arXiv subjects

Jun Heo

Publications and source records attributed to Jun Heo.

21 records · Page 2Linked to original sources

arXiv2012

Codeword stabilized quantum codes on subsystems

Codeword stabilized quantum codes provide a unified approach to constructing quantum error-correcting codes, including both additive and non-additive quantum codes. Standard codeword stabilized quantum codes encode quantum information into subspaces. The more general notion of encoding quantum information into a subsystem is known as an operator (or subsystem) quantum error correcting code. Most operator codes studied to date are based in the usual stabilizer formalism. We introduce operator quantum codes based on the codeword stabilized quantum code framework. Based on the necessary and sufficient conditions for operator quantum error correction, we derive a error correction condition for operator codeword stabilized quantum codes. Based on this condition, the word operators of a operator codeword stabilized quantum code are constructed from a set of classical binary errors induced by generators of the gauge group. We use this scheme to construct examples of both additive and non-additive codes that encode quantum information into a subsystem.

quant-ph↗

arXiv2011

Entanglement-assisted codeword stabilized quantum codes

Entangled qubit can increase the capacity of quantum error correcting codes based on stabilizer codes. In addition, by using entanglement quantum stabilizer codes can be construct from classical linear codes that do not satisfy the dual-containing constraint. We show that it is possible to construct both additive and non-additive quantum codes using the codeword stabilized quantum code framework. Nonadditive codes may offer improved performance over the more common sta- bilizer codes. Like other entanglement-assisted codes, the encoding procedure acts only the qubits on Alice's side, and only these qubits are assumed to pass through the channel. However, errors the codeword stabilized quantum code framework gives rise to effective Z errors on Bob side. We use this scheme to construct new entanglement-assisted non-additive quantum codes, in particular, ((5,16,2;1)) and ((7,4,5;4)) codes.

quant-ph↗

arXiv2010

Pair-wise Markov Random Fields Applied to the Design of Low Complexity MIMO Detectors

Pair-wise Markov random fields (MRF) are considered for application to the development of low complexity, iterative MIMO detection. Specifically, we consider two types of MRF, namely, the fully-connected and ring-type. For the edge potentials, we use the bivariate Gaussian function obtained by marginalizing the posterior joint probability density under the Gaussian assumption. Since the corresponding factor graphs are sparse, in the sense that the number of edges connected to a factor node (edge degree) is only 2, the computations are much easier than that of ML, which is similar to the belief propagation (BP), or sum-product, algorithm that is run over the fully connected factor graph. The BER performances for non-Gaussian input are evaluated via simulation, and the results show the validity of the proposed algorithms. We also customize the algorithm for Gaussian input to obtain the Gaussian BP that is run over the two MRF and proves its convergence in mean to the linear MMSE estimates. The result lies on the same line of those in [16] and [24], but with differences in its graphical model and the message passing rule. Since the MAP estimator for the Gaussian input is equivalent to the linear MMSE estimator, it shows the optimality, in mean, of the scheme for Gaussian input.

cs.IT↗