Bounds on mixed binary/ternary codes

Upper and lower bounds are presented for the maximal possible size of mixed binary/ternary error-correcting codes. A table up to length 13 is included. The upper bounds are obtained by applying the linear programming bound to the product of two association schemes. The lower bounds arise from a number of different constructions     

Bounds on the zero-error capacity of the input-constrainedbit-shift channel

New lower and upper bounds on a maximal achievable rate fur runlength-limited codes, capable of correcting any combination of bit-shift errors (i.e. a zero-error capacity of the bit-shift channel), are presented. The lower bound is a generalization of the bound obtained by Shamai and Zehavi (1991). It is shown that in certain cases, the upper and the lower bounds asymptotically coincide     

Morphological representation of order-statistics filters

We propose a comprehensive theory for the morphological bounds on order-statistics filters (and their repeated iterations). Conditions are derived for morphological openings and closings to serve as bounds (lower and upper, respectively) on order-statistics filters (and their repeated iterations). Under various assumptions, morphological open-closings and close-openings are also shown to serve as (tighter) bounds (lower and upper, respectively) on iterations of order-statistics filters. Simulations of the application of the results presented to image restoration are finally provided.     

Error bounds for trellis-coded MPSK on a fading mobile satellitechannel

Analytical performance bounds are presented for trellis-coded MPSK, transmitted over a satellite-based land mobile channel. Upper bounds are evaluated using the well-known transfer function bounding technique, and lower bounds are achieved through knowledge of exact pairwise error probabilities. In order to analyze practical trellis-codes (four or more states), the uniform properties displayed by a certain class of trellis-codes are exploited, enabling the encoder transfer function to be obtained from a modified state transition diagram, having no more states than the encoder itself. Monte Carlo simulation results are presented in confirmation of all performance bounds and indicate a general weakness in the transfer function upper bounds. A new asymptotically tight upper bound is derived based on a simple modification to the standard transfer function bound, and results are presented for the four- and eight-state trellis-codes in Rician and Rayleigh fading     

Error Rate Bounds for Digital PAM Transmission with Phase Jitter and Intersymbol or Cochannel Interference

A simple method is presented for computing upper and lower bounds for binary PAM signaling over channels with phase jitter. Other impairments to reliable communication are taken to be additive thermal noise and intersymbol or cochannel interference. The important cases of binary and quadrature phase shift keying are cases for which the analysis presented is valid. The method consists of finding upper and lower bounds conditioned on the phase jitter, φ, in a form in which the auguments of theQ-functions involved are linear incos phiandsin phi. When these functions are represented by a piecewise linear approximation, the average of these bounds can be given in closed form. In most cases 5 piecewise linear segments provides an error rate estimate that is accurate to at least 1 dB in system signal-to-noise ratio (SNR).     

An error correcting scheme for defective memory

A scheme for storing information in a memory system with defective memory ceils using "additive" codes was proposed by Kuznetsov and Tsybakov. When a source message is to be stored in a memory with defective cells, a code vectorxmasking the defect pattern of the memory is formed by adding a vector defined by the message and the defect pattern to the encoded message, and thenxis stored. The decoding process does not require the defect information. Considerably better bounds on the information rate of codes of this type which are capable of masking multiple defects and correcting multiple temporary errors are presented. The difference between the upper and lower bounds approaches the difference between the known best upper and lower bounds for random error correcting linear codes as the word length becomes large. Examples of efficient codes for masking double or fewer defects and correcting multiple temporary errors are presented.     

