This paper proposes out-of-bound signal demapping for lattice reduction-aided iterative linear receivers in overloaded MIMO channels. While lattice reduction aided linear receivers sometimes output hard-decision signals that are not contained in the modulation constellation, the proposed demapping converts those hard-decision signals into binary digits that can be mapped onto the modulation constellation. Even though the proposed demapping can be implemented with almost no additional complexity, the proposed demapping achieves more gain as the linear reception is iterated. Furthermore, we show that the transmission performance depends on bit mapping in modulations such as the Gray mapping and the natural mapping. The transmission performance is confirmed by computer simulation in a 6 × 2 MIMO system, i.e., the overloading ratio of 3. One of the proposed demapping called “modulo demapping” attains a gain of about 2 dB at the packet error rate (PER) of 10-1 when the 64QAM is applied.

This paper proposes a low complexity soft input decoding in an iterative linear receiver for overloaded MIMO. The proposed soft input decoding applies two types of lattice reduction-aided linear filters to estimate log-likelihood ratio (LLR) in order to reduce the computational complexity. A lattice reduction-aided linear with whitening filter is introduced for the LLR estimation in the proposed decoding. The equivalent noise caused by the linear filter is mitigated with the decoder output stream and the LLR is re-estimated after the equivalent noise mitigation. Furthermore, LLR clipping is introduced in the proposed decoding to avoid the performance degradation due to the incorrect LLRs. The performance of the proposed decoding is evaluated by computer simulation. The proposed decoding achieves about 2dB better BER performance than soft decoding with the exhaustive search algorithm, so called the MLD, at the BER of 10-4, even though the complexity of the proposed decoding is 1/10 as small as that of soft decoding with the exhaustive search.

Fountain codes are erasure correcting codes realizing reliable communication systems for the multicast on the Internet. The zigzag decodable fountain (ZDF) codes are one of generalization of the Raptor codes, i.e., applying shift operation to generate the output packets. The ZDF codes are decoded by a two-stage iterative decoding algorithm, which combines the packet-wise peeling algorithm and the bit-wise peeling algorithm. By the bit-wise peeling algorithm and shift operation, ZDF codes outperform Raptor codes under iterative decoding in terms of decoding erasure rates and overheads. However, the bit-wise peeling algorithm spends long decoding time. This paper proposes fast bit-wise decoding algorithms for the ZDF codes. Simulation results show that the proposed algorithm drastically reduces the decoding time compared with the previous algorithm.

Racetrack memory (RM) has attracted much attention. In RM, insertion and deletion (ID) errors occur as a result of an unstable reading process and are called position errors. In this paper, we first define a probabilistic channel model of ID errors in RM with multiple read-heads (RHs). Then, we propose a joint iterative decoding algorithm for spatially coupled low-density parity-check (SC-LDPC) codes over such a channel. We investigate the asymptotic behaviors of SC-LDPC codes under the proposed decoding algorithm using density evolution (DE). With DE, we reveal the relationship between the number of RHs and achievable information rates, along with the iterative decoding thresholds. The results show that increasing the number of RHs provides higher decoding performances, although the proposed decoding algorithm requires each codeword bit to be read only once regardless of the number of RHs. Moreover, we show the performance improvement produced by adjusting the order of the SC-LDPC codeword bits in RM.

Concatenated zigzag (CZ) codes are classified as one kind of parallel-concatenated codes with powerful performance and low complexity. This kind of codes has flexible implementation methods and a good application prospect. We propose a modified turbo-type decoder and adaptive extrinsic information scaling method based on the Max-Log-APP (MLA) algorithm, which can provide a performance improvement also under the relatively low decoding complexity. Simulation results show that the proposed method can effectively help the sub-optimal MLA algorithm to approach the optimal performance. Some contrasts with low-density parity-check (LDPC) codes are also presented in this paper.

