Constraint Length Research Articles

Analysis of efficiency of the bioinspired method for decoding algebraic convolutional codes

It has been shown that convolutional codes are widely used, along with various decoding methods, to improve the reliability of information transmission in wireless telecommunication systems. The general principles of synthesis and the parameters and algebraic non-systematic convolutional codes with arbitrary coding rate and maximum achievable code distance have been shown. The basic stages of the bioinspired method for decoding algebraic convolutional codes using a random shift mechanism have been presented. It has been shown that the essence of the presented decoding method implies applying the procedure of differential evolution with the heuristically determined parameters. In addition, this method uses information about the reliability of the adopted symbols to find the most reliable basis for the generalized generator matrix. The mechanism of random shift for the modification of the accepted sequence is additionally applied for the bioinspired search based on various most reliable bases of a generalized generator matrix. The research results established that the bioinspired method for decoding algebraic convolutional codes ensures greater efficiency compared with the algebraic decoding method in the communication channel with additive white Gaussian noise. Depending on the parameters of the algebraic convolutional code and the necessary error coefficient, the energy gain from encoding ranges from 1.6 dB to 3 dB. It was shown that the presented bioinspired decoding method can be used for convolutional codes with a large code constraint length. In doing so, the presented method for decoding algebraic convolutional codes is less efficient than the Viterbi decoding method and turbo codes at a sufficient number of decoding iterations

Performance Analysis of Convolution Code with Variable Constraint Length in Shallow Underwater Acoustic Communication

Performance Analysis of Convolution Code with Variable Constraint Length in Shallow Underwater Acoustic Communication

Design and Simulation of Bit-interleaved SCCPM with Physical-layer Network Coding

Serially concatenated continuous phase modulation (SCCPM) is bandwidth and power efficient in point-to-point communication systems. The physical-layer network coding (PNC) protocol propsed in 2006 can boost the throughput of a two-way relay channel (TWRC). In this paper, we integrate SCCPM with bit interleavers into PNC, i.e., SCCPM-PNC, which inherits the advantages of the both, in wireless TWRC. The decoding structure of the relay for the superimposed SCCPM signals is designed. Furthermore, the influences of various parameters such as the constraint length of convolutional code (CC), the interleaver size and the number of iterations, on the performance of SCCPM-PNC are simulated and discussed.

Low-complexity LDPC-convolutional codes based on cyclically shifted identity matrices

In this study, a construction methodology for low-density parity-check convolutional codes (LDPC-CCs) ensembles based on cyclically shifted identity matrices is proposed. The proposed method directly generates the syndrome former matrices according to the specified code parameters and constraints i.e., code-rate, degree-distribution, constraint length, period and memory, in contrast to the majority of the available approaches that produce relevant error-correcting codes based on either block ones, protographs or spatially-coupled type of codes. Simulation results show that the constructed ensembles demonstrate advanced error-correcting capability of up to 0.2 dB in terms of frame-error and bit-error rates at the convergence region, when compared with the performance of error-correcting schemes adopted by various communication standards, with equivalent hardware complexity even at short codeword-lengths. Specifically, the constructed LDPC-CCs have been assessed against the corresponding error-correcting codes used in WiMAX and G.hn standards for wireless and wireline telecommunications, respectively.

Steganography Performance over AWGN Channel

Steganography can be performed using frequency domain or spatial domain. In spatial domain method, the least significant bits (LSB) is the mostly used method where the least significant bits of the image's pixels binary representation are used to carry the confidential data bits. On the other hand, secret data bits in the frequency domain technique are hidden using coefficients of the image frequency representation such as discrete cosine transform (DCT). Robustness against image attacks or channel's noise is a key requirement in steganography. In this paper, we study the performance of the steganography methods over a channel with Added White Gaussian Noise (AWGN). We use the bit error rate to evaluate the performance of each method over a channel with different noise levels. Simulation results show that the frequency domain technique is more robust and achieves better bit error rate in a noisy channel than the spatial domain method. Moreover, we enhanced the steganography system robustness by using convolution encoder and Viterbi decoder. The effect of the encoder’s parameters, such as rate and constraint length is evaluated.

