Baoming Bai

Low Complexity X-EMS Algorithms for Nonbinary LDPC Codes

The extended min-sum (EMS) algorithm is redescribed as a reduced-search trellis algorithm (called M-EMS algorithm). Two variants of the M-EMS algorithm, called T-EMS algorithm and D-EMS algorithm, are presented. Simulation results show that, these three algorithms (referred to as X-EMS algorithms for convenience), combined with factor correction techniques, perform almost as well as the Q-ary sum-product algorithm (QSPA) but with a much lower complexity.

A Class of Nonbinary LDPC Codes with Fast Encoding and Decoding Algorithms

This letter is concerned with a class of nonbinary low-density parity-check (LDPC) codes, referred to as column-scaled LDPC (CS-LDPC) codes, whose parity-check matrices have a property that each column is a scaled binary vector. The CS-LDPC codes, which include algebraically constructed nonbinary LDPC codes as subclasses, admit fast encoding and decoding algorithms. Specifically, for a code over the finite field F2p, the encoder can be implemented with p parallel binary LDPC encoders followed by a series of bijective mappers, while the decoder can be implemented with an iterative decoder in which no message permutations are required during the iterations. In addition, there exist low-complexity iterative multistage decoders that can be utilized to trade off the performance against the complexity. Simulation results show that the performance degradation caused by the iterative multistage decoding algorithms is relevant to the code structure.

Construction of nonbinary quasi-cyclic LDPC cycle codes based on singer perfect difference set

A low-density parity-check (LDPC) code whose parity-check matrix consists of weight-2 columns is known as a cycle code. In this letter, we propose a construction of nonbinary quasi-cyclic (QC) LDPC cycle codes based on Singer perfect difference set. The Tanner graph has girth 12 and the code length achieves the Gallager lower bound. We further show that constructed codes have exactly a minimum symbol Hamming distance 6. Simulation results show that the proposed codes perform better than random nonbinary LDPC cycle codes.

Nonbinary LDPC codes constructed based on a cyclic MDS code and a low-complexity nonbinary message-passing decoding algorithm

In this letter, we propose a construction of nonbinary quasi-cyclic low-density parity-check (QC-LDPC) codes based on a cyclic maximum distance separable (MDS) code. The parity-check matrices are significantly rank deficient square matrices and their Tanner graphs have a girth of at least 6. The minimum distances of the codes are very respectable as far as LDPC codes are concerned. Based on plurality voting and iterative mechanism, a low-complexity nonbinary massage-passing decoding algorithm is proposed. It only requires finite field operations, integer additions and integer comparisons. Simulation results show that the decoding algorithm is fit for the proposed codes, providing efficient trade-offs between performance and decoding complexity, which suggests that the coding scheme may find some applications in communication or storage systems with high-speed and low-power consumption requirements.

A new ensemble of rate-compatible LDPC codes

In this paper, we presented three approaches to improve the design of Kite codes (newly proposed rateless codes), resulting in an ensemble of rate-compatible LDPC codes with code rates varying “continuously” from 0.1 to 0.9 for additive white Gaussian noise (AWGN) channels. The new ensemble rate-compatible LDPC codes can be constructed conveniently with an empirical formula. Simulation results show that, when applied to incremental redundancy hybrid automatic repeat request (IR-HARQ) system, the constructed codes (with higher order modulation) perform well in a wide range of signal-to-noise-ratios (SNRs).

Spatial Coupling of Generator Matrices: A General Approach to Design Good Codes at a Target BER

For any given short code (referred to as the basic code), block Markov superposition transmission (BMST) provides a simple way to obtain predictable extra coding gain by spatially coupling the generator matrix of the basic code. This paper presents a systematic design methodology for BMST systems to approach the channel capacity at any given target bit error rate (BER) of interest. To simplify the design, we choose the basic code as the Cartesian product of a short block code. The encoding memory is then inferred from the genie-aided lower bound according to the performance gap of the short block code to the corresponding Shannon limit at the target BER. In addition to the sliding-window decoding algorithm, we propose to perform one more phase decoding to remove residual (rare) errors. A new technique that assumes a noisy genie is proposed to upper bound the performance. Under some mild assumptions, these genie-aided bounds can be used to predict the performance of the proposed two-phase decoding algorithm in the extremely low BER region. Using the Cartesian product of a repetition code as the basic code, we construct a BMST system with an encoding memory 30 whose performance at the BER of 10-15 can be predicted within 1 dB away from the Shannon limit over the binary-input additive white Gaussian noise channel.

Comparisons Between Reliability-Based Iterative Min-Sum and Majority-Logic Decoding Algorithms for LDPC Codes

A modified reliability-based iterative majority-logic decoding (MRBI-MLGD) algorithm for two classes of structured LDPC codes is presented based on a recent work by Huang et al. Compared with the original one, the modified algorithm has better performance with slightly increased complexity. Then a reliability-based iterative min-sum decoding (RBI-MSD) algorithm is presented. For the presented RBI-MSD algorithm, reliability-based integer messages are processed and exchanged between variable nodes and check nodes. The main computations include only binary logical operations and integer additions. Different from the conventional min-sum algorithm, the variable nodes pass full messages rather than extrinsic messages to check nodes. This can reduce the memory loads and the computational complexity but with a little (or negligible) performance degradation. Simulation results show that, compared with the (M)RBI-MLGD algorithms, the presented RBI-MSD algorithm achieves better error performance, faster decoding convergence rate and fewer quantization bits with moderate increased computational complexity. Furthermore, the RBI-MSD algorithm is also applicable to decoding random LDPC codes, a distinct difference from the (M)RBI-MLGD algorithms. Finally, we point out that the scaling factors employed in the MRBI-MLGD algorithm and the RBI-MSD algorithm can be optimized using discretized density evolution.

A low-complexity joint detection-decoding algorithm for nonbinary LDPC-coded modulation systems

In this paper, we present a low-complexity joint detection-decoding algorithm for nonbinary LDPC coded-modulation systems. The algorithm combines hard-decision decoding using the message-passing strategy with the signal detector in an iterative manner. It requires low computational complexity, offers good system performance and has a fast rate of decoding convergence. Compared to the q-ary sum-product algorithm (QSPA), it provides an attractive candidate for practical applications of q-ary LDPC codes.

Block Markov Superposition Transmission with Bit-Interleaved Coded Modulation

In this letter, we construct bit-interleaved coded modulation (BICM) using a simple basic code but transmitting multiple times in a way similar to the block Markov superposition transmission (BMST). The system admits a sliding-window decoding/demapping algorithm that can be employed to trade off the performance against the delay. Motivated but different from BMST with binary phase-shift keying (BPSK) signalling, a simple lower bound on performance is derived from an equivalent genie-aided system. Numerical results show that the performances of the BMST systems with BICM using a (2, 1, 2) convolutional basic code match well with the derived lower bounds in lower error rate regions over both additive white Gaussian noise (AWGN) channels and Rayleigh fading channels. We also analyze the effect of the encoding memory and the decoding delay on the performance as well as the decoding complexity.

Low complexity concatenated two-state TCM schemes with near capacity performance

This paper presents a family of concatenated two-state trellis-coded modulation (CT-TCM) schemes. Compared with the existing turbo-type bandwidth-efficient coded modulation schemes, the proposed codes have significantly reduced complexity without sacrificing performance. A joint design strategy for all component codes is established. This leads to so-called asymmetrical and time-varying trellis structures, which possess good Hamming and Euclidean distance distributions. The performance of the proposed codes is demonstrated by simulation results.