Single Symbol Research Articles

Topology-Aware Modulation and Error-Correction Coding for Cooperative Networks

User cooperation in wireless networks is inherently a cross-layer optimization problem. We identify a new direction for cooperative communications: i.e., in addition to the point-to-point communication channel between the transmitter and the receiver, the communication configuration should take the network topology into account. In this paper, we first propose a network modulation (NM) design that can transmit bits with different SNR requirements in a single symbol transmission. We then propose an error-correction coding assisted relay (EAR) scheme that is also configured according to the network topology. We study the performance of NM and EAR in both a three-node collinear network and a two-dimensional cellular network. Extensive simulations have been conducted, which demonstrate the substantial performance gain of the proposed schemes, in terms of both a higher network throughput and a lower bit-energy consumption. Comparing between NM and EAR, NM is more beneficial for the downlink performance and EAR is more beneficial for the uplink performance. Combining NM and EAR leads to a more efficient cooperative network. It is concluded that the topology-aware physical layer design will be a promising direction with many open issues for further study.

Tight bound on the length of distinguishing sequences for non-observable nondeterministic Finite-State Machines with a polynomial number of inputs and outputs

In this paper we show that the upper bound 2n−2 on the length of input sequences that distinguish two sets of states is tight for a non-observable NFSM with n states and a polynomial number of inputs and outputs. For each n⩾2, there exists a non-observable NFSM M with n states, a single input symbol, and n output symbols such that there are two sets of states in M which are not distinguishable by each input sequence of length 2n−3 but can be distinguished by an input sequence of length 2n−2.

Low-Complexity Multi-Stream Space-Time Codes—Part I: Direct-Sum Codes and Design Criteria

Multi-stream codes are used in wireless broadcast services where two or more priority classes of data are transmitted simultaneously, and a receiving terminal may decode one or more of the streams as a function of its receive signal to noise ratio. Present-day commercial cellular-based broadcast services generally utilize hierarchical modulation, a clever technique for embedding high and low-priority streams in a single modulated quadrature symbol. With many cellular standards moving to multiple-transmit antenna configurations, there are opportunities for designing new multi-stream encoding techniques that exploit these antennas. We examine the design of space-time codes that allow simple encoding and decoding of high and low-priority streams of data. A desirable multi-stream space-time code has a combination of good performance and low complexity. Performance is generally measured as coded bit-error rate, assuming max-log maximum aposteriori decoding. Complexity is measured as the effort needed to compute the aposteriori probabilities for either stream. Hierarchical modulation, for single-antenna transmissions, allows each stream to be decoded simply and independently. The paper comprises two parts. In this first part, we establish a general performance criterion for two-stream space-time codes and derive a formula for the complexity of max-log maximum aposteriori decoding of either stream. We also show how existing space-time codes may be combined with hierarchical modulation in a "direct sum". The direct-sum codes have low complexity, but we show in the second part of this paper that these codes can be significantly outperformed by non-direct-sum codes. One of our proposed two-stream codes performs 4 dB better than the Alamouti direct-sum code; it also has the benefit of decoding complexity in one stream that is a bounded function of the rate of the other.

Relay Network Beamforming and Power Control Using Maximization of Mutual Information

In this paper, distributed beamforming and power control are considered for amplify-and-forward wireless relay networks with single antenna nodes. The optimal relay weights are designed by maximizing the mutual information in the case of perfect channel state information, individual node power constraints and the existence of a direct link between the source and destination nodes. In our approach, the source node transmits up to two precoded independent information streams as opposed to several previously proposed techniques in which a single symbol is always transmitted. Our solution to the relay power control given the power allocation at the source node is obtained analytically with linear complexity. Simulations show that the proposed method outperforms the previously proposed techniques in terms of mutual information, outage probability and bit error rate.

An aperiodicity problem for multiwords

Multiwords are words in which a single symbol can be replaced by a nonempty set of symbols. They extend the notion of partial words. A word w is certain in a multiword M if it occurs in every word that can be obtained by selecting one single symbol among the symbols provided in each position of M. Motivated by a problem on incomplete databases, we investigate a variant of the pattern matching problem which is to decide whether a word w is certain in a multiword M. We study the language CERTAIN(w) of multiwords in which w is certain. We show that this regular language is aperiodic for three large families of words. We also show its aperiodicity in the case of partial words over an alphabet with at least three symbols.

