Frequency-hop spread-spectrum packet radio with Hermitian codes

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.

Algebraic codes are important in communication and storage systems where soft information is limited and decoding efficiency is critical. Among them, algebraic-geometric (AG) codes are promising candidates to replace the widely used Reed-Solomon (RS) codes. However, their more sophisticated algebraic structure results in high decoding complexity, hindering their practical application. This paper proposes a novel interpolation-based algebraic soft decoding (ASD) for one of the most important AG codes - Hermitian codes. Given a designed maximum decoding output list size (OLS), the interpolation module is constructed, and the decoding is formulated as finding a desired Gröbner basis of this module that contains the interpolation polynomial. The re-encoding transform (ReT) specifically designed for ASD is proposed, enabling the modified basis reduction (BR) interpolation to achieve lower complexity. The ReT is formulated by defining Lagrange interpolation polynomials over the Hermitian function fields and appropriately choosing the re-encoding points. By exploiting the linear code property, the ReT transforms a subset of interpolation points to have zero <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</i>-coordinates, which allows a common factor to be extracted from the module basis polynomials, thereby simplifying the interpolation. This paper further proposes an improved ReT employing more re-encoding points. It enables the common factor to have a greater degree, yielding a more significant complexity reduction. This also leads to an early termination for the decoding. Theoretical analysis and numerical results demonstrate that the two proposed ReT schemes efficiently facilitate the ASD for Hermitian codes.

In this paper, we introduce Hyper-Dimensional Modulation (HDM) for massive machine-type communications (mMTC). HDM enables robust communication of short packets by spreading information bits across many elements in a hyper-dimensional vector and superimposing a set of such non-orthogonal vectors. The proposed CRC-aided K-best decoding algorithm for HDM can achieve a very low packet error rate (PER) in additive white Gaussian noise (AWGN) channels for short packets. Furthermore, extended decoding algorithms are proposed to combat overwhelming interference in an mMTC network. Comprehensive simulation and real-world experiment results show that HDM outperforms sparse superposition codes in AWGN channels and state-of-the-art short codes such as polar and tail-biting convolutional codes in interference-heavy channels for short packet transmissions.

In multi-hop wireless sensor networks (WSN), the data transmitted from sensor nodes is highly susceptible to error corruption introduced by noisy channels. It is important to use some error correction schemes in order to control the errors introduced and to reduce the number of automatic requests for retransmission. The sensor nodes are typically wireless nodes with limited storage and computational power. Thus the error control schemes should be energy efficient at sensor nodes level. Most of the reported works assume that both encoding and decoding are performed at every node. The idea of this paper is to perform encoding only at the first node and decoding will be done at the base station. We assume that the base station has enough power to run complex decoding algorithms. This paper provides a model for energy consumed and the probability of receiving a correct word for multi-hop WSN at base station when considering a number of coding schemes and hops. The emphasis is on using powerful codes with low complexity encoding. Several powerful codes like Reed-Solomon (RS), list decoded RS codes, multivariate interpolation decoded RS codes (MIDRS) and Hermitian codes are investigated for this scheme. All these codes have very simple encoding based on RS type encoders and we will show that this scheme consumes less power than reported schemes while maintaining a low probability of error.

Motivated by recent results in Joint Source/Channel (JSC) coding and decoding, this paper addresses the problem of soft input decoding of Arithmetic Codes (AC). A new length-constrained scheme for JSC decoding of these codes is proposed based on the Maximum a posteriori (MAP) sequence estimation criterion. The new decoder, called Chase-like arithmetic decoder is supposed to know the source symbol sequence and the compressed bit-stream lengths. First, Packet Error Rates (PER) in the case of transmission on an Additive White Gaussian Noise (AWGN) channel are investigated. Compared to classical arithmetic decoding, the Chase-like decoder shows significant improvements. Results are provided for Chase-like decoding for image compression and transmission on an AWGN channel. Both lossy and lossless image compression schemes were studied. As a final application, the serial concatenation of an AC with a convolutional code was considered. Iterative decoding, performed between the two decoders showed substantial performance improvement through iterations.