Low-complexity LDPC-convolutional codes based on cyclically shifted identity matrices

In this study, a construction methodology for low-density parity-check convolutional codes (LDPC-CCs) ensembles based on cyclically shifted identity matrices is proposed. The proposed method directly generates the syndrome former matrices according to the specified code parameters and constraints i.e., code-rate, degree-distribution, constraint length, period and memory, in contrast to the majority of the available approaches that produce relevant error-correcting codes based on either block ones, protographs or spatially-coupled type of codes. Simulation results show that the constructed ensembles demonstrate advanced error-correcting capability of up to 0.2 dB in terms of frame-error and bit-error rates at the convergence region, when compared with the performance of error-correcting schemes adopted by various communication standards, with equivalent hardware complexity even at short codeword-lengths. Specifically, the constructed LDPC-CCs have been assessed against the corresponding error-correcting codes used in WiMAX and G.hn standards for wireless and wireline telecommunications, respectively.

On Optimizing the PAPR of OFDM Signals With Coding, Companding, and MIMO

One main disadvantage of the multiple-input-multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) system is that the signals transmitted on each antenna may experience high peak-to-average-power ratio (PAPR). We will present a new hybrid PAPR reduction technique that combines and optimizes three methods, namely convolutional code, successive suboptimal cross-antenna rotation and inversion (SS-CARI), and iterative modified companding and filtering. The results for the hybrid PAPR reduction technique show that this scheme significantly reduces the PAPR compared with SS-CARI alone; it can improve the bit error rate to levels better than what obtains with the space–time block coding MIMO-OFDM system, and the spectral splatter due to companding is also controlled by the use of frequency-domain filtering. In addition, it is a flexible technique in which the net gain can be optimized based on the requirements of scheme parameters, such as the code rate, the constraint length of the convolutional code, the number of subblocks for SS-CARI, and the companding parameters.

Complexity considerations: efficient image transmission over mobile communications channels

In this paper the computational complexity of the image transmission over mobile communications channel is investigated. The computational complexity due to the amount of transmitted data and the utilized data protection schemes is analyzed over wireless channel with the different image transmission scenarios. The proposed secured and efficient protection technique is presented in this research work with lower computational complexity. The presented technique is based on chaotic-Baker encryption which is utilized as an interleaver to randomize the data packet in the proposed secured interleaved channel coding technique. The proposed technique is evaluated utilizing convolutional codes with different constraint lengths and single error correction block code. Different images with the size variation are utilized for evaluating the proposed image transmission scenarios. Numerical analysis of the different scenarios is presented. The secret key generation of chaotic-Baker encryption is discussed; it can be generated automatically or manually. Several computer simulation experiments are carried out to evaluate the proposed techniques performance. Different objective measures error based metrics are used such as the Bit Error Rate (BER), Peak Signal to Noise Ratio (PSNR) and Number of Lost packet percentage (NLP%) to measure the error performance of the proposed technique and quality of the received images. Simulation results reveal a good performance and the superiority of the proposed technique with lower computational complexity of the proposed image transmission scenarios.

The predictable degree property and minimality in multidimensional convolutional coding

Convolutional codes inherit from polynomials a natural structure of a filtered module, which is a fundamental structure and therefore should be taken into account. Pursuing this idea, we define higher-dimensional analogs of the predictable degree property, Forney’s indices and overall constraint length; also, we address the important issue of minimality.

An Energy-Efficient Network-on-Chip-Based Reconfigurable Viterbi Decoder Architecture

This paper presents an energy-efficient network-on-chip (NoC)-based multi-core architecture for realizing a reconfigurable Viterbi decoder (VD). The proposed architecture can support a wide range of wireless communication standards that have varied constraint lengths. The energy efficiency in the proposed architecture has been primarily achieved by mapping the add–compare–select operations of the VD onto a $4\times 4$ ZMesh topology-based NoC and then by employing a reconfigurable memoryless survivor memory unit to decode the input symbols. When compared with the existing ASIC-based multi-core VD architectures, the proposed architecture achieves an improvement by at least 3.06 times in the energy consumption per decoded bit (EC) metric. Similarly, when compared with the state-of-the-art single-core VD architectures, the proposed architecture achieves an improvement by at least 4.99 times in the EC metric.