On Viterbi detector path metric differences

This letter continues the investigation of methods for computing exact bounds on the path metric differences in maximum-likelihood sequence detectors based upon the Viterbi algorithm. New upper and lower estimates for these bounds are presented and recast in terms of a collection of linear programming problems. These estimates improve upon previously proposed linear programming bounds. The estimates are applied to derive exact bounds or provably close to exact bounds for several Viterbi detectors corresponding to coded and uncoded partial-response channels of practical interest in digital magnetic and optical recording     

Computationally efficient bounds for the performance ofdirect-sequence spread-spectrum multiple-access communications systemsin jamming environments

An approach for calculating upper and lower bounds for the probability of error for asynchronous multiple-access spread-spectrum communication systems using deterministic codes is presented. The techniques is then generalized to include multiple-tone jamming. The approach utilizes the cumulative distribution function of individual interference terms. The computational complexity of the technique is calculated to the polynomial-like. Results showing the multiple-access performance of gold codes of lengths 31 and 127 in the presence of jamming are shown. The fact that this computational technique gives upper and lower bounds is rigorously proved using the Riemann-Stieltjes integral     

Bounding algorithms for two-terminal network reliability

Determining the exact reliability of a complex network involves extremely large amount of computation. Consequently, it is appropriate to discuss method for approximating network reliability. This paper develops methods for obtaining upper and lower bounds for two-terminal network reliability. Construction of different layers for a network is used to develop an algorithm to compute an upper bound for the reliability of a network. The nodes of this network are completely reliable and arcs fail statistically independently with known probabilities. A simple approach, to obtain a lower bound for the reliability of the network is also presented. Examples illustrate the use of the algorithms and show that the proposed bounds fare better than the well-known Esary and Proschan bounds.     

Moment space upper and lower error bounds for digital systems with intersymbol interference

A method for the evaluation of upper and lower bounds to the error probability of a linear pulse-amplitude modulation (PAM) system with bounded intersymbol interference and additive Gaussian noise is obtained via an isomorphism theorem from the theory of moment spaces. These upper and lower bounds are seen to be equivalent to upper and lower envelopes of some compact convex body generated from a set of kernel functions. Depending on the selection of these kernels and their corresponding moments, different classes of bounds are obtained. In this paper, upper and lower bounds that depend on the absolute moment of the intersymbol interference random variable, the second moment, the fourth moment, and an "exponential moment" are found by analytical, graphical, or iterative approaches. We study in detail the exponential moment case and obtain a family of new upper and a family of new lower bounds. Within each family, expressions for these bounds are given explicitly as a function of an arbitrary real-valued parameter. For two channels of interest, upper and lower bounds are evaluated and compared. Results indicate these bounds to be tight and useful.     

Quantum error correction via codes over GF(4)

The problem of finding quantum error correcting codes is transformed into the problem of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product. Many new codes and new bounds are presented, as well as a table of upper and lower bounds on such codes of length up to 30 qubits     

Error Probability of Asynchronous Spread Spectrum Multiple Access Communication Systems

Several approaches for the evaluation of upper and lower bounds on error probability of asynchronous spread spectrum multiple access communication systems are presented. These bounds are obtained by utilizing an isomorphism theorem in the theory of moment spaces. From this theorem, we generate closed, compact, and convex bodies, where one of the coordinates represents error probability, while the other coordinate represents a generalized moment of the multiple access interference random variable. Derivations for the second moment, fourth moment, single exponential moment, and multiple exponential moment are given in terms of the partial cross correlations of the codes used in the system. Error bounds based on the use of these moments are obtained. By using a sufficient number of terms in the multiple exponential moment, upper and lower error bounds can be made arbitrarily tight. In that case, the error probability equals the multiple exponential moment of the multiple access interference random variable. An example using partial cross correlations based on codes generated from Gold's method is presented.     

Bounds for Binary Codes With Narrow Distance Distributions

New lower bounds are presented on the second moment of the distance distribution of binary codes, in terms of the first moment of the distribution. These bounds are used to obtain upper bounds on the size of codes whose maximum distance is close to their minimum distance. It is then demonstrated how such bounds can be applied to bound from below the smallest attainable ratio between the maximum distance and the minimum distance of codes. Finally, counterparts of the bounds are derived for the special case of constant-weight codes.     

