Xueqin Jiang

Large Girth Non-Binary LDPC Codes Based on Finite Fields and Euclidean Geometries

This letter presents an approach to the construction of non-binary low-density parity-check (LDPC) codes based on alpha-multiplied circulant permutation matrices and hyperplanes of two different dimensions in Euclidean geometries. Codes constructed by this method have large girth and high binary column weight when the order of Galois field is high. Simulation results show that these codes perform very well with fast Fourier transform (FFT) based sum-product algorithm (SPA).

Application of nonbinary LDPC codes based on Euclidean geometries to MIMO systems

This paper first presents an approach to the construction of non-binary low-density parity-check (LDPC) codes based on Euclidean geometries. Codes constructed by this method have multiple code rates and a constant code length. With the proposed codes, the MIMO systems can also support different data rate with the same basic structure. Simulation results show that these codes perform very well with either joint or separate MIMO detection and channel decoding. The complexity comparison shows that the nonbinary coded MIMO systems have lower complexity at the receiver side.

Semi-Random and Quasi-Cyclic LDPC Codes Based on Multiple Parity-Check Codes

This paper introduces a class of Semi-Random (SR) Low-Density Parity-Check (LDPC) codes and a class of Quasi-Cyclic (QC) LDPC codes. Both of them are derived from Multiple Serially Concatenated Multiple Parity-Check (M-SC-MPC) codes and interleavers, therefore, have low encoding complexities. These two codes are called M-SR-LDPC codes and M-QC-LDPC codes, respectively, in this paper. The M-SR-LDPC codes are designed with the modified Progressive Edge-Growth (PEG) algorithm and the M-QC-LDPC codes are designed with the existing cycle-condition formula. Consequently, the proposed codes have large girths. Simulation results show that our codes perform very well over the AWGN channel with iterative decoding.

Modified Progressive Edge-Growth Algorithm for Fast-Encoding LDPC Codes

Progressive edge-growth (PEG) algorithm is known to construct low-density parity-check (LDPC) codes at finite code lengths with large girths. A simple variation of the PEG algorithm, linear-encoding PEG (LPEG) algorithm, can be applied to generate linear encodable LDPC codes. This paper presents a modified LPEG algorithm to construct fast encodable LDPC codes with a certain girth constraint. The presented fast encodable LDPC codes facilitate the parallel encoding processes for parity bit generations. Therefore, their encoding time is much shorter than that of LPEG codes.

Design of irregular quasi-cyclic LDPC codes based on Euclidean geometries

This paper presents an approach to the construction of low-density parity-check (LDPC) codes based on hyperplanes (μ-flats) of different dimensions in Euclidean geometries. Codes constructed by this method have quasicyclic and irregular structure. The degree distributions of these codes are optimized by the curve fitting approach in the extrinsic information transfer (EXIT) charts. By constraining the fraction of degree-2 nodes, we can lower the error floor at the cost of a small increase in the threshold SNR. Simulation results show that these codes perform very well at both of waterfall region and the error floor region with the iterative decoding.

Iteratively Suboptimum Decoder Design for Distributed Space-Time Coding Based on Distributed Interleavers

In [1], the authors have presented a detailed analysis on the problem of distributed space-time coding employing Amplify-and-Forward (AF) protocol for a synchronized wireless relay networks, where maximum likelihood (ML) decoding is employed. In this paper, an iterative turbo-like decoder is introduced to improve system performance by allocating interleavers at each relay node and using multiuser concept. Due to different overall channel gains consisting source-relay link and relay-destination link, ordering and canceling techniques of interferences are considered in our design. Simulation results show an accepted improvement in the high SNR region.

Low-density MIMO codes based on multiple parity-check codes

In this paper, a new approach to construct LDMC codes is introduced. The new codes can be encoded efficiently at the transmitter side and support both of the inner-iterations and outer-iterations at the receiver side. Furthermore they can achieve the design rates and perform very well over MIMO channels.

A combined decoder for STBC and non-binary LDPC codes with spatial diversity

The main problem to apply the non-binary low-density parity (LDPC) codes in multiple-input multiple-output (MIMO) channel with a high order Galois field is to compute the log likelihood ratios (LLRs) for each transmitted symbol. The complexity of computation of LLRs grows exponentially with the number of the order of the Galois field. In this paper, we combine the space-time block coding (STBC) decoder with the LDPC decoder together to achieve the full diversity in MIMO channels. In order to reduce the complexity of computation of LLRs, the multiuser concept is used in our design. Consequently, the complexity grows only linearly with the number of the order of the Galois field. The simulations show that the BER curve exits an accepted gap (0–1dB).

Modified fast Hadamard transform based belief propagation decoding algorithm

In this paper, we propose a new fast Hadamard transform based the belief-propagation (BP) decoding algorithm over GF (2p ) with a modification of the permutations between the check nodes and variable nodes. This scheme is mathematically equivalent to the conventional BP decoding algorithm, but complexity of the proposed scheme is lower. We show by simulation that the non-binary regular and irregular LDPC codes in GF (2p ) have good performance with our proposed modified BP decoding algorithm.

Codes From Generalized Hadamard Matrices

The Hadamard Matrices are widely used in communication systems, data compression, error control coding, cryptography, linear filtering and spectral analysis. Such a popularity of Hadamard matrices is explained by their simplicity and efficiency in a variety of concrete practical realizations. In this paper we consider a family {H_m}, m =1,2,.., of generalized Hadamard matrices of order p^m , where p is a prime number, and construct the corresponding family {C^*m} of generalized p-ary Hadamard codes which meet the Plotkin bound.