Related papers: New Communication Models and Decoding of Maximum R…
In this paper we introduce the class of Spread Codes for the use in random network coding. Spread Codes are based on the construction of spreads in finite projective geometry. The major contribution of the paper is an efficient decoding…
The weighted-Hamming metric generalizes the Hamming metric by assigning different weights to blocks of coordinates. It is well-suited for applications such as coding over independent parallel channels, each of which has a different level of…
Scattered polynomials of a given index over finite fields are intriguing rare objects with many connections within mathematics. Of particular interest are the exceptional ones, as defined in 2018 by the first author and Zhou, for which…
This paper presents Bit-Interleaved Coded Modulation metrics for joint estimation detection using training or reference signal transmission strategies for short to long block length channels. We show that it is possible to enhance the…
The code that combines channel estimation and error protection has received general attention recently, and has been considered a promising methodology to compensate multi-path fading effect. It has been shown by simulations that such code…
In practice, LDPC codes are decoded using message passing methods. These methods offer good performance but tend to converge slowly and sometimes fail to converge and to decode the desired codewords correctly. Recently, tree-reweighted…
In this note, we provide a description of the elements of minimum rank of a generalized Gabidulin code in terms of Grassmann coordinates. As a consequence, a characterization of linearized polynomials of rank at most $n-k$ is obtained, as…
Recursive decoding techniques are considered for Reed-Muller (RM) codes of growing length $n$ and fixed order $r.$ An algorithm is designed that has complexity of order $n\log n$ and corrects most error patterns of weight up to…
A new algorithm for efficient exact maximum likelihood decoding of polar codes (which may be CRC augmented), transmitted over the binary erasure channel, is presented. The algorithm applies a matrix triangulation process on a sparse polar…
In this paper, we investigate completely decomposable rank-metric codes, i.e. rank-metric codes that are the direct sum of 1-dimensional maximum rank distance codes. We study the weight distribution of such codes, characterizing codewords…
It is well known that for Gaussian channels, a nearest neighbor decoding rule, which seeks the minimum Euclidean distance between a codeword and the received channel output vector, is the maximum likelihood solution and hence…
In this paper we study spread codes: a family of constant-dimension codes for random linear network coding. In other words, the codewords are full-rank matrices of size (k x n) with entries in a finite field F_q. Spread codes are a family…
Exponential error bounds for the finite-alphabet interference channel (IFC) with two transmitter-receiver pairs, are investigated under the random coding regime. Our focus is on optimum decoding, as opposed to heuristic decoding rules that…
This paper presents general bounds on the highest achievable rate for list-decodable insertion-deletion codes. In particular, we give novel outer and inner bounds for the highest achievable communication rate of any insertion-deletion code…
We consider decoding of vertically homogeneous interleaved sum-rank-metric codes with high interleaving order $s$, that are constructed by stacking $s$ codewords of a single constituent code. We propose a Metzner--Kapturowski-like decoding…
We define a class of automorphisms of rational function fields of finite characteristic and employ these to construct different types of optimal linear rank-metric codes. The first construction is of generalized Gabidulin codes over…
Random network coding recently attracts attention as a technique to disseminate information in a network. This paper considers a non-coherent multi-shot network, where the unknown and time-variant network is used several times. In order to…
A bound on the maximum information transmission rate through a cascade of Gaussian links is presented. The network model consists of a source node attempting to send a message drawn from a finite alphabet to a sink, through a cascade of…
This paper examines the maximum code rate achievable by a data-driven communication system over some unknown discrete memoryless channel in the finite blocklength regime. A class of channel codes, called learning-based channel codes, is…
In this paper, new techniques are presented to either simplify or improve most existing upper bounds on the maximum-likelihood (ML) decoding performance of the binary linear codes over additive white Gaussian noise (AWGN) channels. Firstly,…