Waterfall Region Research Articles

Experimental demonstration of flexible information rate PON beyond 100 Gb/s with rate-compatible LDPC codes

The applications of rate-compatible low-density parity-check (RC-LDPC) codes are investigated for a 16 quadrature amplitude modulation (16QAM) signal and coherent detection system. With rate-compatible signals, we can provide the flexible net data rate between 135.5 Gb/s and 169.7 Gb/s in a passive optical network (PON) link. Based on the LDPC codes defined in the IEEE 802.3ca standard, we construct two sets of RC-LDPC codes with a fixed and variable information bit length. Since the puncturing operation may degrade the performance of LDPC codes, we apply the protograph-based extrinsic information transfer (PEXIT) technique to optimize the puncturing positions to mitigate the degradation. Additionally, we explore four low-complexity LDPC decoding algorithms (min sum, offset min sum, variable weight min sum, and relaxed min sum with 2 nd min emulation) to investigate the relationship between the computational complexity and decoding performance. Simulation results indicate that the constructed codewords exhibit good performance in the waterfall region across a range of code rates. Finally, we conduct an experimental setup in a dual-polarization 25 GBaud 16QAM coherent PON to verify the effectiveness of the constructed LDPC codes with four decoding algorithms. The experimental results show maximal 4.8 dB receiver sensitivity differences, which demonstrate the feasibility of the method for constructing RC-LDPC codes in future high-speed flexible coherent PON.

New inflation in the waterfall region

New inflation in the waterfall region

Finite-Length Scaling of SC-LDPC Codes With a Limited Number of Decoding Iterations

We propose four finite-length scaling laws to predict the frame error rate (FER) performance in the waterfall region of spatially-coupled low-density parity-check code ensembles under full belief propagation (BP) decoding with a limit on the number of decoding iterations and a scaling law for sliding window decoding, also with limited iterations. The laws for full BP decoding provide a choice between accuracy and computational complexity; a good balance between them is achieved by the law that models the number of decoded bits after a certain number of BP iterations by a time-integrated Ornstein-Uhlenbeck process. This framework is developed further to model sliding window decoding as a race between the integrated Ornstein-Uhlenbeck process and an absorbing barrier that corresponds to the left boundary of the sliding window. The proposed scaling laws yield accurate FER predictions for the semi-structured code ensembles proposed by Olmos and Urbanke.

Composition of herpetofauna in the ecotone between the Cerrado and Atlantic Forest with ecotourism activity around the Itambé Cave and Waterfall, Altinópolis – SP

São Paulo state is renowned for its extensive research on herpetofauna. However, there are still unexplored areas within the state, creating knowledge gaps in biodiversity. This study focused on the Itambé cave and waterfall in Altinópolis, São Paulo, which is an ecotone between the Cerrado and Atlantic Forest and popular among ecotourists. The research aimed to describe the herpetofauna composition in this area. Data collection occurred from April 2022 to January 2023, utilizing various methods. The study assessed the influence of climate variables and seasons on species richness and abundance. The findings identified eight herpetofauna species distributed across six genera. Among them, three lizard species and five anuran species were classified as generalists. Lizard richness peaked in winter, while anuran richness was highest in spring. Precipitation significantly influenced anuran abundance throughout the data collection period. Lizards were evenly distributed between the Cerrado and Atlantic Forest, while anurans were predominantly found in the Atlantic Forest. The research highlights the diverse herpetofauna present in the Itambé cave and waterfall region. However, all species encountered were generalists, suggesting potential human activity impacts on species with specific habitat requirements.