Motivated by recent results in Joint Source/ Channel (JSC) coding and decoding, this paper addresses the problem of soft input decoding of Arithmetic Codes (AC). A new length-constrained scheme for JSC decoding of these codes is proposed based on the Maximum a posteriori (MAP) sequence estimation criterion. The new decoder, called Chase-like arithmetic decoder is supposed to know the source symbol sequence and the compressed bit-stream lengths. First, Packet Error Rates (PER) in the case of transmission on an Additive White Gaussian Noise (AWGN) channel are investigated. Compared to classical arithmetic decoding, the Chase-like decoder shows significant improvements. Results are provided for Chase-like decoding for image compression and transmission on an AWGN channel. Both lossy and lossless image compression schemes were studied. As a final application, the serial concatenation of an AC with a convolutional code was considered. Iterative decoding, performed between the two decoders showed substantial performance improvement through iterations.

Deployment of wireless sensor networks (WSNs) with a large number of nodes have reinstated interest in spread spectrum (SS) technologies as they allow to establish multiple access for nodes with simple hardware and limited power budget. Chaotic spreading is one of the still insufficiently explored areas which can lead to higher security and lower multiple access interference (MAI). This research is intended to bring new information about the performance of binary direct sequence spread spectrum (DSSS) and frequency hopping spread spectrum (FHSS) communication systems which employ chaos-based spreading codes and compare them against classical systems employing m-sequences. Unlike existing research, this investigation is based on the simulation of passband communication systems with up/down-conversion and respective filtering. Performance comparison in terms of bit error ratio (BER) versus signal-to-noise ratio (SNR) at the different number of users and MAI dependence on carrier frequency offset among users in case of additive white Gaussian noise (AWGN) channel are presented. Obtained results highlight several scenarios where chaotic-sequences-based binary DSSS and FHSS systems have advantages over classical solutions.

This paper presents Reed-Solomon (RS) coding applied to an innovative, constant envelope modulation technique that was originally developed by Resnikoff and Tigerman [1]. The general waveform and phaseform are presented as-well-as probability of bit error and symbol error expressions for uncoded binary and uncoded M-ary modulation, respectively. Bit error performance analysis is presented for the case of RS coded waveforms when the modulation symbol size (M) is less than the RS coded symbol size (Q). In addition, upper and lower performance bounds are derived for RS coded waveforms for M less than Q. Performance analysis curves are presented for the M = 8 and Q = 64 case. Finally, simulation results are also presented for the M = 8 and Q = 64 case that strongly agree with analysis.

Bit-error rate (BER) performance analyses are presented for Reed-Solomon coded fast frequency-hopping binary frequency-shift-keying (FFH/BFSK) spread-spectrum (SS) systems under the conditions of additive white Gaussian noise (AWGN) and the worst-case band multitone jamming (MTJ). The FFH system employs the soft-decision linear-combining receiver to obtain the diversity-combining output. The corresponding hard decision of the diversity-combining output is then used to decode the Reed-Solomon codes. The analytical expressions of the BER performance of the coded FFH systems are derived and shown to be applicable to higher diversity levels without much more computational complexity. Numerical results show that there is an optimum code rate for the Reed-Solomon coded system under the worst-case multitone jamming conditions.

A hybrid direct-sequence/frequency-hopping spread-spectrum communication modem for burst format transmission of digital data has been developed. A burst consists of a short synchronisation preamble and the data packet. Data modulation is accomplished by assignment of pairs of pseudonoise sequences with low crosscorrelation for message ones and zeros. The spreading code chip pattern is changed from bit to bit in both the preamble and the message portion of a burst. Receiver signal processing is based on the application of surface-acoustic-wave (SAW) elastic convolvers to programmable matched filtering. The performance of the system in an additive white Gaussian noise channel is analysed, measures of performance being the probability of burst loss and the bit error probability in the case of ideal synchronisation. Evaluations for a particular design are presented, and some experimental results obtained with a test system are shown for comparison.