Practical Estimation of Rapidly Varying Channels for OFDM Systems

We propose a novel pilot-aided algorithm for estimation of rapidly varying wireless channels in OFDM systems. Our approach is specifically designed for channels varying on the scale of a single OFDM symbol duration, which occur, for example, in mobile WiMAX, WAVE, and DVB-T. From the pilot information, we recover information about the channel taps in the framework of the Basis Expansion Model (BEM). We derive explicit formulas for the BEM coefficients in terms of the receive signal. Algebraically, the algorithm is FFT-based, and can be easily implemented in hardware. For a system with L channels taps, our method uses O(L log L) operations and O(L) memory per OFDM symbol. This complexity is the best possible up to the order of magnitude. Previously published methods require O(L2) operations and O(L2) memory. Numerical simulations illustrate performance gains achieved by our estimator at sufficiently high Doppler frequencies. Our approach does not assume any prior statistical information.

Frequency Domain Joint TOA and DOA Estimation in IR-UWB

This paper addresses the problem of TOA and DOA estimation in IR-UWB systems. It considers a frequency domain approach for joint high resolution estimation of Time Of Arrival (TOA) and Direction Of Arrival (DOA). The proposed scheme performs timing acquisition following a two step approach: a first stage where coarse symbol timing is achieved by means of chip energy estimation and a minimum distance criterion based on the time-hopping sequence knowledge, followed by a reduced complexity high resolution TOA estimator that provides fine timing acquisition. The proposed algorithm can resolve time synchronization blindly, without the need for channel estimation and can operate on a single symbol basis. DOA estimation is then obtained from TOA estimates at each array element applying a linear estimator. The joint estimation of TOA and DOA provides robustness and potentially allows positioning with a single reference node. Furthermore, the paper derives the Cramer-Rao Lower Bound from a frequency domain signal model for a multipath channel where no assumptions are made with respect to the paths, which results in a compact closed form.

Identifying time-varying channels with aid of pilots for MIMO-OFDM

In this paper, we consider pilot-aided channel estimation for orthogonal frequency division multiplexing (OFDM) systems with a multiple-input multiple-output setup. The channel is time varying due to Doppler effects and can be approximated by an oversampled complex exponential basis expansion model. We use a best linear unbiased estimator (BLUE) to estimate the channel with the aid of frequency-multiplexed pilots. The applicability of the BLUE, which is referred to as the channel identifiability in this paper, relies upon a proper pilot structure. Depending on whether the channel is estimated within a single OFDM symbol or multiple OFDM symbols, we propose simple pilot structures that guarantee channel identifiability. Further, it is shown that by employing more receive antennas, the BLUE can combat more effectively the Doppler-induced interference and therefore improve the channel estimation performance.

New design of no-zero-entry single symbol ML decodable STBCs based on group precoding

In multiple-input multiple-output (MIMO) systems, space–time block codes (STBCs) from orthogonal designs (ODs) and coordinate interleaved orthogonal designs (CIOD) have been attracting wider attention due to their amenability for fast (single symbol) maximum-likelihood (ML) decoding, and full-rate with full-rank over quasi-static fading channels. However, most of these codes, for transmitting antennas more than 4, have large number of zero entries in their codeword matrix. Due to the zero entries in the design, the transmitting antennas need to be switched on and off imposing severe hardware constraints. To solve this problem, we propose a method to generate a new class of no-zero-entry single symbol maximum likelihood decodable STBCs (NZESSDCs), which is based on coordinate interleaving and group precoding technique. The ability of the proposed group precoding based NZESSDCs (called G-NZESSDCs) on single symbol ML Decoding and full diversity are analyzed and derived. The performance evaluation is accomplished by numerical simulation and is compared with recently reported NZESSDCs (called C-NZESSDCs). Compared with C-NZESSDCs, the proposed G-NZESSDCs have same bit-error-rate (BER) performance and better peak-to-average ratio (PAPR) performance.

BINARY-UNCODED IMAGE AND VIDEO COMPRESSION USING SPIHT-ZTR CODING

When the embedded zerotree wavelet (EZW) algorithm was first introduced by Shapiro, four types of symbols (zerotree (ZTR), isolated zero (IZ), positive (POS), and negative (NEG)) were used to represent the tree structure. An improved version of EZW, the set partitioning in hierarchical trees (SPIHT) algorithm was later proposed by Said and Pearlman. SPIHT removed the ZTR symbol, while keeping the other three symbols in a slightly different form. In the SPIHT algorithm, the coding of the parent node is isolated from the coding of its descendants in the tree structure. Therefore, it is no longer possible to encode the parent and its descendants with a single symbol. When both the parent and its descendants are insignificant (forming a degree-0 zerotree (ZTR)), it cannot be represented using a ZTR symbol. From our observation, the number of degree-0 ZTRs can occur very frequently not only in natural and synthesis images, but also in video sequences. Hence, the ZTR symbol is reintroduced into SPIHT in our proposed SPIHT-ZTR algorithm. In order to achieve this, the order of sending the output bits was modified to accommodate the use of ZTR symbol. Moreover, the significant offspring were also encoded using a slightly different method to further enhance the performance. The SPIHT-ZTR algorithm was evaluated on images and video sequences. From the simulation results, the performance of binary-uncoded SPIHT-ZTR is higher than binary-uncoded SPIHT and close to SPIHT with adaptive arithmetic coding.