Analysis of MMSE Multiuser Detector in a Low-density Parity Check Coded Large Scale MIMO OFDM

Background: Large-scale MIMO OFDM technique satisfies the demands on performance and the service quality preferred in wireless communication systems. Since numerous antenna terminals have been incorporated in the base station, multiuser detection is crucial for retrieving the data appropriately. Thus, the complexities of the detectors increase rapidly in large-scale MIMO OFDM schemes. Objective: This work is a solution to achieve an extensively high rate of data transmission, which will help improve the capacity of the LS MIMO OFDM system. Methods: A unique detection approach of multiuser detection in LS MIMO OFDM model with channel coding, like Low Density Parity Check Codes (LDPC), is suggested in this paper. The LDPCcoded large-scale MIMO OFDM system has also been analysed in the study with users of around ten at the transmitter and several antennas in the base station. Results: BER of the LDPC-coded LS MIMO OFDM exhibited a waterfall region for SNR greater than 6dB as the study has been done with different decoding iterations. The BER performance worsened with the increase in modulation symbols. The study has shown how the BER performance has improved with respect to the increasing fading channels and subcarriers. Conclusion: The proposed system exhibited performance closer to the MIMO capacity with low complexity MMSE detection. The multiuser detector of LDPC-coded LS MIMO OFDM has been analysed by error rate in received bits (BER) with respect to different parameters, such as modulation orders, iteration values, receiving antennas, and OFDM subcarriers.

Block Markov superposition transmission of LDPC codes

In this paper, based on the block Markov superposition transmission (BMST) technique, we present a new class of coupled low-density parity-check (LDPC) codes for the transport block (TB)-based transmission to improve the error-correcting performance. For encoding, the previous LDPC codewords corresponding to a TB (at prior time slot) are interleaved and superimposed onto the current LDPC codewords, resulting in the transmitted codewords. For decoding, the sliding window decoding algorithm with sum-product or min-sum implementations can be employed, inheriting a relatively low-latency decoding. A distinguished advantage of the proposed coded transmission over spatially coupled LDPC (SC-LDPC) codes is that the encoder/decoder of the proposed codes can be designed by reusing the encoder/decoder architecture of component block LDPC codes. To analyze the waterfall performance of BMST-LDPC code ensembles, we present the protograph-based EXIT chart analysis, which can efficiently predict the error-correcting performance in waterfall region. To analyze the error-floor performance of BMST-LDPC codes, we employ the genie-aided (GA) lower bound, which can efficiently predict the error-correcting performance in error-floor region. For ease of implementation, the BMST-LDPC codes are constructed by taking the (2, 4)-raptor-like LDPC codes or the 5G LDPC codes as the basic components. The numerical results reveal that the proposed codes can have capacity-approaching performance, exhibiting a gap of 0.007 ​dB away from the corresponding Shannon limit. They also reveal that, by using the proposed BMST construction, the error-correcting performance of the original 5G block LDPC codes can be significantly improved, achieving coding gains up to one dB over the AWGN channels and two dB over the fast fading channels.

Genetic optimization of 5G-NR LDPC codes for lowering the error floor of BICM systems

With the wide range of commercial uses of fifth generation (5G), new radio (NR) communication networks, the wireless transmission becomes more efficient, reliable and faster. At the same time, high-quality signal transmission for 5G networks and beyond has also encountered new opportunities and challenges. Channel coding is a key technology to ensure reliable information transmission and service quality. However, the 5G-NR LDPC coded bit-interleaved coded modulation (BICM) sometimes suffers from relatively high error floors, so it can not always guarantee the high-quality and low-delay wireless transmission. In this paper, we propose a further redesign of the 5G-NR LDPC coded BICM based on genetic algorithm (GenAlg). By adjusting the number of the non-zero elements, the corresponding positions and shifting values in base matrix, we optimize the 5G-NR LDPC codes with GenAlg according to the error performances of coded BICM schemes. Simulation results show that the optimized 5G-NR LDPC codes which still support length and rate compatible coding have lower error floors with a little performance loss int the waterfall region compared to the standard 5G-NR LDPC codes with different modulation orders.

