Search

The beta encoder was recently proposed as a quantization scheme for analog-to-digital (A/D) conversion; in contrast to classical binary quantization, in which each analog sample x [member of] [-1, 1] is mapped to the first N bits of its base-2 expansion, beta encoders replace each sample x with its expansion in a base [beta] between 1 < [beta] < 2. This expansion is nonunique when 1 < [beta] < 2, and the beta encoder exploits this redundancy to correct inevitable errors made by the quantizer component of its circuit design. The multiplier element of the beta encoder will also be imprecise; effectively, the true value [beta] at any time can only be specified to within an interval [[[beta].sub.low], [[beta].sub.high]]. This problem was addressed by the golden ratio encoder (GRE), a close relative of the beta encoder that does not require a precise multiplier. However, the GRE is susceptible to integrator leak in the delay elements of its hardware design, and this has the same effect of changing [beta] to an unknown value. In this paper, we present a method whereby exponentially precise approximations to the value of [beta] in both GREs and beta encoders can be recovered amidst imprecise circuit components from the truncated beta expansions of a "test" number [x.sub.test] [member of] [-1, 1] and its negative counterpart -[x.sub.test]. That is, beta encoders and GREs are robust with respect to unavoidable analog component imperfections that change the base [beta] needed for reconstruction. Index Terms--Analog-to-digital (A/D) conversion, beta encoders, beta expansions, golden ratio encoder (GRE), quantization, redundancy, sampling, sigma-delta.

In this work, coding for channel with partial state information at the decoder is studied. Specifically, the model under consideration assumes that the encoder is provided with full channel state information (CSI) in a noncausal manner, and the decoder is provided with partial state knowledge, quantified by a rate limit. Coding of side information intended for the channel decoder is a Wyner-Ziv like problem, since the channel output depends statistically on the state, thus serving as side information in retrieving the encoded state. Therefore, coding for such a channel involves the simultaneous solution of a Wyner-Ziv problem and a related Gel'fand-Pinsker problem. A single-letter characterization of the capacity of this channel is developed, that involves two rate constraints, in the form of Wyner-Ziv and Gel'fand-Pinsker formulas. Applications are suggested to watermarking problems, where a compressed version of the host signal is present at the decoder. Two main models are examined: the standard watermarking problem, where the decoder is interested only in the embedded information, and the reversible information embedding problem, where the decoder is interested also in exact reproduction of the host. For both problems, single-letter characterizations of the region of all achievable rate-distortion triples (R, [R.sub.d], D) are given, where R is the embedding rate, [R.sub.d] is the rate limit of the compressed host at the decoder, and D is the average distortion between the host and the composite data set (stegotext). For reversible information embedding, two stages of attack are considered, modeled by a degraded broadcast channel, where the weaker (degraded) channel represents the second attack, and both decoders are required to fully reproduce the host. Index Terms--Degraded broadcast channels, information embedding, noncausal coding, partial side information, reversible information embedding, side information, watermarking.

We perform a numerical analysis of the double random phase encryption--decryption technique to determine how, in the case of both amplitude and phase encoding, the two decryption keys (the image-and Fourier-plane keys) affect the output gray-scale image when they are in error. We perform perfect encryption and imperfect decryption. We introduce errors into the decrypting keys that correspond to the use of random distributions of incorrect pixel values. We quantify the effects that increasing amounts of error in the image-plane key, the Fourier-plane key, and both keys simultaneously have on the decrypted image. Quantization effects are also examined. OCIS codes: 200.4740, 100.2000, 070.2580, 000.4430.

This correspondence presents an upper bound on the minimum distance of serially concatenated codes with interleaver where the inner code is a systematic recursive convolutional encoder and the outer code is any convolutional encoder. The resulting expression shows that the minimum distance of the concatenated code cannot grow more than O([K.sup.1-1/[d.sup.(O).sub.f]]), where K is the information word length, and [d.sup.(O).sub.f]) is the free distance of the outer code. The obtained upper bound is shown to agree with and, in some cases, improve over previously known results. Index Terms--Combinatorial, concatenated, convolutional, minimum distance, performance bounds, serial.

A binary product lattice is generated from two binary component lattices of lower dimensions by employing the Kronecker product. This work focuses on codes carved from binary product lattices. Defined as such, an intriguing problem is that of effectively mapping independent data sequences onto a selected subset of lattice points. A novel approach is disclosed yielding an explicit connection between source bits and lattice points. Decoding methods typically used for binary product codes do not apply for product lattices. Several alternative decoding approaches are discussed. In particular, a provably bounded-distance decoder is presented. It relies on the fact that a product lattice code point may be regarded as a two-dimensional array whose rows and columns are points in the component lattices. The obtained results are compared with classical lattices known in the art. Index Terms--Barnes-Wall lattice, binary code, binary lattice, bounded-distance decoding, lattice, maximum-likelihood (ML) decoding, nearest neighbors, product code, product lattice, Reed-Muller code.

