Construction and properties of the augmented and binary-depletion codes

The potential for capacity increase in multiple-antenna wireless communication systems has drawn considerable attention to space-time codes. However, most of the existing space-time code construction methods have assumed ideal channel models: either quasi-static fading or fast fading. In this work, we propose a systematic space-time trellis code construction method for correlated fading channels. We derive the performance criteria that take into account both spatial and temporal channel correlation, assuming that the space-time correlation matrix is of full rank. Moreover, we introduce a new design criterion and analyze the properties of the space-time trellis codes satisfying the proposed criterion. Using the design criterion, we develop a code construction procedure that jointly considers diversity advantage and coding advantage for an arbitrary number of transmit antennas and any memoryless modulation. The flexibility of the proposed code construction method is demonstrated by designing space-time trellis codes for two, three, and four transmit antennas with quaternary phase-shift keying (QPSK), 8PSK (phase-shift keying), and 4ASK (amplitude-shift keying) modulations. The simulation results demonstrate that not only can our method generate new codes for an arbitrary number of antennas, but in some special cases, where previously proposed codes exist, our codes also perform very well.

We present an explicit construction of linear-time encodable and decodable codes of rate r which can correct a fraction (1 —re)/2 of errors over an alphabet of constant size depending only on e, for every 0 r 0. The error-correction performance of these codes is optimal as seen by the Singleton bound (these are codes). Such near-MDS linear-time codes were known for the decoding from erasures [2]; our construction generalizes this to handle errors as well. Concatenating these codes with good, constant-sized binary codes gives a construction of linear-time binary codes which meet the so-called Zyablov bound. In a nutshell, our results match the performance of the previously known explicit constructions of codes that had polynomial time encoding and decoding, but in addition have linear time encoding and decoding algorithms.We also obtain some results for list decoding targeted at the situation when the fraction of errors is very large, namely (1—e) for an arbitrarily small constant e > 0. The previously known constructions of such codes of good rate over constant-sized alphabets either used algebraic-geometric codes and thus suffered from complicated constructions and slow decoding, or as in the recent work of the authors [9], had fast encoding/decoding, but suffered from an alphabet size that was exponential in 1/e. We present two constructions of such codes with rate close to Ω(e2) over an alphabet of size quasi-polynomial in 1/e. One of the constructions, at the expense of a slight worsening of the rate, can achieve an alphabet size which is polynomial in 1/e. It also yields constructions of codes for list decoding from erasures which achieve new trade-offs. In particular, we construct codes of rate close to the optimal Ω(e) rate which can be efficiently list decoded from a fraction (1—e) of erasures.