The authors propose an adaptive frequency hopping (AFH) algorithm, entitled robust adaptive frequency hopping (RAFH), for providing increased reliability of a wireless medical telemetry system (WMTS) under coexistence environment with non-medical devices. The conventional AFH scheme classifies channels into `good` or `bad` according to the threshold-based on`off decision by packet error rate (PER) measurement, and only uses good channels with a uniform hop probability. Unlike the conventional AFH scheme, RAFH is a novel technique, which solves a constrained entropy maximisation problem and assigns every channel a different hop probability as a decreasing function of the measured PER. The key novelty of RAFH over existing AFH schemes is that it reflects the relative channel condition by assigning non-uniform hop probabilities. By adopting constrained entropy maximisation, RAFH not only improves the average PER, but also reduces the PER fluctuation over time under a dynamic interference environment, both of which increase the reliability of WMTS. Through extensive simulation, we show that RAFH outperforms basic frequency hopping (FH) and the conventional AFH with respect to the PER under various scenarios of dynamic interference.

In this paper, a novel coded modulation scheme named Trellis-Coded Differential Chaotic Modulation (TC-DCM) is proposed, which combines trellis codes with M-ary Differential Chaotic Shift Keying (M-DCSK). The new scheme not only reduces the multipath interference efficiently due to its inherent spreading property, but also avoids the use of Channel State Information (CSI), exact synchronization, despreading and the Rake receiver, making the corresponding receiver design simpler and more suitable for band-limited communication systems under severe multipath propagation conditions. Analytical Bit-Error-Rate (BER) bounds are derived and verified over Additive White Gaussian Noise (AWGN) channels. Both analytical performances and simulation results show that the proposed scheme with different states and different coding rates can obtain significant coding gains, compared to the corresponding uncoded schemes with the same bandwidth over AWGN channels. In addition, it is found from simulations that over multipath Rayleigh fading channels without CSI, the proposed TC-DCM system outperforms the Trellis-Coded Modulation Direct-Sequence Spread-Spectrum (TCM DS/SS) system with the same bandwidth efficiency.

A precise bit-error probability (BEP) analysis method is derived for a multicode direct-sequence code-division multiple-access (DS-CDMA) system in an additive white Gaussian noise channel. The method is applicable to a multicode DS-CDMA system with an arbitrary number of multiple code sequences, and any selection of multiple code sequences. The precise method gives results that discriminate the effect of the selection of different multiple code sequences on the BEP, whereas Gaussian approximations (GAs) do not. Thus, the new method can be used to select the best multicode set for a given system, a task that cannot be achieved using GAs. A two-step analytical procedure enables deriving an explicit, compact form for the CF of the receiver decision statistic in a DS-CDMA system with an arbitrary number of multiple code sequences, and for any selection of multiple code sequences.

Rate (n-1)/n punctured convolutional codes are very effective in conjunction with embedded differential pulse code modulation (EDPCM) in variable-bit-rate speech transmission. The authors investigate the performance of this variable-bit-rate EDPCM system in terms of probability of bit error and audio signal-to-noise ratio (SNR) versus channel SNR in an additive white Gaussian noise and Rayleigh fading channel using soft-decision decoding for specific sets of code generators of punctured convolutional codes. The results show that different sets of code generators affect the performance in terms of both the probability of bit error and the audio SNR. Improvements were obtained in the cases of Gaussian nonfading and Rayleigh fading channels using soft-decision decoding. >

In this paper, the performance of a binary phase shift keyed random\ntime-hopping impulse radio system with pulse-based polarity randomization is\nanalyzed. Transmission over frequency-selective channels is considered and the\neffects of inter-frame interference and multiple access interference on the\nperformance of a generic Rake receiver are investigated for both synchronous\nand asynchronous systems. Closed form (approximate) expressions for the\nprobability of error that are valid for various Rake combining schemes are\nderived. The asynchronous system is modelled as a chip-synchronous system with\nuniformly distributed timing jitter for the transmitted pulses of interfering\nusers. This model allows the analytical technique developed for the synchronous\ncase to be extended to the asynchronous case. An approximate closed-form\nexpression for the probability of bit error, expressed in terms of the\nautocorrelation function of the transmitted pulse, is derived for the\nasynchronous case. Then, transmission over an additive white Gaussian noise\nchannel is studied as a special case, and the effects of multiple-access\ninterference is investigated for both synchronous and asynchronous systems. The\nanalysis shows that the chip-synchronous assumption can result in\nover-estimating the error probability, and the degree of over-estimation mainly\ndepends on the autocorrelation function of the ultra-wideband pulse and the\nsignal-to-interference-plus-noise-ratio of the system. Simulations studies\nsupport the approximate analysis.\n