A Bandwidth Efficient Constant Envelope Modulation with Reed-Solomon Coding

In recent years, conveying information using molecules via diffusion has attracted significant interest in micro and nanoscale applications. Yet, very little research have been conducted on the performance analysis of large-scale molecular communication (MC) systems with swarm of interfering receivers. In this type of MC system, the collective signal strength at a desired receiver can be impaired by the interference caused by other MC transmitters. The paper presents the first tractable analytical framework for the collective signal strength at a partially absorbing receiver due to a desired transmitter under the impact of a swarm of interfering transmitters in a three-dimensional (3D) large-scale MC system using stochastic geometry. We propose Reed Solomon (RS) coding as an error correction technique to combat the effects of interference caused by the multiple transmitters and the delayed molecules from the previous bits. We derive analytical expressions for the bit error probability (BEP) to evaluate the level of reliability that can be achieved by the proposed scheme. The results obtained using Monte Carlo simulations, matched extactly with the anlytical results, justifying the accuracy of the derivations. Results reveal that the RS codes are capable of providing an acceptable level of improvement in terms of BEP. Furthermore, by carefully selecting the code length, n, and the message length, k, of the RS(n, k) code, we can fine tune the BEP improvement to match the system requirements.

This paper presents a comprehensive analysis and implementation of various error correction coding methods, focusing on Reed-Solomon (RS) codes and Liberation codes in RAID6 systems. RS codes are emphasized for their robust error correction capabilities, making them ideal for high-reliability environments such as enterprise data centers and mission-critical systems, where the ability to correct multiple errors or data losses is crucial. In contrast, Liberation codes are noted for their superior encoding efficiency and lower computational complexity, making them well-suited for high-performance systems with stringent speed requirements. Through experimental comparisons, this study also evaluates Cauchy Reed-Solomon (CRS) codes, EVENODD codes, and Blaum-Roth (BR) codes, identifying the strengths and weaknesses of each method in various scenarios. The findings underscore the importance of selecting the appropriate coding technique based on system-specific requirements, as different use cases benefit from different error correction schemes in terms of performance and data reliability. Additionally, this research highlights the potential of these coding methods in broader distributed storage applications and discusses the trade-offs between them. Future research directions are suggested, particularly in optimizing existing codes and expanding their application in more complex and distributed storage environments.

Hermitian codes are an attractive alternative to Reed-Solomon codes for use in frequency-hop (FH) spread-spectrum packet radio networks. For a given alphabet size, a Hermitian code has a much longer block length than a Reed-Solomon code. This and other considerations suggest that Hermitian codes may be superior for certain applications. Analytical results are developed for the evaluation of the packet error probability for FH transmissions using Hermitian coding. We find there are several situations for which Hermitian codes provide much lower packet error probabilities than can be obtained with Reed-Solomon codes. In general, as the code rate decreases or the symbol alphabet size increases, the relative performance of Hermitian codes improves with respect to Reed-Solomon codes. Performance evaluations are presented for an additive white Gaussian noise channel and for a catastrophic partial-band interference channel, and the packet error probability is evaluated for both errors-only and errors-and-erasures decoding.

In this paper, we examine the bit error probability (BEP) performance of binary non-coherent modulations over L-branch selective combining (SC) diversity in frequency-flat, slowly-varying double Rice fading channels. The double Rice fading channel is constructed as the product of two independent but not identically distributed Rice processes. In addition, we assume that the double Rice processes affecting the signal received over the L branches of the diversity system are independent and identically distributed. Under these assumptions, and by using the cumulative distribution function (CDF) approach, we derive an expression for the average BEP performance of binary noncoherent frequency-shift keying (FSK) and differential phase-shift keying (DPSK) modulations. The result elaborated is generic in that it includes the propagation environments described by RayleighxRice and double Rayleigh fading models as special cases. The result is in the form of semi-infinite range integrals, that are easy to compute numerically. Additionally, for the special case of dual-branch SC diversity, i.e., L = 2, relatively simplified expressions for the BEP performance are obtained. Moreover, illustrative numerical results are presented together with corresponding simulation quantities to check the validity of the derived analytical quantities, and analyze the impact of the fading parameters on the BEP performance. The results are useful in assessing the performance of amplify-and-forward (AF) dual-hop vehicle-to-vehicle (V2V) communications with line-of-sight (LOS) paths, and where the additive noise in the relay station can be neglected.

