Link adaptation in FBMC/OQAM systems using NB-LDPC codes

When the code is not long, non-binary low-density parity-check (NB-LDPC) codes can achieve better error-correcting performance than binary LDPC codes at the cost of higher decoding complexity. The recently developed iterative reliability-based majority-logic NB-LDPC decoding can achieve better performance-complexity tradeoffs than previous algorithms. Many existing NB-LDPC code construction schemes lead to quasi-cyclic or cyclic codes. In this paper, efficient low-complexity NB-LDPC decoder architectures are developed for these two types of codes based on the newly proposed iterative hard reliability-based majority-logic decoding (IHRB-MLGD). Particularly, novel schemes are designed to keep a small proportion of messages in order to reduce the memory requirement without causing noticeable performance loss. Moreover, a shift-message structure is proposed by using memories concatenated with variable node units to enable efficient partial-parallel decoding for cyclic NB-LDPC codes. Compared to previous decoders based on the Min-max algorithm, the proposed IHRB-MLGD decoder architectures can achieve tens of times higher efficiency for codes with similar length and rate with moderate coding gain loss.

Short cycles in a nonbinary low-density parity-check (NB-LDPC) code may be even more harmful to its performance if they do not satisfy the so-called full rank condition (FRC). This is because they may induce low-weight codewords or absorbing sets in that case. Thus, it is important to count the number of short cycles not satisfying the FRC as well as the number of short cycles for analyzing the performance of an NB-LDPC code. In this paper, we first develop a novel message-passing algorithm and identify how it is related to the FRC. We then propose a low-complexity algorithm for counting the number of short cycles not satisfying the FRC in an NB-LDPC code, as well as the number of short cycles. Finally, we propose a low-complexity algorithm for designing an NB-LDPC code with low error floor. Depending on the modulation scheme, the codes constructed by the proposed design algorithm have similar or slightly worse performance, compared with those constructed via the method by Poulliat et al. However, the proposed design algorithm does not require a cycle enumeration algorithm with high complexity, and therefore is feasible even in the case of large code length, say ${\geq}5000$ .

In this paper, we first describe a 9-symbol non-uniform signaling scheme based on Huffman code, in which different symbols are transmitted with different probabilities. By using the Huffman procedure, prefix code is designed to approach the optimal performance. Then, we introduce an algorithm to determine the optimal signal constellation sets for our proposed non-uniform scheme with the criterion of maximizing constellation figure of merit (CFM). The proposed nonuniform polarization multiplexed signaling 9-QAM scheme has the same spectral efficiency as the conventional 8-QAM. Additionally, we propose a specially designed GF(32) nonbinary quasi-cyclic LDPC code for the coded modulation system based on the 9-QAM non-uniform scheme. Further, we study the efficiency of our proposed non-uniform 9-QAM, combined with nonbinary LDPC coding, and demonstrate by Monte Carlo simulation that the proposed GF(23) nonbinary LDPC coded 9-QAM scheme outperforms nonbinary LDPC coded uniform 8-QAM by at least 0.8dB.

Non-binary low-density parity-check (NB-LDPC) codes, defined over GF(q), have been extensively studied since analyzed by Davey and Mackay in 1998 [1]. It was demonstrated that the NB-LDPC code has superior error-correcting performance than the binary counterparts in algorithm-level investigation. However, it is hard to directly employ a high-throughput NB-LDPC decoder due to its high processing complexity and excessively long decoding latency. Based on the conventional extended min-sum (EMS) algorithm [2], which reduces the message size without losing the correcting power, we introduce a high-throughput but area-efficient NB-LDPC decoder handling multiple message elements at the same time. The previous variable node processing (VNP) is modified to accept the multiple message elements and to promote parallel processing eventually. For the efficient decoder design, the delay overheads are carefully optimized in the two-stage sorter. The prototype decoder for the (160, 80) NB- LDPC code is implemented in a 22nm FinFET technology, achieving the decoding throughput of 7 Gbps.