A Novel Joint Synchronization Algorithm for OFDM Systems based on Single Training Symbol

A Novel Joint Synchronization Algorithm for OFDM Systems based on Single Training Symbol

Sum of digits sequences modulo [formula omitted

Let s k ( n ) denote the sum of the digits of the base k representation of n . Define the sequence (or word) t k , m = s k ( n ) ( mod m ) n ≥ 0 , which generalizes the well-known Thue–Morse sequence t 2 , 2 . We give a much shorter proof of the main result in Allouche and Shallit (2000) [1], which says that t k , m has no overlaps (that is, contains no subword of the form a x a x a , where x is any finite word and a is a single symbol), using techniques from Cusick and Stănică (2009) [2]. We also give different proofs of some other results from Allouche and Shallit (2000) [1] and one result from Morton and Mourant (1991) [3], using the same techniques.

Constellation Precoded Multiple Beamforming

Beamforming techniques that employ Singular Value Decomposition (SVD) are commonly used in Multi-Input Multi-Output (MIMO) wireless communication systems. In the absence of channel coding, when a single symbol is transmitted, these systems achieve the full diversity order provided by the channel; whereas when multiple symbols are simultaneously transmitted, this property is lost. When channel coding is employed, full diversity order can be achieved. For example, when Bit-Interleaved Coded Modulation (BICM) is combined with this technique, full diversity order of NM in an M x N MIMO channel transmitting S parallel streams is possible, provided a condition on S and the BICM convolutional code rate is satisfied. In this paper, we present constellation precoded multiple beamforming which can achieve the full diversity order both with BICM-coded and uncoded SVD systems. We provide an analytical proof of this property. To reduce the computational complexity of Maximum Likelihood (ML) decoding in this system, we employ Sphere Decoding (SD). We report an SD technique that reduces the computational complexity beyond commonly used approaches to SD. This technique achieves several orders of magnitude reduction in computational complexity not only with respect to conventional ML decoding but also, with respect to conventional SD.

High-Rate and Full-Diversity Space-Time Block Codes with Low Complexity Partial Interference Cancellation Group Decoding

In this letter, we propose a systematic design of space-time block codes (STBC) which can achieve high rate and full diversity when the partial interference cancellation (PIC) group decoding is used at receivers. The proposed codes can be applied to any number of transmit antennas and admit a low decoding complexity while achieving full diversity. For M transmit antennas, in each codeword real and imaginary parts of PM complex information symbols are parsed into P diagonal layers and then encoded, respectively. With PIC group decoding, it is shown that the decoding complexity can be reduced to a joint decoding of M/2 real symbols. In particular, for 4 transmit antennas, the code has real symbol pairwise (i.e., single complex symbol) decoding that achieves full diversity and the code rate is 4/3. Simulation results demonstrate that the full diversity is offered by the newly proposed STBC with the PIC group decoding.

Semiotic combinations in Pan: A comparison of communication in a chimpanzee and two bonobos

Communicative combinations of two bonobos (Pan paniscus) and a chimpanzee (Pan troglodytes) are compared. All three apes utilized ordering strategies for combining symbols (lexigrams) or a lexigram with a gesture to express semantic relations such as agent of action or object of action. Combinatorial strategies used by all three apes revealed commonalities with child language, spoken and signed, at the two-year-old level. However, many differences were also observed: e.g., combinations made up a much smaller proportion and single symbols a much larger proportion of ape production compared with child production at a similar age; and ape combinations rarely exceeded three semiotic elements. The commonalties and differences among three sibling species highlight candidate combinatorial capacities that may underlie the evolution of human language.

SNR Estimation Algorithm Based on Pilot Symbols for DFT-Spread OFDM Systems over Underwater Acoustic Channels

Abstract Effective and low complexity methods for signal to noise ratio (SNR) estimation remain a challenge to underwater acoustic communication due to the ocean environment characteristic which can be summarized as simultaneously severe frequency selectivity and fast-time variability. In this study, a novel SNR estimation method was proposed by using only one training symbols in the pilots and applied to DFT-Spread OFDM transmission system over underwater acoustic channels. The method will be effective against frequency selectivity and fast time varying of underwater acoustic channels. Simulations showed technically feasibility of our proposal. Further, a systematic investigation in the shallow water near Xiamen demonstrated that single training symbol based SNR estimator would be applicable for DFT-Spread OFDM system over underwater acoustic channels.