Adaptive Decoding Algorithm With Variable Sliding Window for Double SC-LDPC Coding System

In this letter, an adaptive decoding algorithm with a variable sliding window for joint source-channel coding (JSCC) scheme based on double spatially coupled low-density parity-check (DSC-LDPC) codes is investigated. For the traditional sliding window decoding (SWD) algorithm, one or more errors occurring in a decoding window may affect the decoding of the next window, which will trigger error propagation. To mitigate the effects, a window extension algorithm based on average log-likelihood ratios (LLRs) will be proposed, but the implement of extension implies higher decoding complexity. In order to trade-off the error rate performance and complexity, the source and channel threshold that determines the window extension are analyzed. In the simulation, the proposed SWD algorithm with acceptable complexity has better error rate performance in the water fall region and the error floor region.

Protograph Designing of P-LDPC Codes via M3 Method

Recently, a mesh model-based merging (M3) method and four basic graph models were proposed to construct the double protograph low-density parity-check (P-LDPC) code pair of the joint source channel coding (JSCC). Designing the protograph (mother code) of the P-LDPC code with both a good waterfall region and lower error floor is a challenge, and few works have existed until now. In this paper, the single P-LDPC code is improved to further verify the availability of the M3 method, and its structure is different from the channel code in the JSCC. This construction technique yields a family of new channel codes with lower power consumption and higher reliability. The structured design and better performance demonstrate that the proposed code is hardware-friendly.

Decoding Short LDPC Codes via BP-RNN Diversity and Reliability-Based Post-Processing

This paper investigates decoder diversity architectures for short low-density parity-check (LDPC) codes, based on recurrent neural network (RNN) models of the belief-propagation (BP) algorithm. We propose a new approach to achieve decoder diversity in the waterfall region, by specializing BP-RNN decoders to specific classes of errors, with absorbing set support. We further combine our approach with an ordered statistics decoding (OSD) post-processing step, which effectively leverages the bit-error rate optimization deriving from the use of the binary cross-entropy loss function. We show that a single specialized BP-RNN decoder combines better than BP with the OSD post-processing step. Moreover, combining OSD post-processing with the diversity brought by the use of multiple BP-RNN decoders, provides an efficient way to bridge the gap to maximum likelihood decoding.

Redesign of Channel Codes for Joint Source-Channel Coding Systems over One-Dimensional Inter-Symbol-Interference Magnetic Recording Channels

Although the joint source-channel coding (JSCC) system based on double protograph low-density parity-check (DP-LDPC) codes has been shown to possess excellent error performance over additive white Gaussian noise (AWGN) channels, it cannot perform well over one-dimensional inter-symbol-interference (OD-ISI) magnetic recording channels. In this study, a new JSCC system with a three-stage serially concatenated framework of Turbo equalization is firstly proposed for OD-ISI magnetic recording channels. Then, a modified joint protograph extrinsic information transfer (M-JPEXIT) algorithm is put forward to analyze the convergence-performance of the proposed system. By applying the M-JPEXIT algorithm, the channel codes are redesigned for this system to improve the error performance. Both the M-JPEXIT analysis and the bit-error-rate (BER) simulation results show the performance improvement of the proposed channel codes, especially in the water-fall region.

Generalized Mutual Information-Maximizing Quantized Decoding of LDPC Codes With Layered Scheduling

In this paper, we propose a framework of the mutual information-maximizing (MIM) quantized decoding for low-density parity-check (LDPC) codes by using simple mappings and fixed-point additions. Our decoding method is generic in the sense that it can be applied to LDPC codes with arbitrary degree distributions, and can be implemented based on either the belief propagation (BP) algorithm or the min-sum (MS) algorithm. In particular, we propose the MIM density evolution (MIM-DE) to construct the lookup tables (LUTs) for the node updates. The computational complexity and implementation complexity are discussed and compared to the LUT decoder variants. To accelerate the convergence speed of decoding quasi-cyclic LDPC codes, we consider the layered schedule, and develop the layered MIM-DE to design the LUTs based on MS algorithm, leading to the MIM layered quantized MS (MIM-LQMS) decoder. An optimization method is further introduced to reduce the memory requirement for storing the LUTs. Simulation results show that the MIM quantized decoders outperform the state-of-the-art LUT decoders in the waterfall region with both 3-bit and 4-bit precision. Moreover, the 4-bit MIM-LQMS decoder can approach the error performance of the floating-point layered BP decoder within 0:1 dB.