Some simple bounds on the symmetric capacity and outage probabilityfor QAM wireless channels with Rice and Nakagami fadings

In this article, quickly computable upper and lower bounds are presented on the symmetric capacity of flat-faded Rice and Nakagami channels with side information (SI) for data-transmissions via finite-size quadrature amplitude modulation (QAM) constellations. The proposed bounds exhibit the appealing feature to be tight and asymptotically exact both for high and low signal-to-noise ratios (SNRs). Furthermore, exponentially tight Chernoff-like formulas are also presented for an analytical evaluation of the resulting system outage probabilities when interleaved packet transmissions are carried out     

Krawtchouk polynomials and universal bounds for codes and designsin Hamming spaces

Universal bounds for the cardinality of codes in the Hamming space F_rⁿ with a given minimum distance d and/or dual distance d' are stated. A self-contained proof of optimality of these bounds in the framework of the linear programming method is given. The necessary and sufficient conditions for attainability of the bounds are found. The parameters of codes satisfying these conditions are presented in a table. A new upper bound for the minimum distance of self-dual codes and a new lower bound for the crosscorrelation of half-linear codes are obtained     

Minimax universal noiseless coding for unifilar and Markov sources (Corresp.)

Constructive upper bounds are presented for minimax universal noiseless coding of unifilar sources without any ergodicity assumptionS. These bounds are obtained by quantizing the estimated probability distribution of source letters with respect to the relative entropy. They apply both to fixed-length to variable-length (FV) and variable-length to fixed-length (VF) codes. Unifilar sources are a generalization of the usual definition of Markov sources, so these results apply to Markov sources as well. These upper bounds agree asymptotically with the lower bounds given by Davisson for FV coding of stationary ergodic Markov sources.     

Bounds on the symmetric cutoff rate for QAM transmissions overtime-correlated flat-faded channels

This article presents new upper and lower bounds on the symmetric cutoff rate for block-coded quadrature-amplitude-modulated (QAM) signaling over links affected by time-correlated Rayleigh-distributed flat-faded phenomena. The proposed bounds assume maximum-likelihood soft-decoding with perfect channel-state-information at the receiving side and hold for any form of QAM constellations. These bounds are quickly computable and constitute an efficient means to estimate the cutoff rate of systems employing very long codewords, so that an exact evaluation of the cutoff rate results. Analytical and numerical evidence of the tightness of the presented bounds is also provided     

Bounds on ε-rate for linear, time-invariant,multiinput/multioutput channels

Upper and lower bounds on the ε-rate of a linear, time-invariant multiple input multiple output channel are derived by using the same volume argument previously used by W.L. Root (1968) for single input single output channels. Because these bounds are not very tight, an approximation to the ε-rate is presented which lies between the upper and lower bounds, and can be used to compare ε-rates for different channels. The extension considered uses a result due to Lerer (1978) on the eigenvalue distribution of a convolution operator with a matrix kernel (impulse response). The present results are used to assess the increase in data rate attainable by designing input signals which exploit the multidimensional nature of the channel, relative to treating each constituent channel in isolation. Numerical results based upon a simple model for two coupled twisted-pair wires are presented     

Evaluation of the reliable data rates supported by multiple-antennacoded wireless links for QAM transmissions

We present some novel results about the reliable information-rate supported by point-to-point multiple-antenna Rayleigh-faded wireless links for coded transmissions that employ two-dimensional (QAM or PSK) data constellations. After deriving the symmetric capacity of these links, we present fast-computable analytical upper and lower bounds that are asymptotically exact both for high and low SNRs, and give rise to a reliable evaluation of the link capacity when perfect channel state information (CSI) is available at the receiver. Furthermore, asymptotically exact simple upper bounds are also presented for a tight evaluation of the outage probability     

基于MIMO几何信道模型的容量界研究

MIMO技术是LTE的最重要技术之一。为了研究MIMO系统中信道容量界限,提出了基于双反射的几何信道模型。基于此模型,推导了信道相关系数及信道容量的表达式,证明了收发相关的MIMO信道容量上、下界。MonteCarlo信道容量仿真结果表明,MIMO信道容量上界在低信噪比的条件下具有紧性;而在高信噪比的条件下,MIMO信道容量的下界具有紧性。