Yixuan Xie

Coded slotted ALOHA schemes for erasure channels

In this paper we investigate the coded slotted ALOHA (CSA) schemes with repetition codes and maximum distance separable (MDS) codes over erasure channels. We derive the extrinsic information transfer (EXIT) functions of the CSA schemes over erasure channels, which allow an asymptotic analysis of the packet recovering process. Moreover, we define a traffic load threshold provided that the recovered probability is more than a given recovery ratio. The optimal distribution of the codes chosen by users in the CSA schemes is then designed to maximize the peak throughput and traffic load threshold. By performing the asymptotic analysis, we show that our optimal distributions improve the traffic load threshold by 60% for ε = 0.1 and 86% for ε = 0.135 compared to the optimal distribution for collision channels. Using repetition codes as an example, simulation results show that the obtained distributions enhance the peak throughput for erasure channels when both packet erasure channels and slot erasure channels are considered.

Quantum synchronizable codes from quadratic residue codes and their supercodes

Quantum synchronizable codes are quantum error-correcting codes designed to correct the effects of both quantum noise and block synchronization errors. While it is known that quantum synchronizable codes can be constructed from cyclic codes that satisfy special properties, only a few classes of cyclic codes have been proved to give promising quantum synchronizable codes. In this paper, using quadratic residue codes and their supercodes, we give a simple construction for quantum synchronizable codes whose synchronization capabilities attain the upper bound. The method is applicable to cyclic codes of prime length.

Channel identification and its impact on quantum LDPC code performance

In this work we probe the impact of channel estimation on the performance of quantum LDPC codes. Our channel estimation is based on an optimal estimate of the relevant decoherence parameter via its quantum Fisher information. Using state-of-the art quantum LDPC codes designed for the quantum depolarization channel, and utilizing various quantum probes with different entanglement properties, we show how the performance of such codes can deteriorate by an order of magnitude when optimal channel identification is fed into a belief propagation decoding algorithm. Our work highlights the importance in quantum communications of a viable channel identification campaign prior to decoding, and highlights the trade-off between entanglement consumption and quantum LDPC code performance.

Coded Slotted ALOHA for Erasure Channels: Design and Throughput Analysis

In this paper, we investigate the design and analysis of coded slotted ALOHA (CSA) schemes in the presence of channel erasure. We design the code probability distributions for CSA schemes with repetition codes and maximum distance separable codes to maximize the expected traffic load, under both packet erasure channels and slot erasure channels. We derive the extrinsic information transfer (EXIT) functions of CSA schemes over erasure channels. By optimizing the convergence behavior of the derived EXIT functions, the code probability distributions to achieve the maximum expected traffic load are obtained. Then, we derive the asymptotic throughput of CSA schemes over erasure channels. In addition, we validate that the asymptotic throughput can give a good approximation to the throughput of CSA schemes over erasure channels.

Euclidean Geometry-Based Spatially Coupled LDPC Codes for Storage

In this paper, we construct binary spatially coupled (SC) low-density parity-check (LDPC) codes based on Euclidean geometry (EG) LDPC codes for storage applications, where high error correction capability, extremely low uncorrectable bit error rate (UBER), and low decoding complexity are required. We propose a systematic way to construct the families of SC LDPC codes from (m,2s) EG LDPC codes, which are termed EG-SC LDPC codes. In the construction method, we propose a 2-D edge-spreading process to construct the base matrix of EG-SC LDPC codes, which consists of matrix unwrapping and periodically time-varying of a protograph. A lower bound on the rank of the parity-check matrix of an EG-SC LDPC code is derived. We evaluate the error rate performance of the constructed EG-SC LDPC codes by using a weighted bit-flipping decoding algorithm for its low decoding complexity. Numerical results show that the UBER performance of the constructed EG-SC LDPC codes is superior to that of their EG LDPC code counterparts, and show no error floor compared with the constructed protograph SC LDPC codes and regular LDPC codes.

q -Ary Chain-Containing Quantum Synchronizable Codes

We propose a general design of quantum synchronizable codes from classical q-ary cyclic codes. With the aid of classical super/subcodes, the proposed method exploits the idea of chain-containing q-ary cyclic codes when designing quantum synchronizable codes. The distance bound of the resulting quantum synchronizable codes of Calderbank-Shor-Steane (CSS) structure is derived using the representation of Mattson-Solomon polynomial.

Quantum stabilizer codes from difference sets

In this work we have developed a new method to construct general quantum stabilizer codes of variable block size by adopting the notion of a difference set. The proposed method comprises an efficient way to obtain the difference set, and from that set the construction of a quantum stabilizer code, which we refer to as a DSS (Difference Set Stabilizer) code. Our efficient method to generate the difference set requires no computer search, instead only a single parameter is required to generate the set.

Design of rate-compatible protograph-based LDPC codes with mixed circulants

We propose a novel design of rate-compatible protograph-based low-density parity-check code families that can cover a wide range of code rates. In contrast to traditional method of lifting, our lifting method use a combination of different circulant matrix sizes for the base protograph and accumulator to increase the number of achievable rates. We apply this method to an existing code family called AR4JA, which can offer variable rates of R = n+1 over n+2 by process of extension. The proposed codes namely mixed-circulant rate-compatible protograph code (MCRC-PC) can reduce the rate step within the AR4JA family. We show that the proposed codes can also retain many of the favorable properties of protograph codes such as a fast encoder and decoder implementation. A set of length k=1024 MCRC-PC codes is designed with decoding thresholds obtained from multi-edge type density evolution, and simulation results show that the rate compatible code family can achieve good performance under message passing decoding algorithm.

On the design of multi-dimensional irregular repeat-accumulate lattice codes

Most multi-dimensional (more than two dimensions) lattice partitions only form additive quotient groups and lack multiplication operations. This prevents us from constructing lattice codes based on multi-dimensional lattice partitions directly from non-binary linear codes over finite fields. In this paper, we design lattice codes from Construction A lattices where the underlying linear codes are non-binary irregular repeat-accumulate (IRA) codes. Most importantly, our codes are based on multi-dimensional lattice partitions with finite constellations. We propose a novel encoding structure that adds randomly generated lattice sequences to the encoder’s messages, instead of multiplying lattice sequences to the encoder’s messages. We prove that our approach can ensure that the decoder’s messages exhibit permutation-invariance and symmetry properties. With these two properties, the densities of the messages in the iterative decoder can be modeled by Gaussian distributions described by a single parameter. With Gaussian approximation, extrinsic information transfer charts for our multi-dimensional IRA lattice codes are developed and used for analyzing the convergence behavior and optimizing the decoding thresholds. Simulation results show that our codes can approach the unrestricted Shannon limit within 0.46 dB and outperform the previously designed lattice codes with 2-D lattice partitions and existing lattice coding schemes for large codeword length.

Reliable Quantum LDPC Codes over GF(4)

We propose a method of constructing quantum LDPC codes from multiplicative groups of order