Increasing Code Length Research Articles

Bit Error Rate Performance in CDMA Free Space Optical Links with SIK Receiver under Fog Conditions

This article presents a novel analytical method for evaluating fog's impact on Bit Error Rate (BER) in an Optical Code Division Multiple Access (OCDMA) Free Space Optical (FSO) connection. The investigation employs an optical encoder and direct detection receiver employing a balanced photo detector with Sequence Inverse Keying (SIK) to explore fog effects. By scrutinizing multi-access interference (MAI) current and signal current values at the SIK receiver's output under varied fog conditions, we deduce BER expressions for diverse scenarios. These encompass different fog thickness levels, code lengths, simultaneous users, and system parameters. The results reveal substantial OCDMA degradation due to fog thickness and users. Also, the system incurs a marked power penalty at a specific BER, especially with higher fog and user density. However, we identify a potential solution: increasing code length, effectively mitigating fog-induced performance decline.

Serially Concatenated Low-density Parity Check Codes as Compatible Pairs

Low-density parity checks (LDPC) codes are considered good performance error correction codes. However, decoder complexity increases with increasing code length. In this study, we introduce short-length serially concatenated LDPC codes. The proposed technique uses pairs of compatible LDPC codes that act as outer and inner serially concatenated codes. In this code pair, the inner code takes input that is the same length as the outer LDPC encoder output. This study examined two cases of LDPC codes as compatible pairs with low numbers of iterations and compared bit error rate (BER) performance to a standalone LDPC code with an additive white Gaussian noise channel. We also considered the quadrature phase shift keying QPSK, 16-quadrature amplitude modulation (QAM), and 64-QAM system modulation schemes. Simulation results demonstrate that the proposed system has good BER performance compared to a standalone LDPC code, the results summarized in table and performance curves.

A Novel c-VEP BCI Paradigm for Increasing the Number of Stimulus Targets Based on Grouping Modulation With Different Codes.

In an existing brain-computer interface (BCI) based on code modulated visual evoked potentials (c-VEP), a method with which to increase the number of targets without increasing code length has not yet been established. In this paper, a novel c-VEP BCI paradigm, namely, grouping modulation with different codes that have good autocorrelation and crosscorrelation properties, is presented to increase the number of targets and information transfer rate (ITR). All stimulus targets are divided into several groups and each group of targets are modulated by a distinct pseudorandom binary code and its circularly shifting codes. Canonical correlation analysis is applied to each group for yielding a spatial filter and templates for all targets in a group are constructed based on spatially filtered signals. Template matching is applied to each group and the attended target is recognized by finding the maximal correlation coefficients of all groups. Based on the paradigm, a BCI with a total of 48 targets divided into three groups was implemented; 12 and 10 subjects participated in an off-line and a simulated online experiments, respectively. Data analysis of the offline experiment showed that the paradigm can massively increase the number of targets from 16 to 48 at the cost of slight compromise in accuracy (95.49% vs. 92.85%). Results of the simulated online experiment suggested that although the averaged accuracy across subjects of all three groups of targets was lower than that of a single group of targets (91.67% vs. 94.9%), the average ITR of the former was substantially higher than that of the later (181 bits/min vs. 135.6 bit/min) due to the large increase of the number of targets. The proposed paradigm significantly improves the performance of the c-VEP BCI, and thereby facilitates its practical applications such as high-speed spelling.

R2PCAH: Hashing with two-fold randomness on principal projections

Hashing based strategies have recently been widely used in fast similarity search on large scale datasets. Data-independent methods such as Locality Sensitive Hashing (LSH) usually adopt random projections as hash functions, with theoretical guarantees that the performance improves with the increasing code length. Thus they require relatively long codes, making them less effective than data-dependent methods. On the other hand, in many data-dependent hashing methods, Principal Component Analysis (PCA) is widely used to generate compact hash codes. However, PCA based methods tend not to be effective for generating long codes because projections with small variances may induce certain redundancy and noise. In order to address these deficiencies, we present a R2PCAH framework that conducts two-fold random transformations based on principal projections for hash code learning. Specifically, only the top PCA projections of the training data are extracted and two-fold random transformations, i.e. random rotations and random shifts are performed on the projected data to generate several pieces of component short codes. The multiple component short codes are then concatenated into one piece of long code. We observe that our method shares the advantages of both LSH and PCA based hashing methods. Extensive experiments demonstrate the effectiveness of the proposed method.

Performance Analysis of Low Complexity Error Correcting Codes

From Shannon limit it is known that, for a particular bandwidth and noise characteristics, there exists a maximum rate at which data can be transmitted with arbitrarily small number of errors. Coding schemes are utilized to improve the data transmission efficiency. The paper aims to represent the comparative performance analysis of Low Density Parity Check (LDPC) codes and Bose-Chaudhuri-Hocquenghem (BCH) codes in transmitting data over noisy channel for different parameters. The performance of LDPC block codes is simulated for different decoding schemes and code rates. Performance analysis of LDPC codes is also shown for regular and irregular codes. For fixed error correcting capability, the BCH coding scheme is further simulated for different code length with increasing code length. The simulated output is worthwhile to analyze the performance of a communication system before the physical implementation of the system.

