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The institute reserves the right to alter the nature and timings of assessment. Sitemap Contact Us. Back to CIT main website. Programmes Modules search. Site Navigation Home Search. Download this module Print View. This is prior learning or a practical skill that is strongly recommended before enrolment in this module. You may enrol in this module if you have not acquired the recommended learning but you will have considerable difficulty in passing i. While the prior learning is expressed as named CIT module s it also allows for learning in another module or modules which is equivalent to the learning specified in the named module s.

These are modules which have learning outcomes that are too similar to the learning outcomes of this module. You may not earn additional credit for the same learning and therefore you may not enrol in this module if you have successfully completed any modules in the incompatible list. Quatity of information, average information and entropy, redundancy, worked examples, conditional entropy, noisy channels, general expression for information transfer, Venn diagram representation, channel capacity, continuous signals, relative entropy, information capacity of continuous channel, deduction from the ideal case, worked examples.

Error control coding, linear block, cyclic and BCH codes, code generation and detection, basic introduction to convolution codes. Programmes Modules. We provide an explicit construction of a dimension expander over linear-sized finite fields. Our approach crucially uses subspace designs and is inspired by recent constructions of list-decodable rank-metric codes. Slides — pm Break — pm Open problem session.

Title: Synchronization Strings Abstract: The talk will give an introduction to synchronization strings which provide a novel way of efficiently reducing synchronization errors, such as insertions and deletions, to much more benign and better understood Hamming errors. Synchronization strings have many applications.

Information theory and neural coding

The talk will focus on using synchronization strings as a new way to generate efficient error correcting block codes for insertions and deletions. In particular, codes that approach the Singleton bound, i. Further applications of synchronization strings will also be briefly discussed including a general method of simulating symbol corruption channels over any given insertion-deletion channel, an efficient and near-optimal coding scheme for interactive communication over insertion-deletion channels, and list-decodable insertion-deletion codes.

This talk is based on a joint work with Bernhard Haeupler. Slides — am Mahdi Cheraghchi Title.

Chapter 1 Information Measures

We develop a systematic approach, based on convex programming and real analysis, for obtaining upper bounds on the capacity of the binary deletion channel and, more generally, channels with i. Other than the classical deletion channel, we give a special attention to the Poisson-repeat channel introduced by Mitzenmacher and Drinea IEEE Transactions on Information Theory, Our framework can be applied to obtain capacity upper bounds for any repetition distribution the deletion and Poisson-repeat channels corresponding to the special cases of Bernoulli and Poisson distributions.

Our techniques essentially reduce the task of proving capacity upper bounds to maximizing a univariate, real-valued, and often concave function over a bounded interval. The corresponding univariate function is carefully designed according to the underlying distribution of repetitions and the choices vary depending on the desired strength of the upper bounds as well as the desired simplicity of the function e. Among our results, we show the following: 1. We derive the first set of capacity upper bounds for the Poisson-repeat channel.

Our results uncover further striking connections between this channel and the deletion channel, and suggest, somewhat counter-intuitively, that the Poisson-repeat channel is actually analytically simpler than the deletion channel and may be of key importance to a complete understanding of the deletion channel. We derive several novel upper bounds on the capacity of the deletion channel. All upper bounds are maximums of efficiently computable, and concave, univariate real functions over a bounded domain. Along the way, we develop several new techniques of potentially independent interest.

Abstract: In the first part of the talk, I will describe the connections between an efficient unbiasing method from Iterated von-Neumann unbiasing , and polar codes. This upper bound is sharp for tests that only use linear combinations of the output. We assume that two vertices can communicate if there is a communication link edge connecting them. In this talk we consider the communication complexity of error detection and correction of the information stored over the vertices of the graph.

For error detection, we obtain general lower bounds for the communication complexity as functions of n, k, d, X , which are tight for several graphs and codes. For error correction, building on the work of Alon, Efremenko and Sudakov, we design a protocol which can efficiently correct a single input error for repetition codes. We conclude with some interesting problems for further research.

In an LRC, any coordinate of a codeword can be recovered by accessing only few other coordinates. In this talk we describe three aspects of LRCs and some open problems. Namely, we look into the rate-distance trade-off of LRCs, the problem of disjoint repair groups, and the capacity of LRCs. Abstract: Maximally recoverable codes are codes designed for distributed storage which combine quick recovery from single node failure and optimal recovery from catastrophic failure.