In this thesis, we cope with the fundamental mathematical and physical problems of the space-time-Doppler UWB system design for fading channels: multi-input multi-output (MIMO) wireless communication with adaptive filtering. The estimation algorithm from equalizer providing an accurate parameters estimate is investigated. UWB radio is a fast emerging technology with uniquely attractively features inviting major advances in wireless communications, networking, radar, imaging, and positioning systems. By its rule-making proposal in 2002, the Federal Communications Commission (FCC) in the United States essentially unleashed huge new bandwidth (3.6-10.6 GHz) at the noise floor, where UWB radios overlaying coexistence RF systems cerate using low-power ultra-short information bearing pulses. Right now, there are three basic types of UWB: multiband OFDM UWB (MB-OFDM UWB), impulse-UWB (I-UWB), and direct sequence UWB (DS-UWB). We focus on I-UWB and MB-OFDM-UWB, and compare their performance. A simple means for spreading the spectrum of low duty cycle pulse trains is time hopping (TH), with pulse position modulation (PPM) for data modulation at the rate of many pulses per data bit. The main contribution of this thesis for I-UWB is the design of leading edge detectors, coherent correlation detector (CCD), and pilot performance enhancement compared with different Rayleigh and Ricean fading conditions. For MB-OFDM UWB, we have considered the performance analysis and design criteria of MIMO OFDM UWB systems for high data-rate wireless transmission. The signal processing of frame detection, time synchronization, frequency synchronization, channel estimation, synchronization tracking using pilot subcarriers and 2-D MIMO detection algorithms is discussed. The main contributions of this thesis are 1) Compared with receiver employing the Maximum Likelihood (ML) detector, the receiver employing a low-complexity linear Minimum Mean Square Error (MMSE) demodulator can perform a limited performance loss in spatially uncorrelated channels. 2) Due to the operations of spreading and dispreading combined with MMSE-based frequency domain equalization, the adverse effects of the low-SNR subcarriers on the average BER performance are potentially improved. This is a direct consequence of spreading, because even if the signal corresponding to a specific chip is obliterated by a deep frequency domain channel fade, after dispreading these effects are spread over the Walsh-Hadamard Transform (WHT) length. Hence there is a high chance of still recovering all the partially affected subcarrier symbols without errors. 3) As a test case, the OFDM-based 200 Mb/s MB-UWB network (IEEE 802.15.3a) are considered, but the simulation results are shown above section. 4) The simulation channel can be easily applied to NOS and NLOS situation with WHT transformation from Simulink model. The fading channels of UWB with low/high signal to noise ratio (SNR), multipath effects, and multiuser interference may introduce large errors in location. The location engine performs the following tasks: █ Data fusion techniques: Different data fusion techniques are implemented using Time Of Arrival (TOA), Angle Of Arrival (AOA), or a combination of both. █ Channel modeling: A multipath, multiuser channel environment is created that models path loss, shadowing, Rayleigh fading, and Doppler frequency effects. █ Parameter estimation: TOA and AOA estimation algorithms are implemented as part of the location finding engine. Different variations of algorithms are implemented for performance and comparison purposes. █ Configuring the physical layer for different wireless networks. Among the programmable parameters are spreading factor, packet size, training length, constellation type, modulation technique, carrier frequency, level of transmitted signal power, and the number of antennas at the transmitter for both sides. █ Configuring the mobile user conditions. The wireless channel models depend on the Doppler frequencies present in the environment. The Doppler frequency depends on the mobile speed and carrier frequencies as input and generates a Rayleigh fading channel with the U-shape Doppler spectrum. █ Configuring the environmental parameters and network geographical structure. One of the factors affecting the performance of the wireless location system is the environment type (e.g., bad urban, urban, suburban, or rural area). For example, in a bad urban area with many blocking objects and buildings, non-line of sight (NLOS) effects plays an important role in the estimation accuracy.

One of the directions to improve the efficiency of modern telecommunication systems is the transition to the use of multidimensional signals for continuous channels of information transmission. As a result of studies carried out in recent years, it has been established that it is possible to ensure high quality of information transmission in continuous channels by combining demodulation and decoding operations into a single procedure that involves the construction of a code construct for a multidimensional signal. This paper considers issues related to estimating the possibility to improve the efficiency of continuous information transmission channel by changing the signal distance of the code structure. It has been established that the code structures of such types as a hierarchical code construct of signals, a hierarchical code construct of signals with Euclidean metric, a reversible code construct of signals, a reversible code construct of signals with Euclidean metric have the potential, when used, to increase the speed of information transmission along a continuous channel. With a signal distance reduced by 10 percent or larger, it could increase by two times or faster. The estimation of the effect of reducing a signal distance on the efficiency of certain types of code structures was carried out. It has been established that the hierarchical reversible code construct, compared to the hierarchical code construct, provides a win of up to two or more times in the speed of information transmission with a halved signal distance. Implementing the modulation procedure has no fundamental difficulties, on the condition that for each code of the code construct the encoding procedure is known when using binary codes. The results reported here make it possible to build an acceptably complex demodulation procedure according to the specified types of code structures

In this chapter, we shall present some fundamental study on relatively self-dual codes over a finite commutative ring. Section 1.1 is devoted to the basic definitions and properties of such codes. In Section 1.2, we shall present our gluing technique for constructing relatively self-dual codes. Several exotic general constructions of self-dual codes over ℤn will be given in Section 1.3. Four constructions of binary self-dual codes by our gluing technique will be given in Section 1.4. In Section 1.5, we shall give some constructional examples of ternary self-dual codes. In Section 1.6, we shall present some families of self-dual codes over ℤ4. Sections 1.1, 1.2 and Constructions III, IV in Section 1.4 were published in [X2].