We consider zero-delay joint source--channel coding of individual source sequences for a general known channel. Given an arbitrary finite set of schemes with finite-memory (not necessarily time-invariant) decoders, a scheme is devised that does essentially as well as the best in the set on all individual source sequences. Using this scheme, we construct a universal zero-delay joint source--channel coding scheme that is guaranteed to achieve, asymptotically, the performance of the best zero-delay encoding--decoding scheme with a finite-state encoder and a Markov decoder, on all individual sequences. For the case where the channel is a discrete memoryless channel (DMC), we construct an implementable zero-delay joint source--channel coding scheme that is based on the "follow the perturbed leader" scheme of Gyorgy et al. for lossy source coding of individual sequences. Our scheme is guaranteed to attain asymptotically the performance of the best in the set of all encoding--decoding schemes with a "symbol-by-symbol" decoder (and arbitrary encoder), on all individual sequences. Index Terms--Discrete memoryless channel (DMC), finite-state encoder/decoder, individual sequences, joint source--channel coding, Markov encoder/decoder, zero-delay schemes.

A vector precoding scheme has been recently proposed for the multiple-input multiple-output (MIMO) Gaussian broadcast channel. This technique minimizes the instantaneous transmitted power of linearly precoded signals, but does not take into account the peak-to-average-power ratio (PAPR). In this paper, we present a modified vector precoding scheme, where a perturbation vector is chosen in order to take into account both the instantaneous power and the instantaneous peak power of the transmitted signal. This is obtained by minimizing the p-norm of the transmitted signal for p [less than or equal to] 2. For this reason, the scheme is referred to as the p-sphere encoder. We demonstrate the performance of the proposed scheme applied to a MIMO independent, identically distributed Rayleigh fading downlink channel with simple channel inversion. We show that by choosing p [less than or equal to] 2, the proposed p-sphere encoder yields a tradeoff between power efficiency, PAPR reduction, and complexity. In particular, with eight antennas, the proposed algorithm significantly reduces the tail of the PAPR distribution, with very small degradation in terms of bit-error rate with respect to standard vector precoding. Index Terms--Multiple-input multiple-output (MIMO) broadcast channel, peak-to-average-power ratio (PAPR), vector precoding.

The output of a discrete-time Markov source must be encoded into a sequence of discrete variables. The encoded sequence is transmitted through a noisy channel to a receiver that must attempt to reproduce reliably the source sequence. Encoding and decoding must be done in real-time and the distortion measure does not tolerate delays. The structure of real-time encoding and decoding strategies that jointly minimize an average distortion measure over a finite horizon is determined. The results are extended to the real-time broadcast problem and a real-time variation of the Wyner-Ziv problem. Index Terms--Markov chains, Markov decision theory, real-time decoding, real-time encoding.

This brief introduces a delayed differential feedback chaos generator with a programmable feedback element. The programmable feedback allows us to implement an arbitrary nonlinearity or modulate the feedback delay time. Delayed differential feedback systems have been suggested for secure communications, and the flexibility of the programmable system is shown to enhance security against published cracking algorithms. Index Terms--Chaos, communication system security, message encoding and decoding.

In this paper, we derive a linear correspondence between the variables of an encoder and those of a corresponding syndrome former. Using the derived correspondence, we show that the log-likelihood ratio of an information bit conditioned on a received sequence can be equally calculated using the syndrome trellis. It is shown that the proposed method also applies to recursive systematic convolutional codes which are typical constituent codes for turbo codes. Moreover, we show that soft-in syndrome decoding considering a priori probabilities of information bits is possible in the same way as for Viterbi decoding based on the code trellis. Hence, the proposed method can be applied to iterative decoding such as turbo decoding. We also show that the proposed method is effective for high-rate codes by making use of trellis modification. Index Terms--Convolutional codes, iterative decoding, reliability value, soft-in/soft-out (SISO) decoding, syndrome trellis, trellis modification.

In this paper, we propose a new architectural technique to reduce energy dissipation of frame memory through adaptive bitwith compression. Unlike related approaches, the technique utilizes the fixed order of memory accesses and data correlation of video sequences by dynamically adjusting the memory bitwidth to the number of bits changed per pixel. Instead of treating data bits independently, we group the most significant bits together, activating the corresponding group of bit lines adaptively to data variation. The approach is not restricted to specific bit patterns, nor does it depend on the storage phase. It works equally well on read and write accesses, as well as during precharging. Simulations show that in using this method, we can reduce the total energy consumption of frame memory by 20% without affecting the picture quality. The implementation scheme is simple yet compact. Index Terms--Bit compression, frame memory, low-power design, video encoders.

