Multi-stage code generator and decoder for communication systems
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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 ...
A communications system includes an encoder that produces a plurality of redundant symbols. For a given key, an output symbol is generated from a combined set of symbols including the input symbols and the redundant symbols. The output symbols are generall ...
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 ...
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 ...
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 ...
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, ...
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 ...
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 ...
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 ...
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 ...
