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Analysis of Identification for the Binary Symmetric Channel and a comparison to decoding problem

Keywords:
Identification, Binary Symmetric Channel, Communication Complexity

Short Description:
Problem of transmission and Identification over the BSC is investigated and analysed. Further it will be shown that identification would be easier than decoding problem in terms of minimum number of bits of communication

Description

Assuming that the communication channel between two processors P1 and P2 makes an error with probability ε>0, the identification problem is to determine whether P1 and P2 have the same n-bit integer. The decoding problem is for P2 to determine the n-bit integer of P1. For the latter problem we show that given any arbitrarily large constant λ>0, there exists an ε, 0<ε<1/2, for which no scheme requiring less than λn bits of communication can guarantee (for large n) any bound q<1 on the error probability. On the other hand, given any arbitrarily small constant γ>0 and any ε, 0<ε<1/2, the identification problem can be solved with (1+γ)n bits of (one-way) communication with an error probability bounded by c2^{-αn}, where c and α are positive constants. 

Prerequisites

Supervisor:

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Identification Without Randomization for the Discrete Memoryless Channel

Keywords:
Identification, Identification Without Randomization, Complexity of Distributive Computing, One-Way/Two-Way Probabilistic Communications

Short Description:
Identification without randomization for a general DMC would be studied and investigated. Method of coding, decoding sets, type I/II errors and a closed-form solution of non-randomized identification capacity will be considered and analysed.

Description

In theory of Identification introduced by Ahlswede and Dueck the perspective of  communications is changed from decoding to identification, i.e., the receiver is only interested to check whether or not his message was sent by transmitter. Ahslwede and Dueck proved that by means of local randomness (at encoder) they can achieve doubly exponential gain in code size which outperfrom substantially the classical scheme of Shannon transmission. (only exponential gain in code size). However, in many cases, there is no need to exploit the Randomization at encoder and thus the view of identification without randomization is introduced.

On the other hand to derive probabilistic complexity of models for one/two way communications for distributive computing (communication between two processors for determine copperatively value of an identification function) similar ideas were discussed. The student should understand those ideas and try to find the link between them and idea of Identification of Ahlswede and Dueck. Ideally the student attempt to derive forward or/and backward proof for non-randomized identification capacity of a general DMC.

Prerequisites

Supervisor:

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Identification Codes via Strongly Universal Hashing

Keywords:
Identification, binary constant weight codes, epsilon-almost strongly universal classes of hash functions

Short Description:
Identification codes construction though strongly universal class of hash functions is studied and their performance are evaluated.

Description

In contrast to Shannon Theory where code size grows only exponentially, in theory of identification, size of the code is a double exponential function in block length. This extra gain in performance of the code motivates studying of Identification theorems, codes and their explicit code schemes.

Student will understand the basic concept of identification and common applications along with existing explicit code construction method based on idea of binary constant weight codes.

epsilon-almost strongly universal classes of hash functions yield better explicit constructions of identification codes than well known version namely binary constant weight codes. Student should be able to understand how the algebraic definitions of ASU are and why it perform better in terms of code parameters.

Prerequisites

Supervisor:

Student

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Simulation and Analysis of Finite Block-length Wiretap Codes by Autoencoders

Keywords:
Finite Block-length Wiretap Codes, Autoencoders, Finite Block-length Information Theory, Wiretap Codes

Description

Implementaiton of finite block-length wiretap codes by means of Autoencoders should be implemented in Python. Models for training and test of the system model should
be written and curves of result for BLER-Leakage must be obtained. The found codeword via implemented AE should be presented.

Prerequisites

Supervisor:

Student

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Identifying Zeros of a Function

Keywords:
Identifikation, Identifying Zeros of a Function

Short Description:
Implementation of stochastic algorithms for estimation of zeros of a function. Furthermore, relation to identification of zeros of functions and theoretical bound is investigated.

Description

Implement an algorithm for Identification of zeros of a stochastically given function.
An study of Identification's fundamental concepts along with theorems for Identifying zeros of a function as well as analysing the algorithm and results must be presented and obtaind.

Prerequisites

Supervisor:

Student