We develop methods for analyzing and constructing combined modulation/error-correctiong codes (ECC codes), in particular codes that employ some form of reversed concatenation and whose ECC decoding scheme requires easy access to soft information (e.g., turbo codes, low-density parity-check (LDPC) codes or parity codes). We expand on earlier work of Immink and Wijngaarden and also of Fan, in which certain bit positions are reserved for ECC parity, in the sense that the bit values in these positions can be changed without violating the constraint. Earlier work has focused more on block codes for specific modulation constraints. While our treatment is completely general, we focus on finite-state codes for maximum transition run (MTR) constraints. We 1) obtain some improved constructions for MTR codes based on short block lengths, 2) specify an asymptotic lower bound for MTR constraints, which is tight in very special cases, for the maximal code rate achievable for an MTR code with a given density of unconstrained positions, and 3) show how to compute the capacity of the set of sequences that satisfy a completely arbitrary constraint with a specified set of bit positions unconstrained. Index Terms--Finite-state encoders, modulation codes, maximum transition run (MTR) codes, reversed concatenation, run-length limited (RLL) codes.

Research is presented concerning modulators of superconductor ADCs which have very high sampling rates. These modulators need other devices for rapid data processing and encoders and decimation filters are examined for this application.

Motion estimation is known to be the main bottleneck in real-time encoding applications, and the search for an effective motion estimation algorithm (in terms of computational complexity and compression efficiency) has been a challenging problem for years. This paper describes a new block-matching algorithm that is much faster than the full search algorithm and occasionally even produces better rate-distortion curves than the full search algorithms. We observe that a piecewise continuous motion field reduces the bit rate for differentially encoded motion vectors. Our motion estimation algorithm exploits the spatial correlations of motion vectors effectively in the sense of producing better rate-distortion curves. Furthermore, we incorporate such correlations in a multiresolution framework to reduce the computational complexity. Simulation shows that this method is successful because of the homogeneous and reliable estimation of the displacement vectors. In nine out of our ten benchmark simulations, the performance of the full search algorithm and that of our subblock multiresolution method is about the same. In one out of our ten benchmark simulations, our method has improvement.

Permutation codes, introduced by Slepian, were shown to perform well on an additive white Gaussian noise (AWGN) channel. Unfortunately, these codes required large lookup tables, making them quite complex to implement even though the maximum-likelihood decoder is very simple. In this correspondence, we present an enumeration scheme which encodes and decodes permutation codes with low complexity. We concentrate on the use of permutation codes for constructing high-rate codes that satisfy runlength-limited constraints. Wolf showed that permutation codes can be used for runlength constraints and that they have rate that asymptotically achieves the capacity of a noiseless, runlength-limited constrained channel. Wolf, however, gave no efficient encoders/decoder. Our code construction is enumerative, but unlike other enumerative codes, has storage requirements that are a function of the runlength parameters d and k instead of the block length n. In addition, these codes have error detection and correction capabilities. Finally, we use this approach to construct (0, G/I) codes whereby all odd-numbered occurrences of double-adjacent errors are detected. As an example, a 99.2% efficient, rate 496/528, (0, 6/3) code is presented. Index Terms - Enumerative coding, magnetic recording, permutation codes, runlength-limited codes.

Let S consist of all words of a code C for which each symbol is in a stipulated subalphabet, possibly different for distinct positions. We consider the special case where C is a linear maximum-distance separable (MDS) code, and the subalphabets are linear subspaces over the ground field with equal dimensions. We give an explicit algorithm for selecting the subspaces in such a way that a straightforward systematic encoding algorithm, based on an encoder for C, can be applied. The number of information symbols that can be encoded with this algorithm equals a well-known lower bound on the dimension of S. Index Terms - Encoding, HDS codes, subspace subcodes.

For a high-performance servo drive system, it is important to estimate and control the motor speed precisely in a wide-speed range. Therefore, the disturbance-rejection ability and the robustness to variations of the mechanical parameters such as inertia should be considered. This paper shows that the adaptive state estimator and self-tuning regulator based on the recursive extended least squares (RELS) parameter identification method can achieve high-performance speed control in a wide-speed range. The RELS method identifies the variations of mechanical parameters, and the estimated mechanical parameters are used to replace the role of manual tuning by adjusting the gain of the speed controller automatically for good dynamic response. Also, these estimated parameters are used to adapt the Kalman filter, which is an optimal state estimator, to provide good estimation performance for the rotor speed, rotor position, and disturbance torque even in a noisy environment. Simulation and experimental results show an improved speed control performance in the wide-speed range. Index Terms- Adaptive state estimator, disturbance-rejection ability, mechanical parameter, recursive extended least squares method, self-tuning regulator.

