Related papers: Complementary Sets, Generalized Reed-Muller Codes,…
Reed-Muller codes encode an $m$-variate polynomial of degree $r$ by evaluating it on all points in $\{0,1\}^m$. We denote this code by $RM(m,r)$. The minimal distance of $RM(m,r)$ is $2^{m-r}$ and so it cannot correct more than half that…
We introduce the notion of fault-tolerant quantum metrology to overcome noise beyond our control -- associated with sensing the parameter, by reducing the noise in operations under our control -- associated with preparing and measuring…
Golay complementary set (GCS) plays a vital role in reducing peak-to-mean envelope power ratio (PMEPR) in orthogonal frequency division multiplexing (OFDM). A more general version of GCS is a multiple shift complementary set (MSCS), where…
Errors are inevitable during all kinds quantum informational tasks and quantum error-correcting codes (QECCs) are powerful tools to fight various quantum noises. For standard QECCs physical systems have the same number of energy levels.…
Phase-noise (PN) estimation and compensation are crucial in millimeter-wave (mmWave) communication systems to achieve high reliability. The PN estimation, however, suffers from high computational complexity due to its fundamental…
In recent years, complementary sequence sets have found many important applications in multi-carrier code-division multiple-access (MC-CDMA) systems for their good correlation properties. In this paper, we propose a construction, which can…
We present analytical results on the effect of pointing errors on the average bit-error probability (ABEP) of optically pre-amplified pulse-position modulation (PPM) receivers. The results show that the beam width plays a key role in the…
Current implementations of OFDM/OQAM are restricted to band-limited symmetric filters. To circumvent this, non-symmetric conjugate root (CR) filters are proposed for OQAM modulation. The system is applied to Generalized Frequency Division…
Universally decodable matrices (UDMs) can be used for coding purposes when transmitting over slow fading channels. These matrices are parameterized by positive integers $L$ and $N$ and a prime power $q$. The main result of this paper is…
Advances in single photon creation, transmission, and detection suggest that sending quantum information over optical fibers may have losses low enough to be correctable using a quantum error correcting code. Such error-corrected…
Orthogonal Frequency Division Multiplexing (OFDM) is an attractive modulation and multiple access techniques for channels with a nonflat frequency response, as it saves the need for complex equalizers. It can offer high quality performance…
We show that quantum expander codes, a constant-rate family of quantum LDPC codes, with the quasi-linear time decoding algorithm of Leverrier, Tillich and Z\'emor can correct a constant fraction of random errors with very high probability.…
In quantum communication via noisy channels, the error probability scales exponentially with the length of the channel. We present a scheme of a quantum repeater that overcomes this limitation. The central idea is to connect a string of…
This paper studies an energy efficient design of precoders for point-to-point multiple-input-multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems. Differently from traditional approaches, the optimal power…
Orthogonal geometric constructions are the basis of many many quantum error-correcting codes (QEC), but strict orthogonality constraints limit design flexibility and resource efficiency. We introduce a quasi-orthogonal geometric framework…
This paper studies coding schemes for the $q$-ary symmetric channel based on binary low-density parity-check (LDPC) codes that work for any alphabet size $q=2^m$, $m\in\mathbb{N}$, thus complementing some recently proposed packet-based…
The classical majority-logic decoder proposed by Reed for Reed-Muller codes RM(r, m) of order r and length 2^m, unfolds in r+1 sequential steps, decoding message symbols from highest to lowest degree. Several follow-up decoding algorithms…
Motivated by applications in in-vivo DNA storage, we study codes for correcting duplications. A reverse-complement duplication of length $k$ is the insertion of the reversed and complemented copy of a substring of length $k$ adjacent to its…
The proximal generalized alternating direction method of multipliers (p-GADMM) is substantially efficient for solving convex composite programming problems of high-dimensional to moderate accuracy. The global convergence of this method was…
Detection algorithms for multiple-input multiple-output (MIMO) wireless systems based on orthogonal frequency-division multiplexing (OFDM) typically require the computation of a QR decomposition for each of the data-carrying OFDM tones. The…