A comprehensive performance analysis of relay-aided CDMA communications over dissimilar fading channels

This paper presents a parallel architecture for a high-speed Reed-Solomon (RS) encoder and decoder (codec) LSI. Since the architecture allows H symbols to be processed in parallel the codec LSI achieves a data rate of mLH b/s. where m is the symbol size (m bits per symbol), L is the clock frequency of the circuit, and H is an arbitrary integer. As an example, we investigate hardware complexity, delay and critical path length for a (255.251) RS code. It is shown that both the hardware complexity and the delay for a parallel circuit is much less than that with the parallel operation of H conventional circuits. Although the only problem with, this parallel architecture is that the encoder's critical path length increases with H, the proposed architectures is more efficient than a setup using H conventional circuits for high data rate applications. It is also suggested that parallel RS codecs, which can keep up with optical transmission rates, i.e. several giga bits/sec. could be implemented on one LSI chip, using current CMOS technology.

An efficient network is critical to support the rapid growth in traffic on mobile networks, since current network PCS1900 (2G) cannot support such a huge demand. The objective of the third-generation (3G) UMTS (Universal Mobile Telecommunication System) of wireless communication is to provide high speed wireless communication to support multimedia, large data, and video. However, the co-existence of the two mobile radio systems (PCS1900 and UMTS) which share the same frequency band leads to a major issue. A serious issue of co-existence occurs when the downlink of the system is closer to the frequency bands of the concerned system. The PCS-1900 downlink band (1,930-1,990) and WCDMA (UMTS) uplink band (1,920-1,980) widely overlap, which causes interference between UMTS mobile unit and PCS-1900 base station. Therefore the objectives of this paper is to study the effect from PCS 1900 base station interference on UMTS mobile unit performance in terms of the probability of bit error by developing the Probability of bit error equation of DSS-QPSK from the existing Probability of bit error equation. This paper also evaluates the degradation of UMTS mobile unit performance in terms of probability of bit error when the system is interfered by PCS1900 base station.

We analyzed the bit error probability of a single RS codeword with symbol overlapping. By symbol overlapping, we mean that the bits in each modulation symbol can belong to 2 or more RS symbols and vice versa. We propose two novel designs for Reed-Solomon (RS) coded modulation with symbol overlapping. For an RS code with symbol size GF(2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> ), the information bits are first RS coded. For the first strategy, the coded bits are matrix interleaved prior to modulation and for the second strategy, the RS symbols are matrix interleaved and the resulting coded symbols are shifted circularly by n/2 bits prior to modulation. In this paper, we considered a M = 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> -ary modulation scheme. The received signal is demodulated appropriately, de-interleaved and RS decoded. The decoded symbols are interleaved and sent to the demodulator where it makes use of the decoded symbols from other codewords to re-demodulate the signals. This process is repeated until there is no improvement in the bit error rate. It is observed that this simple coded modulation design scheme has about 0.5 dB better performance than one that does not employ symbol overlapping over an AWGN channel at bit error rate of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> . An improvement of 1 dB is observed over a Rayleigh fading channel

Enhanced connectivity through double RIS uplink MIMO and advanced modulation

Performance of single and dual-polarized optically preamplified M-ary PPM systems with finite extinction ratios over FSO fading channels

Smart building is an effective solution to address the issue of energy consumption in today's cyber-physical systems (CPSs) connected world. As an important tool to collect information from a fleet of electric appliance that installed in the building scope, a wireless sensor network is widely employed for this purpose. In this paper, we propose to incorporate forward error correction into the media access control layer of IEEE 802.15.4 standard for packets transmission, as the originally used automatic repeat request mechanism is a timing and energy consumed process that should be avoided in a noisy wireless channel of a smart building environment. Based on the developed CPS simulation platform, the bits error rate and packets error rate of convolutional codes (CCs), Reed-Solomon (RS) codes, and their concatenated codes are intensively investigated, on condition of been applied to different packet length and code rates. We show that the CCs are superior to other codes in most cases. However, the RS and CCs concatenated codes are good candidates, and the RS codes with larger symbol length are preferred for a longer packet. In this regard, future research will concentrated on non-line-of-sight wireless channel, and take the pulse interference from other devices into account.

