Related papers: Computational Complexity of Decoding Orthogonal Sp…
Optimal (v, 4, 2, 1) optical orthogonal codes (OOC) with $v<=75$ and $v\ne 71$ are classified up to equivalence. One $(v, 4, 2, 1)$ OOC is presented for all $v\le 181$, for which an optimal OOC exists.
Quantum convolutional code was introduced recently as an alternative way to protect vital quantum information. To complete the analysis of quantum convolutional code, I report a way to decode certain quantum convolutional codes based on the…
In this paper we present an alternative separable implementation of L2-orthogonal space-time codes (STC) for continuous phase modulation (CPM). In this approach, we split the STC CPM transmitter into a single conventional CPM modulator and…
The most famous error-decoding algorithm for convolutional codes is the Viterbi algorithm. In this paper, we present a new reduced complexity version of this algorithm which can be applied to a class of binary convolutional codes with…
When a neural network (NN) is used to decode a polar code, its training complexity scales exponentially as the code block size (or to be precise, as a number of message bits) increases. Therefore, existing solutions that use a neural…
Quantum error correction (QEC) is critical for scalable fault-tolerant quantum computing. Topological codes, such as the toric code, offer hardware-efficient architectures but their Tanner graphs contain many girth-4 cycles that degrade the…
In this report, we describe three encodings of the multiple constant multiplication (MCM) problem to pseudo-boolean satisfiability (PBS), and introduce an algorithm to solve the MCM problem optimally. To the best of our knowledge, the…
Quantum technologies have the potential to solve certain computationally hard problems with polynomial or super-polynomial speedups when compared to classical methods. Unfortunately, the unstable nature of quantum information makes it prone…
Graphs with high symmetry or regularity are the main source for experimentally hard instances of the notoriously difficult graph isomorphism problem. In this paper, we study the computational complexity of isomorphism testing for line…
We consider the sets of dimensions for which there is an optimal sphere packing with special regularity properties (respectively, a lattice, or a periodic set with a given bound on the number of translations, or an arbitrary periodic set).…
A fundamental problem in shape matching and geometric similarity is computing the maximum area overlap between two polygons under translation. For general simple polygons, the best-known algorithm runs in $O((nm)^2 \log(nm))$ time [Mount,…
We obtain a characterization on self-orthogonality for a given binary linear code in terms of the number of column vectors in its generator matrix, which extends the result of Bouyukliev et al. (2006). As an application, we give an…
We consider the problem of triangulating a polygon with $n$ vertices and $h$ holes, or relatedly the problem of computing the trapezoidal decomposition of a collection of $h$ disjoint simple polygonal chains with $n$ vertices total.…
The surface code is a promising platform for a quantum memory, but its threshold under coherent errors remains incompletely understood. We study maximum-likelihood decoding of the square-lattice surface code in the presence of single-qubit…
The exponential speedups promised by Hamiltonian simulation on a quantum computer depends crucially on structure in both the Hamiltonian $\hat{H}$, and the quantum circuit $\hat{U}$ that encodes its description. In the quest to better…
In this paper, we further investigate the constructions on three-dimensional $(u\times v\times w,k,1)$ optical orthogonal codes with the at most one optical pulse per wavelength/time plane restriction (briefly AM-OPP $3$-D $(u\times v\times…
We classify the time complexities of three important decoding problems for quantum stabilizer codes. First, regardless of the channel model, quantum bounded distance decoding is shown to be NP-hard, like what Berlekamp, McEliece and Tilborg…
Classical low-density parity-check (LDPC) codes are a widely deployed and well-established technology, forming the backbone of modern communication and storage systems. It is well known that, in this classical setting, increasing the girth…
We show that approximating the trace norm contraction coefficient of a quantum channel within a constant factor is NP-hard. Equivalently, this shows that determining the optimal success probability for encoding a bit in a quantum system…
In this paper will be presented methodology of encoding information in valuations of discrete lattice with some translational invariant constrains in asymptotically optimal way. The method is based on finding statistical description of such…