Gopalan et al [SODA ] studied the alphabet size needed for such codes in grid topologies and gave a combinatorial characterization for it. The upper bound is a recursive construction which beats the random construction. The lower bound follows by first relating the problem to the independence number of the Birkhoff polytope graph, and then providing tight bounds for it using the representation theory of the symmetric group. Slides — pm Sivakanth Gopi Title : Maximally Recoverable Local Reconstruction Codes Abstract: Protecting huge amounts of data stored in the cloud from server crashes resulted in distributed storage systems transitioning to erasure coding based schemes.

They have many good properties of simply replicating data while being much more storage efficient and crash resilient. MR LRCs have already been deployed in Microsoft storage systems, outperforming traditional erasure coding systems. Designing such codes over small finite fields is crucial for applications. Unfortunately, we are far from understanding the minimal field size required for these codes. In this talk, we prove the first polynomially growing lower bounds on field size for MR LRCs using an interesting connection to incidence geometry, prior to our work no super linear lower bounds were known.

We also present some linear field size MR LRC constructions in some parameter ranges which are very relevant in practice. An arc S in Fkq is a subset of vectors with the property that every subset of size k of S is a set of linearly independent vectors. In , the MDS conjecture was verified for q prime.

Slides — pm Break — pm Rump Session. Abstract: This talk gives a communication-optimal document exchange protocol and an efficient and near optimal derandomization, which also implies new codes for small number of insertions and deletions. The size of our summary is information-theoretically order optimal for all values of k. This concludes a long series of better and better protocols which produce larger summaries for sub-linear values of k. This directly leads to binary error correcting codes for k insdel errors with the same redundancy.

Conference on Algebraic Geometry, Representation theory and Mathematical Physics

We explain his approach and describe families of AG codes used to achieve several versions of his result. Schedule: Monday, April 9 Time. Events , Past Events. Previous Next. Related Posts. Yip Annual Lecture.

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Join our seminars mailing list:. Title: Improved list-decoding and local-list-decoding of algebraic codes Abstract: We show new and improved error-correcting properties of folded Reed-Solomon codes and multiplicity codes. Title: Distributed independence testing and a new question related to hypercontractivity Abstract: Two parties observing sequences of unbiased, random bits seek to determine if the bits are independent or have a specified correlation.

Title: Algorithmic stability and generalization in machine learning: an information-theoretic analysis Abstract: Machine learning algorithms can be viewed as stochastic transformations or channels, in information-theoretic parlance that map training data to hypotheses. In this talk, based on joint work with Aolin Xu and Sasha Rakhlin, I will discuss several information-theoretic measures of algorithmic stability based on mutual information and erasure mutual information, and illustrate their use for upper-bounding the generalization bias of learning algorithms.

Latin American Week on Coding and Information

Joint work with Venkat Guruswami and Chaoping Xing. Title: Iterated von-Neumann unbiasing and Trace reconstruction for the deletion channel Abstract: In the first part of the talk, I will describe the connections between an efficient unbiasing method from Iterated von-Neumann unbiasing , and polar codes. Joint work with Chong Shangguan. Title: The independence number of the Birkhoff polytope graph, and applications to maximally recoverable codes.

Title : Maximally Recoverable Local Reconstruction Codes Abstract: Protecting huge amounts of data stored in the cloud from server crashes resulted in distributed storage systems transitioning to erasure coding based schemes.

Instead of linear programming, we use a new approach that relies on bounding the first moment of isotropic measures. Joint work with Chris Cox. The real and complex cases are quite different. In this talk, I will briefly introduce the problems in quantum information theory which gave rise to the complex versions of these questions.

I will discuss connections to association schemes, coding theory and finite geometry and I will summarize recent work of my student, Brian Kodalen. Title: The stochastic block model: where we stand Abstract: The talk overviews some of the recent developments on the stochastic block model, staring with the two community case, and extending to multiple communities. We will cover various recovery requirements, phase transitions, algorithms and the information-computation gap.

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Information theory and coding theory with applications to data security and privacy | IML

Time permitting, geometric block models and open problems will be discussed. Title: MDS codes with optimal repair bandwidth Abstract: MDS codes are widely used in distributed storage systems to protect data from node failures, where each storage node stores one coordinate of the codeword. In the event of node failure erasure , the failed erased node connects to the functional nodes and downloads certain amount of data to recover itself.

The repair bandwidth is the smallest amount of data that is needed for the recovery of failed node s. In this talk I will present several simple constructions of MDS codes with optimal repair bandwidth. Title: MDS Codes with Small Sub-packetization and Near-optimal Repair Bandwidth Abstract: Minimum storage regenerating MSR codes form a special sub-class of maximum distance separable MDS codes by providing mechanisms for exact regeneration of a single code-block by downloading the minimum amount of information from the remaining code-blocks.