and over 0.2 dB for R=0.5 at L=32.","PeriodicalId":6708,"journal":{"name":"2019 IEEE International Symposium on Information Theory (ISIT)","volume":"16 1","pages":"1772-1776"},"PeriodicalIF":0.0,"publicationDate":"2019-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87000516","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}
{"title":"Weight Enumerating Function, Number of Full Rank Sub-matrices and Network Coding","authors":"Mahesh Babu Vaddi, B. Rajan","doi":"10.1109/ISIT.2019.8849273","DOIUrl":"https://doi.org/10.1109/ISIT.2019.8849273","url":null,"abstract":"In most of the network coding problems with k messages, the existence of binary network coding solution over ${mathbb{F}_2}$ depends on the existence of adequate sets of k-dimensional binary vectors such that each set comprises of linearly independent vectors. In a given k×n (n ≥ k) binary matrix, there exist $ binom{n}{k}$ binary sub-matrices of size k×k. Every possible k×k submatrix may be of full rank or singular depending on the columns present in the matrix. In this work, for full rank binary matrix G of size k×n satisfying certain condition on minimum Hamming weight, we establish a relation between the number of full rank sub-matrices of size k×k and the weight enumerating function of the error correcting code with G as the generator matrix. We give an algorithm to compute the number of full rank k×k submatrices.","PeriodicalId":6708,"journal":{"name":"2019 IEEE International Symposium on Information Theory (ISIT)","volume":"59 1","pages":"867-871"},"PeriodicalIF":0.0,"publicationDate":"2019-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84921580","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}
{"title":"Linear-Time Encoders for Codes Correcting a Single Edit for DNA-Based Data Storage","authors":"Y. M. Chee, H. M. Kiah, T. T. Nguyen","doi":"10.1109/ISIT.2019.8849643","DOIUrl":"https://doi.org/10.1109/ISIT.2019.8849643","url":null,"abstract":"An indel refers to a single insertion or deletion, while an edit refers to either a single insertion, deletion or substitution. We investigate codes that combat either a single indel or a single edit and provide linear-time algorithms that encode binary messages into these codes of length n. Over the quaternary alphabet, we provide two linear-time encoders. One corrects a single edit with 2⌈log n⌉ + 2 redundant bits, while the other corrects a single indel with ⌈log n⌉ + 2 redundant bits. The latter encoder reduces the redundancy of the best known encoder of Tenengolts (1984) by at least four bits. Over the DNA alphabet, exactly half of the symbols of a GC-balanced word are either C or G. Via a modification of Knuth’s balancing technique, we provide a linear-time map that translates binary messages into GC-balanced codewords and the resulting codebook is able to correct a single edit. The redundancy of our encoder is 3⌈log n⌉ + 2 bits and this is the first known construction of a GC-balanced code that corrects a single edit.","PeriodicalId":6708,"journal":{"name":"2019 IEEE International Symposium on Information Theory (ISIT)","volume":"33 1","pages":"772-776"},"PeriodicalIF":0.0,"publicationDate":"2019-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74814232","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}