Coset‐based QC‐LDPC codes without small cycles

A novel construction method of quasi-cyclic low-density parity-check (QC-LDPC) code is proposed based on the finite field multiplicative group, which has easier construction, more flexible code-length code-rate adjustment and lower encoding/decoding complexity. Moreover, a regular QC-LDPC(5334,4962) code is constructed. The simulation results show that the constructed QC-LDPC(5334,4962) code can gain better error correction performance under the condition of the additive white Gaussian noise (AWGN) channel with iterative decoding sum-product algorithm (SPA). At the bit error rate (BER) of 10−6, the net coding gain (NCG) of the constructed QC-LDPC(5334,4962) code is 1.8 dB, 0.9 dB and 0.2 dB more than that of the classic RS(255,239) code in ITU-T G.975, the LDPC(32640,30592) code in ITU-T G.975.1 and the SCG-LDPC(3969,3720) code constructed by the random method, respectively. So it is more suitable for optical communication systems.

SUMMARYLow encoding complexity is very important for quasi‐cyclic low‐density parity‐check (QC‐LDPC) codes used in wireless communication systems. In this paper, a new scheme is presented to construct QC‐LDPC codes with low encoding complexity. This scheme is called two‐stage particle swarm optimization (TS‐PSO) algorithm, in which both the threshold and girth distribution of QC‐LDPC codes are considered. The proposed scheme is composed of two stages. In the first stage, we construct a binary base matrix of QC‐LDPC code with the best threshold. The matrix is constructed by combining a binary PSO algorithm and the protograph extrinsic information transfer (PEXIT) method. In the second stage, we search an exponent matrix of the QC‐LDPC code with the best girth distribution. This exponent matrix is based on the base matrix obtained in the first stage. Consequently, the parity‐check matrix of the QC‐LDPC code with the best threshold and best girth distribution are constructed. Furthermore, bit error rate performances are compared for the QC‐LDPC codes constructed by proposed scheme, the QC‐LDPC code in 802.16e standard, and the QC‐LDPC code in Tam's study. Simulation results show that the QC‐LDPC codes proposed in this study are superior to both the 802.16e code and the Tam code on the additive white Gaussian noise (AWGN) and Rayleigh channels. Moreover, proposed scheme is easily implemented, and is flexible and effective for constructing QC‐LDPC codes with low encoding complexity. Copyright © 2012 John Wiley & Sons, Ltd.

In this paper, a transmission scheme based on Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes with an invertible quasi-cyclic Matrix Q is proposed over Additive White Gaussian Noise (AWGN) channel in order to obtain faster convergence of hard-decision decoding. Combined with the soft information from channel, another improved Reliability-based Q (RQ) decoding algorithm is proposed. The new design can also be applied to QC-LDPC codes in IEEE 802.16e Standards. The simulation results show that the proposed scheme with Q or RQ decoding algorithm has better error correction performance and lower average number of iterations than Bit-Flipping (BF) or weighted Bit-Flipping (WBF) decoding algorith

Seeking good error correcting codes to improve the efficiency of continuous-variable quantum key distribution (CVQKD) reconciliation is a concerning issue. Due to the introduction of multidimensional reconciliation, the error correcting techniques in the classical binary-input additive white Gaussian noise channel are applicable to CVQKD. In this Letter, we apply the quasi-cyclic low-density parity-check (QC-LDPC) codes, which are specified in 5G protocol, to the reconciliation process. Simulation results show that the reconciliation efficiency can reach 92.6% when the code rate is 22/68 and the signal-to-noise ratio is 0.623. Such a new error correcting code points out a new direction for the development of CVQKD.

In this paper, we propose a simple mathematical structure to improve the BER (bit error rate) performance of quasi-cyclic low-density parity-check (QC-LDPC) codes. Since the proposed structure can be defined in-between those of random codes and structured codes, these proposed QC-LDPC codes not only perform as well as random-LDPC codes, but also preserve the advantage of structured LDPC codes which is easier to implement over coding hardware. Moreover, the proposed structure, constructed from balanced incomplete block design (BIBD), can reduce the density of parity-check matrix and hence reduce the number of short cycles, which generally lead to better performance. At the end, we show that the error floor performance of QC-LDPC codes can be improved by proposed hybrid structures and perform well over binary-input additive white Gaussian noise (BI-AWGN) channel.