For low-density parity-check codes, spatial coupling was proved to boost the performance of iterative decoding up to the optimal performance. As an application of spatial coupling, in this paper, bit-interleaved coded modulation (BICM) with spatially coupled (SC) interleaving — called SC-BICM — is considered to improve the performance of iterative channel estimation and decoding for block-fading channels. In the iterative receiver, feedback from the soft-in soft-out decoder is utilized to refine the initial channel estimates in linear minimum mean-squared error (LMMSE) channel estimation. Density evolution in the infinite-code-length limit implies that the SC-BICM allows the receiver to attain accurate channel estimates even when the pilot overhead for training is negligibly small. Furthermore, numerical simulations show that the SC-BICM can provide a steeper reduction in bit error rate than conventional BICM, as well as a significant improvement in the so-called waterfall performance for high rate systems.

Majority-logic algorithms are devised for decoding non-binary LDPC codes in order to reduce computational complexity. However, compared with conventional belief propagation algorithms, majority-logic algorithms suffer from severe bit error performance degradation. This paper presents a low-complexity reliability-based algorithm aiming at improving error correcting ability of majority-logic algorithms. Reliability measures for check nodes are novelly introduced to realize mutual update between variable message and check message, and hence more efficient reliability propagation can be achieved, similar to belief-propagation algorithm. Simulation results on NB-LDPC codes with different characteristics demonstrate that our algorithm can reduce the bit error ratio by more than one order of magnitude and the coding gain enhancement over ISRB-MLGD can reach 0.2-2.0dB, compared with both the ISRB-MLGD and IISRB-MLGD algorithms. Moreover, simulations on typical LDPC codes show that the computational complexity of the proposed algorithm is closely equivalent to ISRB-MLGD algorithm, and is less than 10% of Min-max algorithm. As a result, the proposed algorithm achieves a more efficient trade-off between decoding computational complexity and error performance.

A soft-decision recursive decoding algorithm (RDA) for the class of the binary linear block codes recursively generated using a u|u+v-construction method is proposed. It is well known that Reed-Muller (RM) codes are in this class. A code in this class can be decomposed into left and right components. At a recursive level of the RDA, if the component is decomposable, the RDA is performed for the left component and then for the cosets generated from the left decoding result and the right component. The result of this level is obtained by concatenating the left and right decoding results. If the component is indecomposable, a proposed iterative bounded-distance decoding algorithm is performed. Computer simulations were made to evaluate the RDA for RM codes over an additive white Gaussian-noise channel using binary phase-shift keying modulation. The results show that the block error rates of the RDA are relatively close to those of the maximum-likelihood decoding for the third-order RM code of length 26 and better than those of the Chase II decoding for the third-order RM codes of length 26 and 27, and the fourth-order RM code of length 28.

Bit-patterned medium (BPM) is one of the promising approaches for ultra-high density magnetic recording systems. However, BPM requires precise write synchronization, and exhibits write-errors due to insufficient write field gradient, medium switching field distribution (SFD), demagnetization field from adjacent islands, and island position variation. In this paper, an iterative decoding system using a non-binary low-density parity-check (LDPC) code is considered for a BPM R/W channel with write-errors at an areal recording density of 2Tbit/inch2 including the coding rate loss. The performance of the iterative decoding system using the non-binary LDPC code over the Galois field GF(28) is evaluated by computer simulation, and it is compared with the conventional iterative decoding system using a binary LDPC code. The results show that the non-binary LDPC system has a larger write margin than the binary LDPC system.

In this paper, through extrinsic information transfer (EXIT) band chart analysis, an adaptive iterative decoding approach (AIDA) is proposed to reduce the iterative decoding complexity and delay for finite-length differentially encoded Low-density parity-check (DE-LDPC) coded systems with multiple-symbol differential detection (MSDD). The proposed AIDA can adaptively adjust the observation window size (OWS) of the MSDD soft-input soft-output demodulator (SISOD) and the outer iteration number of the iterative decoder (consisting of the MSDD SISOD and the LDPC decoder) instead of setting fixed values for the two parameters of the considered systems. The performance of AIDA depends on its stopping criterion (SC) which is used to terminate the iterative decoding before reaching the maximum outer iteration number. Many SCs have been proposed; however, these approaches focus on turbo coded systems, and it has been proven that they do not well suit for LDPC coded systems. To solve this problem, a new SC called differential mutual information (DMI) criterion, which can track the convergence status of the iterative decoding, is proposed; it is based on tracking the difference of the output mutual information of the LDPC decoder between two consecutive outer iterations of the considered systems. AIDA using the DMI criterion can adaptively adjust the out iteration number and OWS according to the convergence situation of the iterative decoding. Simulation results show that compared with using the existing SCs, AIDA using the DMI criterion can further reduce the decoding complexity and delay, and its performance is not affected by a change in the LDPC code and transmission channel parameters.