Cooperative sensing (CS) is important for efficiently acquiring spectrum awareness in cognitive radio systems. The main focus of this paper is on the BEP (bit error probability) walls for soft decision (SD) based CS in cognitive radios. The BEP wall is a performance limitation for CS caused by imperfect reporting channels. In this paper, a distributed detection system using parallel sensing topology and a fusion center (FC) is considered. Each secondary user (SU) sends energy-based multibit SD to the FC over a reporting channel with a certain BEP. The maximum output entropy (MOE) quantization is considered for quantizing the estimated energy. For the considered case, it is established that the BEP wall values for SD based CS with MOE quantization are identical for arbitrary number of bits for quantization. Moreover, the BEP wall values for SD based CS with MOE quantization are proven to be the same as the BEP wall values for the Chair-Varshney fusion rule, which is an optimal fusion rule for one-bit hard decision based CS. Later relation between the BEP wall values of the SD based CS and the K-out-of-N fusion rules is also established.

In this paper, analytical methods for calculating the average probability of bit error of direct sequence ultra wideband (DS-UWB) system and time hopping pulse position modulation (TH-PPM) UWB system are given. In our proposed multiuser DS UWB system, the bipolar pulse amplitude modulation is used in order to achieve better performance. As we know, more attention is paid to the TH-PPM UWB systems recently. In this paper, we first introduce the accurate BER calculation methods of the multiuser DS-PAM and TH-PPM UWB systems and then give the performance analysis over an ideal AWGN channel and a correlation receiver. Furthermore, we also introduce their applications in image transmission and data transmission and give the simulation results. The analytical method yields simple and exact formulas relating the performance to the system parameters.

Polar codes have attracted much recent attention as one of the first codes with low computational complexity that provably achieve optimal rate-regions for a large class of information-theoretic problems. One significant drawback, however, is that for current constructions the probability of error decays sub-exponentially in the block-length more detailed designs improve the probability of error at the cost of significantly increased computational complexity. In this work we show how the the classical idea of code concatenation - using "short" polar codes as inner codes and a "high-rate" Reed-Solomon code as the outer code - results in substantially improved performance. In particular, code concatenation with a careful choice of parameters boosts the rate of decay of the probability of error to almost exponential in the block-length with essentially no loss in computational complexity. We demonstrate such performance improvements for three sets of information-theoretic problems - a classical point-to-point channel coding problem, a class of multiple-input multiple output channel coding problems, and some network source coding problems.

We demonstrate experimentally for the first time the impact of forward error correction (FEC) on the performance of 622/1244 Mb/s burst-mode clock and data recovery (BM-CDR) with instantaneous phase acquisition (0 bit) for any phase step (plusmn27pi rads) for gigabit-capable passive optical network (GPON) optical line terminator (OLT) applications with (255, 239) Reed-Solomon (R-S) codes. Our design is based on commercially available SONET CDRs operated in 2times over sampling mode. This burst-mode receiver (BM-RX) provides a ~5 dB coding gain at bit error ratio (BER) of 10-10. We also show that this novel technique of employing FEC on BM-CDRs with fast phase acquisition time, provides a solution for fast burst-error correction giving reliable and predictable BERs in bursty-channels. The BM-RX meets the GPON physical media dependent layer specifications defined in the ITU-T G.984.2 recommendation. The coding gain can be used to increase the optical link budget as specified in the ITU-T G.984.3 standard, that is, support higher bit rates, achieve longer physical reach between the OLT and the optical network units (ONUs), as well as increase the number of splits per single PON tree.