The generator matrix of quasi-cyclic low-density parity-check (QC-LDPC) codes is not, in general, in systematic form. Therefore, finding the message corresponding to a detected codeword at the receiver is not as straightforward as it is in the case of systematic codes. In this paper, we propose two methods for finding the message from the codeword in a QC-LDPC code. The first method is a general scheme which views the problem as a set of linear equations. This method is not realizable with pure digital circuits and may be implemented by having a processor core in the design. The second method is rather an alternative scheme which makes use of a particular structure in generator matrices of QC-LDPC codes in order to find the message from a non-systematic codeword. We examine a large class of non-systematic Latin squares QC-LDPC codes and one of the IEEE 802.16e standard QC-LDPC codes, and show that they have the required structure to be usable by the algorithm. The latter method is realizable in hardware and can be implemented with a digital circuit consisting of XOR gates.

This paper presents asymptotic multiuser efficiency (AME) performance analysis of the decorrelator based successive interference cancellation (DBSIC) DS-CDMA multiuser receiver DBSIC is similar to the conventional SIC receiver except that a decorrelator is used at each detection stage prior to cancellation. AMEs of DBSIC are compared with those of single-user matched filter, optimum, decorrelating and conventional SIC receivers over both additive white Gaussian noise (AWGN) and Rayleigh fading channels. It is shown that over AWGN channels, DBSIC AME is lower than the optimum receiver AME when the interfering user is weaker than the user of interest but approaches the unity optimum receiver AME as the interferer becomes stronger than the user of interest. For all spreading codes cross-correlation considered, DBSIC has a similar AME curve shape as the conventional SIC receiver but has a higher AME which remains positive for all user energy ratios, illustrating its near-far resistance over AWGN channels. The AME of DBSIC is better than that of the decorrelating detector when the interferer is much weaker or slightly stronger than the user of interest and has worse performance when the interferer is not much weaker. It is shown that DBSIC is completely near-far resistant over Rayleigh fading channels with the same AME as the decorrelating scheme for user 1 and as the optimum scheme for user 2, both AMEs being independent of the user energy ratio. This shows that DBSIC is preferable compared to the decorrelating detector, while still being less complex than the optimum scheme over Rayleigh fading channels

This correspondence analyzes the performance of concatenated coding systems and modulation schemes operating over the additive white Gaussian noise (AWGN) channel by examining the loss of capacity resulting from each of the processing steps. The techniques described in this correspondence allow the separate evaluation of codes and decoders and thus the identification of where loss of capacity occurs. Knowledge of this capacity loss is very useful for the overall design of a communications system, e.g., for evaluating the benefits of inner decoders that produce information beyond the maximum-likelihood (ML) estimate. The first two sections of this correspondence provide a general technique for calculating the composite capacity of an orthogonal or a bi-orthogonal code and the AWGN channel in isolation. The later sections examine the composite capacities of an orthogonal or a bi-orthogonal code, the AWGN channel, and various inner decoders including the decoder estimating the bit-by-bit probability of a one, as is used in turbo codes. The calculations in these examples show that the ML decoder introduces a large loss in capacity. Much of this capacity loss can be regained by using only slightly more complex inner decoders, e.g., a detector for M-ary frequency-shift keying (MFSK) that puts out the two most likely frequencies and the probability the ML estimate is correct produces significantly less degradation than one that puts out only the most likely frequency.

Modulo lattice additive noise (MLAN) channels appear in the analysis of structured lattice codes with lattice decoding for Costa's dirty-paper channel and the additive white Gaussian noise (AWGN) channel. Building on the recent result on the optimal density of an infinite constellation over an AWGN channel, in this paper, it is shown that with a proper choice of the shaping lattice and the scaling parameter, the dispersion of the MLAN channel is asymptotically the same as that of the (zero-interference) AWGN channel at the same signal-to-noise ratio.

This paper investigates an iterative multiuser detection for nonbinary low density parity check (LDPC) coded multicarrier multiple level frequency shift keying system to increase system performance under specific signal-to-noise ratio and data rate. We propose three-level hard-limited detection probabilities over both additive white Gaussian noise (AWGN) channels and Rayleigh fading channels. During multiuser detection (MUD) process, the hard-limited detection probabilities are computed in advanced and stored in tables. By using table looking up, the MUD soft outputs can be computed efficiently. We test the reliability of soft outputs from nonbinary LDPC channel decoder for all users. If the soft output exceeds a reliability threshold, the user is declared as a reliable user. For each symbol, we count the number of reliable users on it, and, use this information to update the soft output of MUD during the iterative multiuser detection and decoding process, which cancel multiple access interference iteratively. Numerical results show that the performances of three-level hard-limited systems outperform two-level hard-limited systems over AWGN channels and Rayleigh fading channels.

