Multi-stage code generator and decoder for communication systems

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The beginning of 21st century provided us with many answers about how to reach the channel capacity. Polarization and spatial coupling are two techniques for achieving the capacity of binary memoryless symmetric channels under low-complexity decoding algor ...

We give a direct construction of a specific central idempotent in the endomorphism algebra of a finite lattice T. This idempotent is associated with all possible sublattices of T which are totally ordered. A generalization is considered in a conjectural fa ...

The Boolean lattice (2[n],subset of) is the family of all subsets of [n]={1,MIDLINE HORIZONTAL ELLIPSIS,n}, ordered by inclusion. Let P be a partially ordered set. We prove that if n is sufficiently large, then there exists a packing P of copies of P in (2 ...

Coding techniques have been well studied and used for improving communication quality by combating noise and mitigating interference. Recently, it has been shown that the same coding techniques can also be exploited to further improve communication perform ...

In any communication system, there exist two dimensions through which the information at the source becomes distorted before reaching the destination: the noisy channel and time. Messages transmitted through a noisy channel are susceptible to modification ...

Let P be a partially ordered set. The function La* (n, P) denotes the size of the largest family F subset of 2([n]) that does not contain an induced copy of P. It was proved by Methuku and Palvolgyi that there exists a constant C-P (depending only on P) su ...

Consider the problem of constructing a polar code of block length N for a given transmission channel W. Previous approaches require one to compute the reliability of the N synthetic channels and then use only those that are sufficiently reliable. However, ...

Deep unfolding is a method of growing popularity that fuses iterative optimization algorithms with tools from neural networks to efficiently solve a range of tasks in machine learning, signal and image processing, and communication systems. This survey sum ...

In his landmark paper "A Mathematical Theory of Communication," the founding father of information theory and coding theory, Claude E. Shannon, established the largest rate at which reliable communication is possible and he revealed that the key to this re ...

Let P be a partially ordered set. If the Boolean lattice (2[n],⊂) can be partitioned into copies of P for some positive integer n, then P must satisfy the following two trivial conditions: (1) the size of P is a power of 2, (2) P has a unique maximal and m ...

We consider the dynamics of message passing for spatially coupled codes and, in particular, the set of density evolution equations that tracks the profile of decoding errors along the spatial direction of coupling. It is known that, for suitable boundary c ...

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A method of encoding data for transmission from a source to a destination over a communications channel is provided. The method operates on an ordered set of input symbols and includes generating a plurality of redundant symbols from the input symbols base ...

While both fundamental limits and system implementations are well understood for the point-to-point communication system, much less is developed for general communication networks. This thesis contributes towards the design and analysis of advanced coding ...

The year 2016, in which I am writing these words, marks the centenary of Claude Shannon, the father of information theory. In his landmark 1948 paper "A Mathematical Theory of Communication", Shannon established the largest rate at which reliable communica ...

Polar codes are a new class of block codes with an explicit construction that provably achieve the capacity of various communications channels, even with the low-complexity successive-cancellation (SC) decoding algorithm. Yet, the more complex successive-c ...

Polar codes are an exciting new class of error correcting codes that achieve the symmetric capacity of memoryless channels. Many decoding algorithms were developed and implemented, addressing various application requirements: from error-correction performa ...

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The general subject considered in this thesis is a recently discovered coding technique, polar coding, which is used to construct a class of error correction codes with unique properties. In his ground-breaking work, Arikan proved that this class of codes, ...

For positive integers w and k, two vectors A and B from Z(w) are called k-crossing if there are two coordinates i and j such that A[i] - B[i] >= k and B[j] - A[j] >= k. What is the maximum size of a family of pairwise 1-crossing and pairwise non-k-crossing ...

Multi-stage code generator and decoder for communication systems

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