In this work, a simple doped accumulator (DACC)-assisted relay system is proposed by using bit-interleaved coded modulation with iterative decoding (BICM-ID). An extrinsic information transfer (EXIT) chart analysis shows that DACC keeps the convergence tunnel of the EXIT curves open until almost the (1, 1) point of the mutual information, which avoids the error floor. In the relay system, errors may happen in the source-relay link (intra-link), however, they are allowed in our proposed technique where the correlation knowledge between the source and the relay is exploited at the destination node. Strong codes are not needed and even the systematic source bits can be simply extracted at the relay even though the systematic part may contain some errors. Hence, the complexity of the relay can be significantly reduced, and thereby the proposed system is energy-efficient. Furthermore, the error probability of the intra-link can be estimated at the receiver by utilizing the a posteriori log-likelihood ratios (LLRs) of the two decoders, and it can be further utilized in the iterative processing. Additionally, we provide the analysis of different relay location scenarios and compare the system performances by changing the relay's location. The transmission channels in this paper are assumed to suffer from additive white Gaussian noise (AWGN) and block Rayleigh fading. The theoretical background of this technique is the Slepian-Wolf/Shannon theorem for correlated source coding. The simulation results show that the bit-error-rate (BER) performances of the proposed system are very close to theoretical limits supported by the Slepian-Wolf/Shannon theorem.

In this paper, we reformulate the issue related to wireless mesh networks (WMNs) from the Chief Executive Officer (CEO) problem viewpoint, and provide a practical solution to a simple case of the problem. It is well known that the CEO problem is a theoretical basis for sensor networks. The problem investigated in this paper is described as follows: an originator broadcasts its binary information sequence to several forwarding nodes (relays) over Binary Symmetric Channels (BSC); the originator's information sequence suffers from independent random binary errors; at the forwarding nodes, they just further interleave, encode the received bit sequence, and then forward it, without making heavy efforts for correcting errors that may occur in the originator-relay links, to the final destination (FD) over Additive White Gaussian Noise (AWGN) channels. Hence, this strategy reduces the complexity of the relay significantly. A joint iterative decoding technique at the FD is proposed by utilizing the knowledge of the correlation due to the errors occurring in the link between the originator and forwarding nodes (referred to as intra-link). The bit-error-rate (BER) performances show that the originator's information can be reconstructed at the FD even by using a very simple coding scheme. We provide BER performance comparison between joint decoding and separate decoding strategies. The simulation results show that excellent performance can be achieved by the proposed system. Furthermore, extrinsic information transfer (EXIT) chart analysis is performed to investigate convergence property of the proposed technique, with the aim of, in part, optimizing the code rate at the originator.

This letter presents a novel weighted reliability-based (WRB) algorithm for decoding low-density parity-check (LDPC) codes. Viewing the well-known normalized min sum (NMS) algorithm as reliability-based, the WRB algorithm can be seen as a simplified version of the NMS algorithm. Unlike the NMS algorithm, the WRB algorithm does not update the soft information sent between the variable nodes and check nodes, which greatly reduces the decoding complexity. For finite geometry LDPC codes with larger row redundancy and column weights, simulation results show that the WRB algorithm almost matches the error performance of the NMS algorithm.

The convergence behavior of turbo APPM (TAPPM) decoding is analyzed by using a three-dimensional extrinsic information transfer (EXIT) chart and the decoding trajectory. The signal-to-noise ratio (SNR) threshold, below which iterative decoding fails to converge, is predicted by using the 3-D EXIT chart analysis. Bit error rate performances of TAPPM schemes validate the EXIT-chart-based SNR threshold predictions. Outer constituent codes of TAPPM are chosen to show the lowest SNR threshold with the aid of EXIT chart analysis.

