Related papers: Spectral Graph Analysis of Quasi-Cyclic Codes
Given a random $n \times n$ symmetric matrix $\boldsymbol W$ drawn from the Gaussian orthogonal ensemble (GOE), we consider the problem of certifying an upper bound on the maximum value of the quadratic form $\boldsymbol x^\top \boldsymbol…
Binary-input memoryless channels with a runlength constrained input are considered. Upper bounds to the capacity of such noisy runlength constrained channels are derived using the dual capacity method with Markov test distributions…
In \cite{butman1976} the linear coding scheme is applied, $X_t =g_t\Big(\Theta - {\bf E}\Big\{\Theta\Big|Y^{t-1}, V_0=v_0\Big\}\Big)$, $t=2,\ldots,n$, $X_1=g_1\Theta$, with $\Theta: \Omega \to {\mathbb R}$, a Gaussian random variable, to…
In this paper, we introduce a new definitions of the Gray weight and the Gray map for linear codes over $\mathbb{Z}_9+u\mathbb{Z}_9$ with $u^2=u$. Some results on self-dual codes over this ring are investigated. Further, the structural…
A quantum error correction code is assessed over its ability to correct errors in noisy quantum circuits. This task requires extensive simulations of faulty quantum circuits, which are often made tractable by considering stochastic Pauli…
This paper is concerned with bounds on the maximum-likelihood (ML) decoding error probability of Reed-Solomon (RS) codes over additive white Gaussian noise (AWGN) channels. To resolve the difficulty caused by the dependence of the Euclidean…
Linear codes are considered over the ring $\mathbb{Z}_4+v\mathbb{Z}_4$, where $v^2=v$. Gray weight, Gray maps for linear codes are defined and MacWilliams identity for the Gray weight enumerator is given. Self-dual codes, construction of…
This paper considers the problem of closed-loop identification of linear scalar systems with Gaussian process noise, where the system input is determined by a deterministic state feedback policy. The regularized least-square estimate (LSE)…
We give sufficient conditions for self-orthogonality with respect to symplectic, Euclidean and Hermitian inner products of a wide family of quasi-cyclic codes of index two. We provide lower bounds for the symplectic weight and the minimum…
We consider the problem of transmission of a sequence of real data produced by a Nyquist sampled band-limited analog source over a band-limited analog channel, which introduces an additive white Gaussian noise. An analog coding scheme is…
For $q,n,d \in \mathbb{N}$, let $A_q^L(n,d)$ denote the maximum cardinality of a code $C \subseteq \mathbb{Z}_q^n$ with minimum Lee distance at least $d$, where $\mathbb{Z}_q$ denotes the cyclic group of order $q$. We consider a…
We analyze permutation routing of rigid blocks representing surface code patches of $d_C^2$ atoms on a reconfigurable lattice with hypergraph transformations. For a hypergraph $H$, code distance $d_C$, $s=d_C^2$, number of blocks $N_L$, and…
We propose an approach for optimizing nonbinary (NB) quasi-cyclic (QC) LDPC codes. This approach combines constructing of base parity-check matrices by simulated annealing and labeling the obtained base matrices aimed at maximizing the…
In this paper, we study the structure of cyclic, quasi-cyclic, constacyclic codes and their skew codes over the finite ring R=Z_3+vZ_3+v^2Z_3, v^3=v. The Gray images of cyclic, quasi-cyclic, skew cyclic, skew quasi-cyclic and skew…
A quasi-complementary sequence set (QCSS) refers to a set of two-dimensional matrices with low non-trivial aperiodic auto- and cross- correlation sums. For multicarrier code-division multiple-access applications, the availability of large…
In a recent paper [1] an improved analysis concerning the analysis of List Decoding was presented. The event that the correct codeword is excluded from the list is central. For the additive white Gaussian noise (AWGN) channel an important…
Quasi-cyclic (QC) low-density parity-check (LDPC) codes are an important instance of proto-graph-based LDPC codes. In this paper we present upper bounds on the minimum Hamming distance of QC LDPC codes and study how these upper bounds…
An $(n,k,r)$ \emph{locally repairable code} (LRC) is an $[n,k,d]$ linear code where every code symbol can be repaired from at most $r$ other code symbols. An LRC is said to be optimal if the minimum distance attains the Singleton-like bound…
We investigate linear codes over the ring $\mathbb{Z}_4 + u\mathbb{Z}_4 + v\mathbb{Z}_4 + w\mathbb{Z}_4 + uv\mathbb{Z}_4 + uw\mathbb{Z}_4 + vw\mathbb{Z}_4 + uvw\mathbb{Z}_4$, with conditions $u^2=u$, $v^2=v$, $w^2=w$, $uv=vu$, $uw=wu$ and…
We investigate the Peak-Power Limited (PPL) Additive White Gaussian Noise (AWGN) channels in which the signal is band-limited, and its instantaneous power cannot exceed the power P. This model is relevant to many communication systems;…