Non-binary low-density parity-check (NB-LDPC) codes can exhibit more considerable coding gain than their binary counterparts in numerous cases. To further exploit the benefit of NB-LDPC codes, in this letter, a novel type of non-binary LDPC codes, alterable subset non-binary LDPC (AS-NB-LDPC) codes, is proposed for reducing the peak-to-average power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) systems. Firstly, we design the alteration scheme of AS-NB-LDPC codes to make <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula> -ary LDPC codes generate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula> valid codewords through one alterable subset, and the codeword with the minimum PAPR is selected for transmission. Then inspired by the invertible subset for binary LDPC codes, the necessary and sufficient conditions for alterable subset generation are derived. Furthermore, we propose an improved progressive edge growth (PEG) construction method to obtain AS-NB-LDPC codes with favorable frame error rate (FER) performance. Simulation results verify the effectiveness of the proposed NB-LDPC codes.

This paper studies an iterative multiuser detection and decoding for nonbinary low density parity check (LDPC) coded multicarrier M-ary frequency shift keying (MC MFSK) multiple access system to increase system spectral efficiency under specific signal-to-noise ratio. At multiuser detection side, soft metric for each symbol is quantized to 2 levels (2L) or 3 levels (3L) and then pass to the decoder. When the soft output of a symbol from decoder exceeds a threshold, the user is declared as a reliable symbol. The reliable information is fed back to the detection side and updates the symbol soft output when iterative processing is carried out. Numerical results show that system spectral efficiency is improved for 3L system over Rayleigh fading. Index Terms - Nonbinary LDPC codes, Multicarrier MFSK, Multiple Access.

In multiple-input multiple-output (MIMO) transmission systems, the channel state information (CSI) at the transmitter can be used to add linear precoding to the transmitted signals in order to improve the performance and the reliability of the transmission system. This paper investigates how to properly join precoded closed-loop MIMO systems and nonbinary low density parity check (NB-LDPC). Theqelements in the Galois field, GF(q), are directly mapped toqtransmit symbol vectors. This allows NB-LDPC codes to perfectly fit with a MIMO precoding scheme, unlike binary LDPC codes. The new transmission model is detailed and studied for several linear precoders and various designed LDPC codes. We show that NB-LDPC codes are particularly well suited to be jointly used with precoding schemes based on the maximization of the minimum Euclidean distance (max-dmin) criterion. These results are theoretically supported by extrinsic information transfer (EXIT) analysis and are confirmed by numerical simulations.

Forward error correction is an essential part of digital communication systems. Non-binary low-density parity-check (NB-LDPC) codes have an excellent communications performance for short block lengths. The higher the field size is, the better the communications performance is. Non-binary LDPC codes can outperform all other state-of-the-art code classes. However, the algorithmic decoding complexity grows with the field size. For an intended, future use of these codes in real systems, an efficient hardware implementation is mandatory. Hardware architectures for binary LDPC codes are well investigated, but efficient implementation of non-binary LDPC decoders is still an open field. To the best of our knowledge, this paper studies for the first time the hardware implementation costs for non-binary LDPC decoders with Galois field sizes of 4, 16 and 256 on FPGA and a 65nm ASIC technology.

In this paper we design non-uniform bit-wise puncturing distributions for irregular non-binary LDPC (NB-LDPC) codes. The puncturing distributions are optimized by minimizing the decoding threshold of the punctured LDPC code, the threshold being computed with a Monte-Carlo implementation of Density Evolution. First, we show that Density Evolution computed with Monte-Carlo simulations provides accurate (very close) and precise (small variance) estimates of NB-LDPC code ensemble thresholds. Based on the proposed method, we analyze several puncturing distributions for regular and semi-regular codes, obtained either by clustering punctured bits, or spreading them over the symbol-nodes of the Tanner graph. Finally, optimized puncturing distributions for non-binary LDPC codes with small maximum degree are presented, which exhibit a gap between 0.2 and 0.5 dB to the channel capacity, for punctured rates varying from 0.5 to 0.9.