In this paper a programmable and area-efficient decoder architecture supporting two decoding algorithms for Block-LDPC codes is presented. The novel decoder can be configured to decode in either TPMP or TDMP decoding mode according to different Block-LDPC codes, essentially combining the advantages of two decoding algorithms. With a regular and scalable data-path, a Reconfigurable Serial Processing Engine (RSPE) is proposed to achieve area efficiency. To verify our proposed architecture, a flexible LDPC decoder fully compliant to IEEE 802.16e applications is implemented on a 130 nm 1P8M CMOS technology with a total area of 6.3 mm2 and maximum operating frequency of 250 MHz. The chip dissipates 592 mW when operates at 250 MHz frequency and 1.2 V supply.

Kudekar et al. recently proved that for transmission over the binary erasure channel (BEC), spatial coupling of LDPC codes increases the BP threshold of the coupled ensemble to the MAP threshold of the underlying LDPC codes. One major drawback of the capacity-achieving spatially-coupled LDPC codes is that one needs to increase the column and row weight of parity-check matrices of the underlying LDPC codes. It is proved, that Hsu-Anastasopoulos (HA) codes and MacKay-Neal (MN) codes achieve the capacity of memoryless binary-input symmetric-output channels under MAP decoding with bounded column and row weight of the parity-check matrices. The HA codes and the MN codes are dual codes each other. The aim of this paper is to present an empirical evidence that spatially-coupled MN (resp. HA) codes with bounded column and row weight achieve the capacity of the BEC. To this end, we introduce a spatial coupling scheme of MN (resp. HA) codes. By density evolution analysis, we will show that the resulting spatially-coupled MN (resp. HA) codes have the BP threshold close to the Shannon limit.

In this paper, a novel receiver architecture is proposed for multiple-input-multiple-output (MIMO) systems; the proposed architecture helps achieve superior performance in multipath fading channels when the number of layered streams exceeds the number of receiving antennas. In this architecture, the concept of “virtual channel” is adopted to attain diversity gain even when successive detection is applied for reducing computational complexity, while orthogonal frequency division multiplexing (OFDM) is employed to combat multipath fading. Actually, successive detection is carried out in all possible virtual channels, and the virtual channel with the minimum error probability is detected with the assistance of the maximum a-posteriori (MAP) decoder in the architecture. In addition, soft input and soft output (SISO) iterative detection is introduced in the virtual channel estimation scheme. The performance of the proposed architecture is verified by computer simulations. This architecture can be implemented with lesser complexity than that in maximum likelihood detection (MLD), but the gain in the former case exceeds that in the latter by 4.5 dB at the BER of 10-3 for 42 MIMO-OFDM.

A novel signaling scheme is proposed for iterative channel estimation and data decoding in fast fading channels. The basic idea is to bias the occurrence probability of transmitted symbols. A priori information about the bias is utilized for channel estimation. The bias-based scheme is constructed as a serially concatenated code, in which a convolutional code and a biased nonlinear block code are used as the outer and inner codes, respectively. This construction allows the receiver to estimate channel state information (CSI) efficiently. The proposed scheme is numerically shown to outperform conventional pilot-based schemes in terms of spectral efficiency for moderately fast fading channels.

We develop a mathematical framework for the extrinsic information transfer (EXIT) analysis to assess the convergence behavior of maximum a posteriori (MAP)-based joint iterative decoding of correlated sources, which are separately encoded and transmitted over noisy channels. Unlike the previous work, our approach focuses on the case side information about the correlation is not perfectly given at the joint decoder but is extracted from decoder output and updated in an iterative manner. The presented framework provides a convenient way to compare between schemes. We show that it allows us to easily and accurately predict joint decoding gain and turbo cliff position.

For decoding non-binary low-density parity-check (LDPC) codes, logarithm-domain sum-product (Log-SP) algorithms were proposed for reducing quantization effects of SP algorithm in conjunction with FFT. Since FFT is not applicable in the logarithm domain, the computations required at check nodes in the Log-SP algorithms are computationally intensive. What is worth, check nodes usually have higher degree than variable nodes. As a result, most of the time for decoding is used for check node computations, which leads to a bottleneck effect. In this paper, we propose a Log-SP algorithm in the Fourier domain. With this algorithm, the role of variable nodes and check nodes are switched. The intensive computations are spread over lower-degree variable nodes, which can be efficiently calculated in parallel. Furthermore, we develop a fast calculation method for the estimated bits and syndromes in the Fourier domain.