A new, to our knowledge, design for a cylindrical-type diffractive optical encoder is proposed. The wave-front aberrations induced by the power of the rotation disk in this encoder can be canceled out completely. Wave-front-aberration cancellation and desensitization to the grating misalignment are achieved by means of positioning the virtual point source, which was induced by the cylindrical grating with respect to two sets of modified telescopes with a magnification ratio of one: 1x telescopes. For evaluating the performance envelope of this newly designed optical system a CODE v-based optical-design software program was adopted to simulate the performance of the optical system. From tolerance-analysis results it was found that this newly developed cylindrical encoder system has the capability to compensate for most aberrations and, in addition, possesses a high tolerance for optical-component misalignment. For verifying the performance of the developed system the cylindrical diffractive encoder system was cross-referenced with a Hewlett-Packard Model HP-5529 laser interferometer positioning signal. The experimental results confirm the merits of this newly developed cylindrical encoder.

We present a continuous dual of multiterminal source encoding with one distortion criterion (the "Berger-Yeung problem"). A continuous source X is encoded with "high resolution" ([D.sub.x] [approaches] 0), with the aid of a "helper," i.e., a correlated discrete or continuous source Y, that is encoded separately subject to some arbitrary distortion criterion [D.sub.y]. We find the asymptotic form of the set of achievable coding rates R([D.sub.x], [D.sub.y]) of the X- and Y-encoders as [D.sub.x] [approaches] 0. Two extreme cases of our result provide high-resolution interpretations to the classical work of Wyner, Ahlswede, Korner, and Ziv on source coding with side information. Index Terms - Berger-Yeung problem, high resolution, multiterminal source coding, Shannon lower bound, side information, Wyner-Ziv problem.

An important issue in analog circuit design is the problem of digital-to-analog conversion, i.e., the encoding of Boolean variables into a single analog value which contains enough information to reconstruct the values of the Boolean variables. A natural question is: What is the complexity of implementing the digital-to-analog encoding function? That question was recently answered by Wegener, who proved matching lower and upper bounds on the size of the circuit for the encoding function. In particular, it was proven that [(3n - 1)/2] 2-input arithmetic gates are necessary and sufficient for implementing the encoding function of n Boolean variables. However, the proof of the upper bound is not constructive. In this paper, we present an explicit construction of a digital-to-analog encoder that is optimal in the number of 2-input arithmetic gates. In addition, we present an efficient analog-to-digital decoding algorithm. Namely, given the encoded analog value, our decoding algorithm reconstructs the original Boolean values. Our construction is suboptimal in that it uses constants of maximum size n log n bits; the nonconstructive proof uses constants of maximum size 2n + [log n] bits. Index Terms - Complexity, construction, decoding, digital-to-analog, encoding.

One describes procedures to generate the codewords of a Reed-Solomon code over GF([2.sup.m]) having all their symbols in a GF(2)-subspace of GF([2.sup.m]). Some of the described encoders are systematic binary encoders and some are only partly systematic. Index Terms - Partly nonsystematic encoders, Reed-Solomon codes, subalphabet subcodes, systematic encoders.

Tabulations of binary systematic and nonsystematic polynomial convolutional encoders with an optimum distance profile for rate 1/2, 1/3, and 1/4 are given. The reported encoders are found by computer searches that optimize over the weight spectra. The free distances for rate l/3 and 1/4 are compared with Heller's and Griesmer's upper bounds. Index Terms - Convolutional encoders, free distance, optimum distance profile.

This paper presents generalized expressions for the probabilities of correct decoding and decoder error for Reed-Solomon (RS) codes. In these expressions, the symbol error and erasure probabilities are different in each coordinate in a codeword. The above expressions are used to derive the expressions for reliability and delay for Type-I hybrid ARQ (HARQ-I) systems when each symbol in a packet (multiple codewords per packet) has unique symbol error and erasure probabilities. Applications of the above results are demonstrated by analyzing a bursty-correlative channel in which the symbols and codewords within the packet are correlated. Index Terms - Bursty-correlative channel, decoder error probability, Reed-Soloman codes.

The differential encoding principle from a nonlinear signal processing perspective dependent on the multilag high-order instantaneous moment (ml-HIM) was analyzed. Phase errors involved in digital communications can be precompensated by differential encoding at the transmitter and at the receiver. It was observed that information transmission between differential phase-shift-keying (PSK) encoding system and the doubly differential PSK were reinterpreted through the ml-HIM which resulted to cases of generalized differential decoder corresponding to the second- and third-order HIM.