Distributed multiple-input multiple-output (MIMO) system is a new architecture for next generation wireless communication systems with distributed multiple antennas. In this paper, an uplink model for multiuser distributed MIMO systems with wideband code-division multiple-access (CDMA) technology is presented. We focus on the case where there is no channel state information at the transmitter, but channel state information is assumed at the receiver. The spectral efficiency of the uplink system with single-user detectors at the base stations under multipath fading channels is investigated carefully. Two cases with different assumptions of interference knowledge are studied in detail. The spreading sequences of the CDMA systems are assumed to employ loosely synchronized (LS) spreading sequences and random spreading sequences respectively. LS spreading sequences exhibit a so-called interference free window (IFW), where both the auto-correlation and cross-correlation of the codes become zero. Therefore LS sequences have the promise of mitigating the effects of inter symbol interference (ISI) and multiple access interference (MAI) in multipath fading channels. It is shown by numerical results that the uplink spectral efficiency of the distributed MIMO-CDMA system using LS sequences can significantly outperform that of the system using random spreading sequences. Copyright © 2005 John Wiley & Sons, Ltd.

An automaton is synchronizing if there exists a word that sends all states of the automaton to a single state. A coloring of a digraph with a fixed out-degree k is a distribution of k labels over the edges resulting in a deterministic finite automaton. The famous road coloring theorem states that every primitive digraph has a synchronizing coloring. We study recent conjectures claiming that the number of synchronizing colorings is large in the worst and average cases. Our approach is based on the spectral properties of the adjacency matrix A(G) of a digraph G. Namely, we study the relation between the number of synchronizing colorings of G and the structure of the dominant eigenvector v of A(G). We show that a vector v has no partition of coordinates into blocks of equal sum if and only if all colorings of the digraphs associated with v are synchronizing. Furthermore, if for each b there exists at most one partition of the coordinates of v into blocks summing up to b, and the total number of partitions is equal to s, then the fraction of synchronizing colorings among all colorings of G is at least (k-s)/k. We also give a combinatorial interpretation of some known results concerning an upper bound on the minimal length of synchronizing words in terms of v.

For the purpose of investigating two complex networks' hybrid synchronization, a controller with fractional-order is provided. Regarding hybrid synchronization which includes the outer synchronization and inner synchronization, some hybrid synchronization's sufficient conditions according to the Lyapunov stability theorem and the LaSalle invariance principle are proposed. Theoretical analysis suggests that, only when the state of driving-response networks is outer synchronization and each network is in inner synchronization, two coupled networks' hybrid synchronization under some suitable conditions could be reached. Finally, theoretical results are illustrated and validated with the given numerical simulations.

In this thesis, based on transmitter specification of DVB-T, multi-antenna 4x4 MIMO-OFDM transmitter was designed to replace traditional single-antenna system. Furthermore, new generation image-coding technique H.264 was also presented to be an alternate for MPEG-2. In order to simulate the non-ideal effects of wireless communication environment, base-band channel model including Multi-path Fading effect, AWGN effect, CFO effect was took into account. Under such an environment and according to its structure and non-ideal characteristics, the receiver including four major sections was designed: synchronization, channel response estimation and compensation, adaptive modulation and channel decoding. First, in the synchronization section, initial estimation, symbol boundary estimation and CFO estimation/compensation were contained.Second, in the channel estimation, scattered pilots was estimated in two-dimensional time and frequency domain, and then compensated by the MIMO detector. Thirdly, adaptive modulation mechanism was proposed, with modulation variable α、β corresponded with different channel condition. The adaptive modulation technique classified the image data into different level, and then transmits each level through its corresponding protection mechanism. In the last, a concatenate error-correction decoder was used, where Viterbi Decoder and Reed-Solomon Decoder were corrected by the error of channel effect. In the hardware part, with the aim of reducing cost and size, 4x4 MIMO-OFDM system was reduced to 2x2 MIMO-OFDM system; the transmitter, channel model and receiver were verified by two FPGA board.