Constellation Precoded Multiple Beamforming

Beamforming techniques that employ Singular Value Decomposition (SVD) are commonly used in Multi-Input Multi-Output (MIMO) wireless communication systems. In the absence of channel coding, when a single symbol is transmitted, these systems achieve the full diversity order provided by the channel; whereas when multiple symbols are simultaneously transmitted, this property is lost. When channel coding is employed, full diversity order can be achieved. For example, when Bit-Interleaved Coded Modulation (BICM) is combined with this technique, full diversity order of NM in an MxN MIMO channel transmitting S parallel streams is possible, provided a condition on S and the BICM convolutional code rate is satisfied. In this paper, we present constellation precoded multiple beamforming which can achieve the full diversity order both with BICM-coded and uncoded SVD systems. We provide an analytical proof of this property. To reduce the computational complexity of Maximum Likelihood (ML) decoding in this system, we employ Sphere Decoding (SD). We report an SD technique that reduces the computational complexity beyond commonly used approaches to SD. This technique achieves several orders of magnitude reduction in computational complexity not only with respect to conventional ML decoding but also, with respect to conventional SD.

Mind as Music

Cognitive neuroscience typically develops hypotheses to explain phenomena that are localized in space and time. Specific regions of the brain execute characteristic functions, whose causes and effects are prompt; determining these functions in spatial and temporal isolation is generally regarded as the first step toward understanding the coherent operation of the whole brain over time. In other words, if the task of cognitive neuroscience is to interpret the neural code, then the first step has been semantic, searching for the meanings (functions) of localized elements, prior to exploring neural syntax, the mutual constraints among elements synchronically and diachronically. While neuroscience has made great strides in discovering the functions of regions of the brain, less is known about the dynamic patterns of brain activity over time, in particular, whether regions activate in sequences that could be characterized syntactically. Researchers generally assume that neural semantics is a precondition for determining neural syntax. Furthermore, it is often assumed that the syntax of the brain is too complex for our present technology and understanding. A corollary of this view holds that functional MRI (fMRI) lacks the spatial and temporal resolution needed to identify the dynamic syntax of neural computation. This paper examines these assumptions with a novel analysis of fMRI image series, resting on the conjecture that any computational code will exhibit aggregate features that can be detected even if the meaning of the code is unknown. Specifically, computational codes will be sparse or dense in different degrees. A sparse code is one that uses only a few of the many possible patterns of activity (in the brain) or symbols (in a human-made code). Considering sparseness at different scales and as measured by different techniques, this approach clearly distinguishes two conventional coding systems, namely, language and music. Based on an analysis of 99 subjects in three different fMRI protocols, in comparison with 194 musical examples and 700 language passages, it is observed that fMRI activity is more similar to music than it is to language, as measured over single symbols, as well as symbol combinations in pairs and triples. Tools from cognitive musicology may therefore be useful in characterizing the brain as a dynamical system.

The Error Performance and Fairness of CUWB Correlated Channels

Abstract The symbol period becomes smaller compared to the channel delay in multiband orthogonal frequency division multiplexing (MB-OFDM) cognitive ultra wideband (CUWB) wireless communications, the transmitted signals experiences frequency-selective fading and leads to performance degradation. In this paper, a new design method for space-time trellis codes in MB-OFDM systems with correlated Rayleigh fading channels is introduced. This method converts the single output code symbol into several STTC code symbols, which are to be transmitted simultaneously from multiple transmitter-antennas. By using Viterbi optimal soft decision decoding algorithm, we investigate both quasi-static and interleaved channels and demonstrate how the spatial fading correlation affects the performance of space–time codes over these two different MB-OFDM wireless channel models. Simulation results show that the performance of space–time code is to be robust to spatial correlation. When the system bandwidth increases, the long term fairness quality will gradually become better and finally converges to 1.

On the Generative Power of Cancel Minimal Linear Grammars with Single Nonterminal Symbol except the Start Symbol

This paper concerns cancel minimal linear grammars ([5]) that was introduced to generalize Geffert normal forms for phrase structure grammars. We consider the generative power of restricted cancel minimal linear grammars: the grammars have only one nonterminal symbol C except the start symbol S, and their productions consist of context-free type productions, the left-hand side of which is S and the right-hand side contains at most one occurrence of S, and a unique cancellation production Cm → e that replaces the string Cm by the empty string e. We show that, for any given positive integer m, the class of languages generated by cancel minimal linear grammars with Cm → e, is properly included in the class of linear languages. Conversely, we show that for any linear language L, there exists some positive integer m such that a cancel minimal linear grammar with Cm → e generates L. We also show how the generative power of cancel minimal linear grammars with a unique cancellation production Cm → e vary according to changes of m and restrictions imposed on occurrences of terminal symbols in the right-hand side of productions.