Pump encoding in distributed Brillouin fiber sensors

Pump encoding is an effective approach to enhance the weak signal detection in distributed Brillouin fiber sensors. In this paper, a new encoding matrix that can improve the detection performance is proposed. Furthermore, a distributed fiber sensor for both single and encoding pump operations is numerically analyzed by using Brillouin-scattering coupled amplitudes equations. The results demonstrate that the matrix can reduce the transmission times for pumping light and simplify the coding process. The power of the scattering signal and the coding gain can be improved with the increasing code length. The detected scattering optical power is almost three orders of magnitude higher than that of the single pulse pump, as the coding length is 31, corresponding to 14.4 % improvement for the coding gain compared with the S matrix encoding method. At the same time, the temperature uncertainty can also be decreased.

Low-Complexity Soft-Decoding Algorithms for Reed–Solomon Codes—Part I: An Algebraic Soft-In Hard-Out Chase Decoder

In this paper, we present an algebraic methodology for implementing low-complexity, Chase-type, decoding of Reed-Solomon (RS) codes of length n . In such, a set of 2 ? test-vectors that are equivalent on all except ? ? n coordinate positions is first produced. The similarity of the test-vectors is utilized to reduce the complexity of interpolation, the process of constructing a set of polynomials that obey constraints imposed by each test-vector. By first considering the equivalent indices, a polynomial common to all test-vectors is constructed. The required set of polynomials is then produced by interpolating the final ? dissimilar indices utilizing a binary-tree structure. In the second decoding step (factorization) a candidate message is extracted from each interpolation polynomial such that one may be chosen as the decoded message. Although an expression for the direct evaluation of each candidate message is provided, carrying out this computation for each polynomial is extremely complex. Thus, a novel, reduced-complexity, methodology is also given. Although suboptimal, simulation results affirm that the loss in performance incurred by this procedure is decreasing with increasing code length n, and negligible for long (n > 100) codes. Significant coding gains are shown to be achievable over traditional hard-in hard-out decoding procedures (e.g., Berlekamp-Massey) at an equivalent (and, in some cases, lower) computational complexity. Furthermore, these gains are shown to be similar to the recently proposed soft-in-hard-out algebraic techniques (e.g., Sudan, Ko?tter-Vardy) that bear significantly more complex implementations than the proposed algorithm.

Cost effective operator training

The graphical front-ends of large scale operator training simulators traditionally consist of hundreds of thousands of lines of code. Given the undiminished and expanding demand for increased graphical complexity, this figure is set to approach or exceed tens of millions of lines of code by the end of this decade. The scale of this trend is such that the conventional development of training simulators using procedural code will become disproportionately costly, difficult to update and ultimately unmanageable. To counteract the implications of increasing code length and program complexity, graphical interfaces can now be developed using object-oriented programming methods. To produce cost effective operator training, advantage may also be taken from other recent developments in computing technology, notably the rise in power of the personal computer (PC) combined with a decrease in its cost. This paper explores currently available simulation based operator training platforms and the extent to which PCs can be used for the provision of low cost dynamic operator training. The example involves the use of a novel object-orientated programming method for the front-end which has then been linked to a dynamic simulation package executing either on a networked workstation or on a PC.

Coherent ultrashort light pulse code-division multiple access communication systems

A new technique for encoding and decoding of coherent ultrashort light pulses is analyzed. In particular, the temporal and statistical behavior of pseudonoise bursts generated by spectral phase coding of ultrashort optical pulses is discussed. the analysis is motivated by recent experiments that demonstrate high-resolution spectral phase coding of picosecond and femtosecond pulses and suggest the possibility of ultrahigh speed code-division multiple-access (CDMA) communications using this technique. The evolution of coherent ultrashort pulses into low intensity pseudonoise bursts as a function of the degree of phase coding is traced. The results are utilized to analyze the performance of a proposed CDMA optical communications system based upon encoding and decoding of ultrashort light pulses. The bit error rate (BER) is derived as a function of data rate, number of users, and receiver threshold, and the performance characteristics are discussed for a variety of system parameters. It is found that performance improves greatly with increasing code length. >

Decoding of triple and quadruple error‐correcting BCH codes by direct solving of error‐locator polynomials

AbstractThe error‐correcting codes have been used extensively to increase the reliability of digital systems in data communication. However, with increasing error‐correcting capability, the complexity of decoders also increases. At present, only one‐bit and two‐bit error‐correcting codes are used. This paper proposes a decoding algorithm for triple and quadruple error‐correcting BCH codes. In decoding the BCH codes, the error‐locator polynomials must be solved by Chien's algorithm. In his method, however, with increasing code length, the decoder becomes complicated and the efficiency deteriorates. In the method proposed in this paper, the fourth‐or lower‐order equations are reduced to the quadratic equation and, therefore, the efficiency is good. This method is also independent of the code length. Its function and efficiency are confirmed by simulation using microcomputer. The present decoding algorithm enables one to realize an efficient decoder with hardware construction using the ROM.

Long BCH codes are bad

The BCH bound approaches zero with increasing code length for any fixed value of the ratio of minimum distance to code length. Does this happen because the codes actually deteriorate or does the bound just become loose? It is shown that the BCH bound gives the true minimum distance within a factor of two. We conclude that it is the codes, not the bound, which deteriorate with increasing code length.