Spatially coupled serially concatenated codes: Analysis and extension

Spatially coupled serially concatenated codes (SC-SCCs) perform well in the error floor region over additive white Gaussian noise (AWGN) channel. In this paper, firstly, we investigate the impact of the component codes on the performances of SC-SCCs. Simulation results show that, by properly selecting the component codes, we can trade off the performances of the SC-SCCs over the error floor region and the waterfall region. Secondly, we introduce a class of spatially coupled multiple-concatenated codes, the recursive-superposition-based SC-SCCs (RS-SC-SCCs). We derive the exact density evolution (DE) equations of the RS-SC-SCCs over the binary erasure channels (BECs). These equations can be used to guide the selection of the component codes and the coupling ratios. Simulation results over the AWGN channels show that the proposed RS-SC-SCCs perform better than the SC-SCC in both the waterfall region and the error floor region.

Species Diversity of Epiphyte Fern Plants in Curug Lawe Waterfall Region, Semarang District

Epiphyte fern plants are fern plants that grow attached to the phorophyte tree. Existence of fern plants are effected by tree bark and environmental condition in which they grow. This research aimed to study the species composition, important value index, diversity index, evenness index, and similarity index of epiphyte fern plants in the Curug Lawe Waterfall Region Semarang District. This research was conducted on 5 research stations i.e. clove plantations area (CPA), irrigation canal (IC), mixed forest (MF), river flow (RF), and waterfall area (WA). The research used plot technique with plot size 10 m x 10 m. The results showed 11 species of epiphyte fern from 8 families were found. The highest important value index is obtained by Goniophlebium serratifolium. The diversity index of epiphyte fern plants are categorized as low and moderate. The evenness index of epiphyte fern plants are categorized as not evenly distributed, quite evenly distributed, and almost evenly distributed. The highest similarity index is in irrigation canal (IC) and river flow (RF). Environmental conditions in Curug Lawe Waterfall Region are suitable for epiphyte fern plants habitat. This research is novel as it provides some information about the community structure of epiphyte ferns in Curug Lawe Waterfall Region and to engage all peoples to maintain our biodiversity keep sustainable.

Systematic Convolutional Low Density Generator Matrix Code

In this paper, we propose a systematic low density generator matrix (LDGM) code ensemble, which is defined by the Bernoulli process. We prove that, under maximum likelihood (ML) decoding, the proposed ensemble can achieve the capacity of binary-input output symmetric (BIOS) memoryless channels in terms of bit error rate (BER). The proof technique reveals a new mechanism, different from lowering down frame error rate (FER), that the BER can be lowered down by assigning light codeword vectors to light information vectors. The finite length performance is analyzed by deriving an upper bound and a lower bound, both of which are shown to be tight in the high signal-to-noise ratio (SNR) region. To improve the waterfall performance, we construct the systematic convolutional LDGM (SysConv-LDGM) codes by a random splitting process. The SysConv-LDGM codes are easily configurable in the sense that any rational code rate can be realized without complex optimization. As a universal construction, the main advantage of the SysConv-LDGM codes is their near-capacity performance in the waterfall region and predictable performance in the error-floor region that can be lowered down to any target as required by increasing the density of the uncoupled LDGM codes. Numerical results are also provided to verify our analysis.

Error correction in data storage systems using polar codes

This paper investigates error correction in two-dimensional (2-D) intersymbol interference (ISI) channels using polar codes. 2-D channels offer high data storage capacity compared to traditional one-dimensional (1-D) channels but suffer from greater ISI effects. Error correction codes can be used to mitigate the effects of ISI in 2-D data storage systems and improve their performance and reliability. Polar codes achieve the symmetric capacity for the class of binary-input discrete memoryless channels (B-DMCs). A post-processing technique is proposed to improve the performance of polar codes in the 2-D ISI channel. The simplified successive cancellation (SSC) polar decoder is useful for data storage systems owing to its good waterfall region performance, low error floors and good throughput rates and is therefore adopted for the study. Simulation results indicate that the proposed technique has an error correction performance comparable to some existing decoders and has better performance than other decoding techniques.