In this paper, we propose a construction method for two-level quantum error-correcting codes via non-binary LDPC codes over an extended field of order 2p, p an integer p > 1. The proposed quantum error-correcting codes are based on binary quasi-cyclic LDPC codes which have almost achieved a “Bounded Distance Decoding (BDD)” limit but have not surpassed the limit yet. Quantum codes constructed from the proposed method surpass the BDD limit. Furthermore the codes outperform the efficiently-decodable state-of-the-art quantum codes.

This paper considers the ensemble enumerators of protograph-based nonbinary (PB NB) LDPC codes. Equipped with combinatorial definitions extended to the nonbinary domain, ensemble enumerators of codeword weight, trapping set size and stopping set size are calculated. The exact enumerators are presented in the finite-length regime, and the corresponding growth rates are calculated in the asymptotic regime. Our results can provide useful analytical tools for a range of communication and storage applications employing nonbinary LDPC codes.

This paper presents the performance of outer-loop control for adaptive modulation and coding (AMC) using mutual information (MI) based mapping between the block error rate (BLER) and received signal-to-interference plus noise power ratio (SINR) in the multiple-input multiple-output (MIMO)-orthogonal frequency division multiplexing (OFDM) downlink employing maximum likelihood detection (MLD). In AMC, we generate a mapping table between the BLER and MI per bit in advance, which is computed from the received SINR, assuming typical channel conditions including the path model and fading maximum Doppler frequency. Then, in the proposed outer-loop control, the measured MI per bit value for selecting the best modulation and coding scheme (MCS) is adjusted so that the measured BLER after turbo decoding satisfies the prescribed target value. Computer simulation results show that the outer-loop control achieves almost the same throughput as that with a mapping table assuming channel conditions identical to those for the actual measurement, while achieving nearly the identical target BLER. Moreover, we show that the best step size, which provides nearly the maximum throughput, differs according to the change in the maximum Doppler frequency in contrast to the relative feedback delay of the AMC loop. Nevertheless, it is insensitive to the target BLER value and frequency-selectivity of a channel model.

This paper introduces a novel class of non-binary graph-based codes, built upon graph covers of non-binary protograph LDPC codes. This new ensemble is more restrictive than previously considered constructions, but in turn is much simpler to design and implement. The simplifications in design allow for the enumeration of codeword weight, trapping set size, stopping set size, and pseudo codeword weights, both as exact quantities in the finite-length regime and as corresponding growth rates in the asymptotic setting. The presented construction and the accompanying enumerations enhance the analytical toolbox of non-binary LDPC codes.

Motivated by the superior performance of array-based non-binary low-density parity-check (LDPC) codes, we study in this paper their structural properties by combinational and graphical techniques. The main results are summarized as follows. First, we show that there exist codewords with symbol weight six and seven in array-based non-binary LDPC (NBLDPC) codes with column weight 3. Second, we characterize the graphical substructures induced by weight-6 and weight-7 codewords. Finally, we carry out comparisons to confirm the performance advantage of array-based NBLDPC codes.

This paper presents a novel truncation rule for the extended min-sum (EMS) decoding of non-binary low-density parity-check (NB-LDPC) codes. The conventional NB-LDPC decoders involve vector-messages of length equal to the field size $q$ . The complexity of these decoders increases significantly as $q$ increases. In the EMS algorithm, the vector-messages are truncated by discarding the less-likely symbols. In this paper, we propose a truncation rule so that the lengths of the vector-messages are reduced to the so-far best limit without compromising on the error correction capability. We devise a proximity matrix which helps to identify the essential components of a vector-message for truncation. The proposed truncation rule has been applied to several NB-LDPC codes of different field sizes. Simulation results for these codes show that the proposed rule can achieve the maximum truncation with negligible performance loss.