In this thesis, a jointed preamble/boundary detection and fractional CFO estimation design is presented which supports dual SC/HSI modes of IEEE 802.15.3c applications. Based on correlation based algorithms which utilizes the structure of preamble, an efficiency architecture is proposed which realizes synchronization detection with a sequential detection scheme and a single hardware for dual SC/HSI modes and three detection operations. In order to achieve the requirement of sampling frequency, the baseband design is 8x parallelism and is operating at 333 MHz clock rate. The achieved bit error rate (uncoded) at 12 dB SNR for SC and HSI modes are 8.92×10-4 and 1.43×10-2, respectively. The proposed architecture of synchronization detection is implemented using 65 nm 1P9M CMOS process and the total gate count is 189k with power consumption of 60.16 mW including memory elements which occupies 63.26 % and can be shared with the frequency domain equalizer. Moreover, the power consumption is saved 42.5 % by applying low power techniques.

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.

When transmitting wireless ECG data from a heart monitor, it is useful to compress the data with a Huffman encoding so energy is saved and battery lifetime extended. However, single bit errors in Huffman can cause error propagation over multiple symbols. It is well known that different configurations of Huffman encoding can result in different amounts of error propagation. Therefore, using a highly synchronizing Huffman encoding for ECG transmission should result in more accurate data. This paper demonstrates through simulation that using Huffman codes which are highly synchronizing will result in higher fidelity ECG data than codes generated through a standard tree algorithm. In addition, using these codes produces no additional cost in transmission. The simulation is performed using a sample of existing ECG datasets from the MIT-BIH database [14] which are read and compressed using both standard and fixed-order [23] Huffman encodings. Each packet set is then subjected to a Gilbert-Elliot [7] [5] error channel to simulate transmission errors. Packets are then decoded and the waveform reconstructed. Result data is compared to the original data for its error content in terms of RMSE, R-Point detection, and two types of arrhythmia detection. Simulation shows that in every evaluation the reconstructed data from the fixed-order codes is superior to the standard. Further, the same degree of compression is achieved from both encodings. Results indicate that using highly synchronizing Huffman codes for compression of ECG data is a practical method to reduce error and comes at no additional transmission cost.

Deep holes are very important in the decoding of generalized RS codes, and deep holes of RS codes have been widely studied, but there are few works on constructing general linear codes based on deep holes. Therefore, we consider constructing binary linear codes by combining deep holes with binary BCH codes. In this article, we consider the 2-error-correcting binary primitive BCH codes and the extended codes to construct new binary linear codes by combining them with deep holes, respectively. Furthermore, three classes of binary linear codes are constructed, and then we determine the parameters and the weight distributions of these new binary linear codes.

Locally decodable codes are error correcting codes with the extra property that, in order to retrieve the correct value of just one position of the input with high probability, it is sufficient to read a small number of positions of the corresponding, possibly corrupted codeword. A breakthrough result by Yekhanin showed that 3-query linear locally decodable codes may have subexponential length. The construction of Yekhanin, and the three query constructions that followed, achieve correctness only up to a certain limit which is $1 - 3 delta$ for nonbinary codes, where an adversary is allowed to corrupt up to delta fraction of the codeword. The largest correctness for a subexponential length 3-query binary code is achieved in a construction by Woodruff, and it is below 1 - 3 delta. We show that achieving slightly larger correctness (as a function of $delta$) requires exponential codeword length for 3-query codes. Previously, there were no larger than quadratic lower bounds known for locally decodable codes with more than 2 queries, even in the case of 3-query linear codes. Our results hold for linear codes over arbitrary finite fields and for binary nonlinear codes. Considering larger number of queries, we obtain lower bounds for q-query codes for q>3, under certain assumptions on the decoding algorithm that have been commonly used in previous constructions. We also prove bounds on the largest correctness achievable by these decoding algorithms, regardless of the length of the code. Our results explain the limitations on correctness in previous constructions using such decoding algorithms. In addition, our results imply tradeoffs on the parameters of error correcting data structures.

We propose a construction of full-rank q-ary 1-perfect codes. This is a generalization of the construction of full-rank binary 1-perfect codes by Etzion and Vardy (1994). The properties of the i-components of q-ary Hamming codes are investigated, and the construction of full-rank q-ary 1-perfect codes is based on these properties. The switching construction of 1-perfect codes is generalized to the q-ary case. We propose a generalization of the notion of an i-component of a 1-perfect code and introduce the concept of an (i, σ)-component of a q-ary 1-perfect code. We also present a generalization of the Lindström–Schönheim construction of q-ary 1-perfect codes and provide a lower bound for the number of pairwise distinct q-ary 1-perfect codes of length n.