Performance analysis of short length low density parity check codes

Outstanding bit error rate LDPC design in waterfall region and error floor region is one of the challenging tasks for the past decade. This chapter, focuses on the design of LDPC encoder with the low error floor and waterfall region of BER with minimum trapping set. Scheduled Progressive Edge-Growth (SPEG) LDPC encoder is used, and the simulation result of density evolution and exit chart are giving the better convergence of LDPC encoder. BER performance in error floor can controlled by minimum trapping set and waterfall region controlled by scheduled PEG LDPC encoder (1000, 500) with code length (n) is less than 600. The girth of the SPEG encoder is 8. SPEG with minimum trapping set will perform well for short length code also and it converges faster than the other PEG encoder.

Spatially coupled serially concatenated codes via parity re‐encoding

The recently introduced spatially coupled turbo-like codes are attractive in trading-off performances between the error-floor region and the water-fall region. This letter is concerned with the construction of spatially coupled serially concatenated codes. Particularly, a new construction of spatially coupled serially concatenated codes is presented, in which a portion of the encoding output of the previous inner encoder is taken as the input of the current inner encoder. The authors show that by proper selection of the component codes and the re-encoding ratio, performance gain about 0.25 dB is obtained with the proposed construction.

Deep Ensemble of Weighted Viterbi Decoders for Tail-Biting Convolutional Codes.

Tail-biting convolutional codes extend the classical zero-termination convolutional codes: Both encoding schemes force the equality of start and end states, but under the tail-biting each state is a valid termination. This paper proposes a machine learning approach to improve the state-of-the-art decoding of tail-biting codes, focusing on the widely employed short length regime as in the LTE standard. This standard also includes a CRC code. First, we parameterize the circular Viterbi algorithm, a baseline decoder that exploits the circular nature of the underlying trellis. An ensemble combines multiple such weighted decoders, and each decoder specializes in decoding words from a specific region of the channel words’ distribution. A region corresponds to a subset of termination states; the ensemble covers the entire states space. A non-learnable gating satisfies two goals: it filters easily decoded words and mitigates the overhead of executing multiple weighted decoders. The CRC criterion is employed to choose only a subset of experts for decoding purpose. Our method achieves FER improvement of up to 0.75 dB over the CVA in the waterfall region for multiple code lengths, adding negligible computational complexity compared to the circular Viterbi algorithm in high signal-to-noise ratios (SNRs).

Eksplorasi Lumut (Bryophyta) di Kawasan Air Terjun Bukit Gatan Provinsi Sumatera Selatan

<p><em>This study aims to determine the type of moss in the Bukit Gatan Waterfall Region of Ulu Terawas STL Musi Rawas Regency, as well as Abiotic Factors in the Bukit Gatan Waterfall Area in the District of Ulu Terawas STL Musi Rawas District. This research is descriptive Descriptive: direct observation in the location of the Bukit Gatan Waterfall Area, STL Ulu Terawas Musi Rawas Regency with a roaming method or exploring the Waterfall Area. Data were analyzed descriptively qualitatively. Types of moss found in 2 Classes namely Bryopsida and Hepaticopsida, consisting of 5 Orders namely Pottiales, Bryales, Fissidentales, Hypnales, and Jungermaniales, consisting of 5 Families namely Pottiaceae, Batramiaceae, Fissidentaceae, Hypnaceae and Plagiochilaceae, consisting of 6 Genus Hyophila, Philotiphll, Philotropll , and Plagiochila, consisting of 7 species namely Hyophila javanica, Philonotis hastata, Fissidens atroviridis, Hyophila apiculata, Ectropothecium sp., Taxiphyllum sp., and Plagiochila asplenoides. The Abioic Factor is pH Temperature which is an average of 6.6, temperatures with an average of 27 ºC, humidity with an average of 6.3% and at an appropriate light intensity of 285lux.</em></p>