Planar Lithium Battery Cell Development to Advance in-Operando Nano-CT Imaging of Graphite Electrodes

In-operando nano-scale resolution X-ray computed tomography (nano-CT) imaging provides an excellent new possibility to investigate a wide variety of phenomena in the electrodes of Li-ion batteries. The 3D X-ray imaging provides direct observation of internal morphological changes in electrodes with up to 50 nm resolution regarding standard materials and electrolyte, which is difficult or impossible to achieve by electron microscopy. Such fine resolution enables the possibility to observe detailed structural changes like the deposition of electrolyte decomposition products within the electrode, transition from Li intercalation to electroplating on graphite, and lithium dendrite formation and growth. One task for applying in-situ nano-CT imaging on Li-ion battery imaging is to develop special lithium battery cells compatible with both the nano-CT instrument’s sample size constraint and X-ray attenuation length limits of higher atomic number materials. Herein, we have developed a planar cell design that allows us to use commercial electrode, separator, and electrolyte. Successful charging and discharging has been achieved with this planar cell design using commercial graphite, LiMn2O4, and lithium foil electrodes. In-operando nano-CT imaging is performed on planar cell lithium battery with focus on graphite anodes. The experimental methodology developed in this study has applicability to test wide ranges of electrolyte, separators and other electrode materials in Li-ion batteries.

Efficient Search of Compact QC-LDPC and SC-LDPC Convolutional Codes With Large Girth

We propose a low-complexity method to find quasi-cyclic low-density parity-check block codes with girth 10 or 12 and length shorter than those designed through classical approaches. The method is extended to time-invariant spatially coupled low-density parity-check convolutional codes, permitting to achieve small syndrome former constraint lengths. Several numerical examples are given to show its effectiveness.

A Low-Complexity Maximum-Likelihood Decoder for Tail-Biting Convolutional Codes

Due to the growing interest in applying tail-biting convolutional coding techniques in real-time communication systems, fast decoding of tail-biting convolutional codes has become an important research direction. In this paper, a new maximum-likelihood decoder for tail-biting convolutional codes is proposed. It is named bidirectional priority-first search algorithm (BiPFSA) because priority-first search algorithm has been used both in forward and backward directions during decoding. Simulations involving the antipodal transmission of (2, 1, 6) and (2, 1, 12) tail-biting convolutional codes over additive white Gaussian noise channels shows that BiPFSA not only has the least average decoding complexity among the state-of-the-art decoding algorithms for tail-biting convolutional codes but can also provide a highly stable decoding complexity with respect to growing information length and code constraint length. More strikingly, at high SNR, its average decoding complexity can even approach the ideal benchmark complexity, obtained under a perfect noise-free scenario by any sequential-type decoding. This demonstrates the superiority of BiPFSA in terms of decoding efficiency.

Efficacy Estimation of O-IDMA with Convolutional Codes of Variable Constraint Lengths at Merest Loss using Multi farious Inter-leaver

Efficacy Estimation of O-IDMA with Convolutional Codes of Variable Constraint Lengths at Merest Loss using Multi farious Inter-leaver

A multistandard and resource-efficient Viterbi decoder for a multimode communication system

We present a novel standard convolutional symbols generator (SCSG) block for a multi-parameter reconfigurable Viterbi decoder to optimize resource consumption and adaption of multiple parameters. The SCSG block generates all the states and calculates all the possible standard convolutional symbols corresponding to the states using an iterative approach. The architecture of the Viterbi decoder based on the SCSG reduces resource consumption for recalculating the branch metrics and rearranging the correspondence between branch metrics and transition paths. The proposed architecture supports constraint lengths from 3 to 9, code rates of 1/2, 1/3, and 1/4, and fully optional polynomials. The proposed Viterbi decoder has been implemented on the Xilinx XC7VX485T device with a high throughput of about 200 Mbps and a low resource consumption of 162k logic gates.