DOI: 10.1049/cp:20061337 ISBN: 0 86341 644 6 Location: Hangzhou, China Conference date: 6-9 Nov. 2006 Format: PDF The BER performance of presented quasi-cyclic (QC) low-density parity-check (LDPC) codes is not good as that of randomly constructed LDPC codes, while the lack of structure of randomly constructed LDPC codes implies serious disadvantages in terms of storing and accessing a large parity-check matrix. To solve the problems, this paper proposes a design of good quasi-cyclic (QC) low-density parity-check (LDPC) codes, the obtained algebraically structured codes have large minimum distances and good BER performance. The proposed design is based on index matrices, which determines the shifts of the circulant matrices of the sparse parity-check matrices. Compared with the presented design of QC LDPC codes, the designed QC LDPC codes are free from girth 4, sometimes free from girth 6, and have much larger minimum distances. Based on the algebraic code structure, the conditions of the girth and minimum distance of the codes are found. The BER performance of the designed QC LDPC block codes compares with that of randomly constructed LDPC codes for any block lengths. Better BER performance is obtained by increasing the circulant size of the base QC code. Simulations verify the construction of the QC LDPC codes to be valid. (4 pages) Inspec keywords: AWGN channels; error statistics; channel coding; algebraic codes; parity check codes; sparse matrices Subjects: Algebra; Other topics in statistics; Codes

The combination of multiple-input multiple-output (MIMO) and bit-interleaved coded modulation (BICM)/BICM with iterative demapping (BICM-ID) is one of the key technologies to meet the high-transmission-rate requirement of the next generation broadcasting systems. However, conventional low-density parity check (LDPC) coded MIMO BICM schemes always show poor performance with iterative demapping, and vice versa. In this paper, a subset of spatially coupled codes, finite-length spatially coupled (SC-) quasi-cyclic (QC-) LDPC code, is proposed and the universality of spatially coupled codes is utilized to achieve a good tradeoff between MIMO BICM and BICM-ID schemes. Due to the specific code structure of SC-QC-LDPC, the tool of multi-edge type density evolution (MET-DE) is employed for the performance analysis and code optimization. As an example, a finite-length SC-QC-LDPC code is optimized in binary-input additive white Gaussian noise channel, and then bit error rate simulations are carried out to verify the universality of the designed code in MIMO BICM and BICM-ID schemes.

Coding Schemes for Energy Constrained IoT Devices

Multiple trellis coded modulation of constant envelope frequency and phase modulated signal sets (MTCM/FPM) is investigated for performance on the additive white Gaussian noise (AWGN) channel and on the one-sided normal, Rayleigh and Rician fading channels. The Nakagami-m fading model is used as an alternative to the Rician fading model to calculate the error probability upper bound for trellis-coded schemes on the fading channel. The likeliness and the disparity between the upper bounds to the error probability for the two fading models are discussed. The design criteria for the one-sided normal fading channel, modeled by the Nakagami-m distribution, are observed to be the same as those for the Rayleigh-fading channel. For the MTCM/FPM schemes, it is demonstrated that the set partitioning designed to maximize symbol diversity (optimum for fading channels) is optimum for performance on the AWGN channel as well. The MTCM/FPM schemes demonstrate improved performance over MTCM/MPSK schemes and TCM/FPM schemes on the AWGN channel and the fading channel.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Recently, the differential detection scheme has attracted considerable attention as a demodulated scheme for digital mobile communications because of its robustness in the frequency nonselective fading channel. A problem of the differential detection scheme is that its bit error rate (BER) performance in the additive white Gaussian noise (AWGN) channel is inferior to that of the coherent detection scheme. To solve this problem, many methods to improve BER performance of the differential detection in the AWGN channel have been proposed. However, those methods require complex signal processings.This paper proposes a novel differential detection scheme as a simpler improvement method which estimates the differential phase of the transmitted signal by a sequence estimation scheme using the Viterbi algorithm. The proposed scheme is simplified in a manner such that its signal processing is composed of only additions and subtractions on the phase information of the received signal. Results of computer simulation show that BER performance of the proposed scheme is close to that of the ideal coherent detection in the AWGN channel. In addition, the trellis diagram of the Viterbi algorithm can be reduced without performance degradation introducing the signal processing similar to the Scarece State Transition (SST) type Viterbi decoding. The proposed scheme also is useful in the case of the fast Rician fading channel and the slow Rayleigh fading channel.