Quantum error-correcting codes from matrix-product codes related to quasi-orthogonal and quasi-unitary matrices

Simple Rate-1/3 Convolutional and Tail-Biting Quantum Error-Correcting Codes

Simple rate-1/3 single-error-correcting unrestricted and CSS-type quantum convolutional codes are constructed from classical self-orthogonal $\F_4$-linear and $\F_2$-linear convolutional codes, respectively. These quantum convolutional codes have higher rate than comparable quantum block codes or previous quantum convolutional codes, and are simple to decode. A block single-error-correcting [9, 3, 3] tail-biting code is derived from the unrestricted convolutional code, and similarly a [15, 5, 3] CSS-type block code from the CSS-type convolutional code.

On Galois hulls of linear codes and new entanglement-assisted quantum error-correcting codes

The Galois hull of a linear code is the intersection of itself and its Galois dual code, which has aroused the interest of researchers in these years. In this paper, we study Galois hulls of linear codes. Firstly, the symmetry of the dimensions of Galois hulls of linear codes is found. Some new necessary and sufficient conditions for linear codes being Galois self-orthogonal codes, Galois self-dual codes, and Galois linear complementary dual codes are characterized. Then, we propose explicit methods to construct Galois self-orthogonal codes of larger length from given Galois self-orthogonal co…

Quantum Stabilizer Codes from Maximal Curves

A curve attaining the Hasse-Weil bound is called a maximal curve. Usually classical error-correcting codes obtained from a maximal curve have good parameters. However, the quantum stabilizer codes obtained from such classical error-correcting codes via Euclidean or Hermitian self-orthogonality do not always possess good parameters. In this paper, the Hermitian self-orthogonality of algebraic geometry codes obtained from two maximal curves is investigated. It turns out that the stabilizer quantum codes produced from such Hermitian self-orthogonal classical codes have good parameters.

Block-Level Unitary Query: Incorporating Orthogonal-like Space-time Code with Query Diversity for MIMO Backscatter RFID

Because of the emerging field of Internet of Things (IoT), future backscatter RFID is required to be more reliable and data intensive. Motivated by this, orthogonal space-time block code (OSTBC), which is very successful in mobile communications for its low complexity and high performance, has already been investigated for backscatter RFID. On the other hand, a recently proposed scheme called unitary query was shown to be able to considerably improve the reliability of backscatter radio by exploiting query diversity. Therefore incorporating the classical OSTBC (at the tag end) with the recentl…

Concatenating Decoherence Free Subspaces with Quantum Error Correcting Codes

An operator sum representation is derived for a decoherence-free subspace (DFS) and used to (i) show that DFSs are the class of quantum error correcting codes (QECCs) with fixed, unitary recovery operators, and (ii) find explicit representations for the Kraus operators of collective decoherence. We demonstrate how this can be used to construct a concatenated DFS-QECC code which protects against collective decoherence perturbed by independent decoherence. The code yields an error threshold which depends only on the perturbing independent decoherence rate.

一类优良自正交准循环码无限族的构造

A Construction of Infinite Families of Good Self-Orthogonal Quasi-Cyclic Codes

本文通过域扩张上的组成码构造了无限族准循环码，使其在欧几里得和内积下自正交，并计算了维数和最小距离的平方根型下界，进而利用CSS构造得到参数良好的量子纠错码。

Convolutional and tail-biting quantum error-correcting codes

Rate-(n-2)/n unrestricted and CSS-type quantum convolutional codes with up to 4096 states and minimum distances up to 10 are constructed as stabilizer codes from classical self-orthogonal rate-1/n F_4-linear and binary linear convolutional codes, respectively. These codes generally have higher rate and less decoding complexity than comparable quantum block codes or previous quantum convolutional codes. Rate-(n-2)/n block stabilizer codes with the same rate and error-correction capability and essentially the same decoding algorithms are derived from these convolutional codes via tail-biting.

Steepest Gradient-Based Orthogonal Precoder For Integer-Forcing MIMO

In this paper, we develop an orthogonal precoding scheme for integer-forcing (IF) linear receivers using the steepest gradient algorithm. Although this scheme can be viewed as a special case of the unitary precoded integer-forcing (UPIF), it has two major advantages. First, the orthogonal precoding outperforms its unitary counterpart in terms of achievable rate, outage probability, and error rate. We verify this advantage via theoretical and numerical analyses. Second, it exhibits lower complexity as the dimension of orthogonal matrices is half that of unitary matrices in the real-valued domai…

Performance Analysis of Massive MIMO Networks with Random Unitary Pilot Matrices

A common approach to obtain channel state information for massive MIMO networks is to use the same orthogonal training sequences in each cell. We call this the full-pilot reuse (FPR) scheme. In this paper, we study an alternative approach where each cell uses different sets of orthogonal pilot (DOP) sequences. Considering uplink communications with matched filter (MF) receivers, we first derive the SINR in the large system regime where the number of antennas at the base station, the number of users in each cell, and training duration grow large with fixed ratios. For tractability in the analys…

Iterative Detection for Orthogonal Time Frequency Space Modulation with Unitary Approximate Message Passing

The orthogonal-time-frequency-space (OTFS) modulation has emerged as a promising modulation scheme for high mobility wireless communications. To harvest the time and frequency diversity promised by OTFS, some promising detectors, especially message passing based ones, have been developed by taking advantage of the sparsity of the channel in the delay-Doppler domain. However, when the number of channel paths is relatively large or fractional Doppler {shifts have} to be considered, the complexity of existing detectors is a concern, and the message passing based detectors may suffer from performa…

在阶为25的交换非酉环上自正交码的构造

Construction of self-orthogonal codes over a commutative non-unitary ring of order 25

研究阶为25的交换非酉环\(I_5\)上的线性码，定义三类线性\(I_5\) - 码并研究其结构，对长度至多为4的三类码进行单项式等价完全分类，同时纠正了\(I_5\)上拟自对偶码分类的错误。