Shancheng Zhao

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.

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).

Construction of High-Performance Array-Based Non-Binary LDPC Codes With Moderate Rates

Based on arrays, excellent low-density parity-check (LDPC) codes with high rates have been constructed. In this letter, we propose to construct high-performance nonbinary LDPC (NBLDPC) codes with moderate rates based on arrays. The proposed construction combines masking and column selection. First, we construct a masking matrix M based on asymptotic thresholds and certain error-prone substructures. Second, we generate a number of column selection sets (CSS) based on Golomb rulers. Based on M, we construct a parity-check matrix for each CSS. Third, we compute the cycle distribution of each parity-check matrix and select the one with the best cycle distribution as output. To assess the effectiveness of the proposed construction, error performances of several NBLDPC codes are presented. Comparisons with other codes are also carried out to show the advantages of our construction.

A Variant of the EMS Decoding Algorithm for Nonbinary LDPC Codes

This letter is concerned with low-complexity decoding algorithms for nonbinary low-density parity-check (NB-LDPC) codes. A new truncation rule based on an adaptive threshold μ is proposed for the extended min-sum (EMS) algorithm. The threshold μ is determined by the mean of the message vector. Therefore, it can be matched to channel observation and decoding iteration. The resulting algorithm is referred to as μ-EMS algorithm. Simulation results show that the μ-EMS algorithm performs almost as well as the Q-ary sum-product algorithm (QSPA). Simulation results also show that the μ-EMS algorithm is simpler than the other X-EMS algorithms for NB-LDPC over high order finite fields.

Kite codes over groups

Kite codes, which were originally defined over the binary field, are generalized to arbitrary abelian groups in this paper. Kite codes are a special class of prefix rateless codes over groups, which can generate potentially infinite (or as many as required) random-like parity-check symbols. In this paper, we consider four kinds of Kite codes, which are binary Kite codes, Kite codes over one-dimensional lattices, Kite codes over M-PSK signal constellations and Kite codes over multi-dimensional lattices. It is shown by simulations that the proposed codes perform well over additive white Gaussian noise channels.

A New Joint Source-Channel Coding Scheme Based on Nested Lattice Codes

In this paper, we propose a new joint source-channel coding (JSCC) method for transmission of a Gaussian source through an additive white Gaussian noise (AWGN) channel whose bandwidth is higher than that of the source. Firstly, a sequence of random variables from a Gaussian source is discretized with a lattice-based quantizer, resulting in a sequence of lattice points. Secondly, by driving an encoder of a systematic group code, these lattice points are utilized to compute a sequence of parity lattice points. Thirdly, both the systematic and the parity lattice points are scaled and transmitted over an AWGN channel. Simulation results show that, with moderate code length, our scheme performs well when compared with the Shannon limits.

A Serial Concatenation-Based Coding Scheme for Dimmable Visible Light Communication Systems

Dimming control is desirable for visible light communication (VLC) systems to provide different levels of brightness. In this letter, we propose a new coding scheme for dimmable VLC systems based on serial concatenation of column-scaled (CS) low-density parity-check (LDPC) codes and constant weight codes (CWCs). In the proposed scheme, the cardinality of the finite field on which the CS LDPC code is defined varies adaptively according to the CWC. Hence, transformation between symbol metrics and bit metrics is avoided. Other advantages of the proposed scheme are described as follows: 1) its coding rates are not constrained by the dimming range as error control and dimming control are decoupled; 2) it can be easily configured to support a wide range of dimming targets; and 3) it requires essentially the same hardware architecture to implement the encoder/decoder pair. Hence, the proposed coding scheme provides an attractive candidate for VLC systems with both error and dimming control.

Joint detection-decoding of majority-logic decodable non-binary low-density parity-check coded modulation systems: an iterative noise reduction algorithm

In this study, the authors present a low-complexity iterative joint detection–decoding algorithm for majority-logic decodable non-binary low-density parity-check (LDPC) coded modulation systems. In the proposed algorithm, a hard-in–hard-out decoder is combined with a hard-decision signal detector in an iterative manner. Each iteration consists of five phases. Firstly, the detector makes hard decisions based on the iteratively updated ‘received’ signals; secondly, these hard decisions are distributed via variable nodes to check nodes; thirdly, check nodes compute hard extrinsic messages; fourthly, each variable node counts hard extrinsic messages from its adjacent check nodes and feeds back to the detection node the symbol with the most votes as well as the difference between the most votes and the second most votes; finally, these feedbacks are used to shift each ‘received’ signal point along an estimated direction to possibly reduce noise. The proposed algorithm requires only integer operations and finite field operations and consequently can be implemented with simple combinational logic circuits in practical systems. Simulation results show that the proposed algorithm performs well and hence serves as an attractive candidate for trading off performance against complexity for majority-logic decodable non-binary LDPC codes.

Joint detection/decoding algorithms for non-binary low-density parity-check codes over inter-symbol interference channels

This study is concerned with the application of non-binary low-density parity-check (NB-LDPC) codes to binary input inter-symbol interference channels. Two low-complexity joint detection/decoding algorithms are proposed. One is referred to as max-log-MAP/X-EMS algorithm, which is implemented by exchanging soft messages between the max-log-MAP detector and the extended min-sum (EMS) decoder. The max-log-MAP/X-EMS algorithm is applicable to general NB-LDPC codes. The other one, referred to as Viterbi/GMLGD algorithm, is designed in particular for majority-logic decodable NB-LDPC codes. The Viterbi/GMLGD algorithm works in an iterative manner by exchanging hard-decisions between the Viterbi detector and the generalised majority-logic decoder (GMLGD). As a by-product, a variant of the original EMS algorithm is proposed, which is referred to as µ-EMS algorithm. In the µ-EMS algorithm, the messages are truncated according to an adaptive threshold, resulting in a more efficient algorithm. Simulations results show that the max-log-MAP/X-EMS algorithm performs as well as the traditional iterative detection/decoding algorithm based on the BCJR algorithm and theQ-ary sum–product algorithm, but with lower complexity. The complexity can be further reduced for majority-logic decodable NB-LDPC codes by executing the Viterbi/GMLGD algorithm with a performance degradation within one dB. These algorithms provide good candidates for trade-offs between performance and complexity.

Sphere bound revisited: A new simulation approach to performance evaluation of binary linear codes over AWGN channels

In this paper, the sphere bound (SB) is revisited within a general bounding framework based on nested Gallager regions. We show that the SB proposed by Herzberg et al. is equivalent to the SB proposed by Kasami et al.. Interestingly, this general framework provides a new way to evaluate the performance of binary linear codes over additive white Gaussian noise (AWGN) channels. This simulation approach relies on only the geometry structure of the code itself. Therefore, simulation results can be used to evaluate not only the performance over AWGN channels but also that over other symmetrical real channels. Numerical results obtained with the new performance evaluation approach are presented.