Design and Implementation of Viterbi Decoder Using VHDL

A digital design conversion of Viterbi decoder for ½ rate convolutional encoder with constraint length k = 3 is presented in this paper. The design is coded with the help of VHDL, simulated and synthesized using XILINX ISE 14.7. Synthesis results show a maximum frequency of operation for the design is 100.725 MHz. The requirement of memory is less as compared to conventional method.

Systematic Block Markov Superposition Transmission of Repetition Codes

In this paper, we propose systematic block Markov superposition transmission of repetition (BMST-R) codes, which can support a wide range of code rates but maintain essentially the same encoding/decoding hardware structure. The systematic BMST-R codes resemble the classical rate-compatible punctured convolutional codes, except that they are typically non-decodable by the Viterbi algorithm due to the huge constraint length induced by the block-oriented encoding process. The information sequence is partitioned equally into blocks and transmitted directly, while their replicas are interleaved and transmitted in a block Markov superposition manner. By taking into account that the codes are systematic, we derive both upper and lower bounds on the bit-error-rate (BER) under maximum a posteriori decoding. The derived lower bound reveals connections among BER, encoding memory and code rate, which provides a way to design good systematic BMST-R codes and also allows us to make trade-offs among efficiency, performance, and complexity. Numerical results show that: 1) the proposed bounds are tight in the high signal-to-noise ratio region; 2) systematic BMST-R codes perform well in a wide range of code rates; and 3) rate 1/2 systematic BMST-R codes outperform the considered (3,6)- and (4,8)-regular spatially coupled low-density parity-check codes under an equal decoding latency constraint.

Systematic Wavelet Codes: Designed and Decoded by DFT Vectors

A class of complex-valued convolutional codes, wavelet codes, that encode numbers into numbers, is constructed by assigning consecutively indexed discrete Fourier transform (DFT) vectors to the parity-checking requirements. For a rate $k/n$ code with constraint length $m$ , the parameters must satisfy (m + 1)(n-k) $m$ , the errors can be corrected by extracting from the convolutional code’s syndromes, new syndromes associated with a DFT block code inherent in the code’s algebraic structure. A modified Berlekamp–Massey algorithm computes the error locations and the correcting values are determined by an inverse DFT operation. Systematic forms of these codes are developed by manipulating the original generating transfer function. Each systematic form is a subcode of the original wavelet code from which it was determined. Moreover, this form may be decoded by DFT code methods too. Extensive simulation results verify the power and viability of both forms of the codes and their decoding techniques.

Improving PSD of PPM-IR for UWB Signal Using Turbo Encoder

The repression of the spectral line is a matter of main attention in designing of Time Hopping Impulse Radio (TH-IR) Ultra-Wide Band (UWB) systems. This case has been usually processed by randomizing the locations of every pulse. This requires to employ of very long Pseudo Noise (PN) sequences to suppress the capabilities of spectral lines. This research aims to improve the Power Spectral Density (PSD) by constructing the proposed system using Turbo code technique inside MATLAB’s Simulink. We found that our proposed system provides high performance than Conventional PPM-TH-IR in term of eliminating the spectral lines or make it smoother. We also found that the increasing in interleaver length and constraint length enhances PSD.

Design and Analysis of Time-Invariant SC-LDPC Convolutional Codes With Small Constraint Length

In this paper, we deal with time-invariant spatially coupled low-density parity-check convolutional codes (SC-LDPC-CCs). Classic design approaches usually start from quasi-cyclic low-density parity-check block codes and exploit suitable unwrapping procedures to obtain SC-LDPC-CCs. We show that the direct design of the SC-LDPC-CCs syndrome former matrix or, equivalently, the symbolic parity-check matrix, leads to codes with smaller syndrome former constraint lengths with respect to the best solutions available in the literature. We provide theoretical lower bounds on the syndrome former constraint length for the most relevant families of SC-LDPC-CCs, under constraints on the minimum length of cycles in their Tanner graphs. We also propose new code design techniques that approach or achieve such theoretical limits.