A lower bound on the cutoff rate for Gaussian channels withpeak-limited inputs

A lower bound on the cutoff rate R_O of a dispersive Gaussian channel with peak- rather than average-power-limited input is evaluated and compared to the lower bound on capacity under the same input constraints. It is assumed that the input symbols are independent and uniformly distributed. Both bounds exhibit the same behavior as a function of an appropriately defined signal-to-noise ratio (SNR), with a discrepancy of 1.68 dB to the disadvantage of R_O, at high SNRs. The lower bound on R_O is evaluated for peak- and slope-limited signals that model magnetic recording systems and is compared to the lower bound on capacity     

An upper bound on the cutoff rate of sequential decoding

An upper bound is given on the cutoff rate of discrete memoryless channels. This upper bound, which coincides with a known lower bound, determines the cutoff rate, and settles a long-standing open problem     

Optimal reception, performance bound, and cutoff rate analysis ofreferences-assisted coherent CDMA communications with applications

Coherent spread-spectrum communications with transmitted reference-based, also called pilot-based, channel estimation is considered for code-division multiple-access (CDMA) communications over fading channels. Both noncontiguous time-division multiplexed reference symbol-based and continuous code-division multiplexed channel-based schemes are described. Assuming mean square error or optimal robust channel estimation, we derive the optimal receiver structure with a maximum-likelihood convolutional decoder. In addition, the Bhattacharyya bound and the cutoff rate of the reference-assisted coherent communications are derived. These analytical results are used for evaluating system performance and for selecting parameters such as coding rate and the data to reference power ratio to optimize system performance. Simulation results are given showing that the reverse link performance in a CDMA system can be significantly improved by using the reference-assisted coherent communication instead of noncoherent reception of orthogonally coded signal     

The two-user cutoff rate for an asynchronous and a synchronous multiple-access channel are the same

The cutoff rate region for block coding of a two-sender one-receiver multiple-access channel is shown to be the same with and without frame synchronization between the two senders.     

Capacity and cutoff rate for Poisson-type channels

The capacity of a Poisson-type channel subject both to peak amplitude and average energy constraints is calculated, and its relation to the cutoff rate given by Snyder and Rhodes is determined in the "very noisy" case.     

The cutoff rate for on-off keying

It is well known that on-off keying (OOK), i.e. the transmission of a pulse for a data one (mark) and transmission of no signal for a data zero (space), exhibits a 3 dB inferiority to antipodal signalling, in terms of the signal-to-noise ratio required to achieve a specified bit error probability. When the channel is characterized by the cutoff rate R₀, this 3 dB inferiority persists, in the sense that the required E_b/N₀ to operate at a given value of R₀ is 3 dB greater for the OOK channel than for the antipodal channel. However, it is shown that, if the definition of cutoff rate is generalized in an appropriate way to reflect the fact that signal energy is expended only in the transmission of marks, part of this penalty is recovered. In fact, it is shown that, in the limit of low R₀, there is no penalty in signal-to-noise ratio. Even at rates of realistic interest, the penalty is significantly less than the expected 3 dB     

Cutoff rate and signal design for the quasi-static Rayleigh-fadingspace-time channel

We consider the computational cutoff rate and its implications on signal design for the complex quasi-static Rayleigh flat-fading spatio-temporal channel under a peak-power constraint where neither transmitter nor receiver know the channel matrix. The cutoff rate has an integral representation which is an increasing function of the distance between pairs of complex signal matrices. When the analysis is restricted to finite-dimensional sets of signals, interesting characterizations of the optimal rate-achieving signal constellation can be obtained. For an arbitrary finite dimension, the rate-optimal constellation must admit an equalizer distribution, i.e., a positive set of signal probabilities which equalizes the average distance between signal matrices in the constellation. When the number N of receive antennas is large, the distance-optimal constellation is nearly rate-optimal. When the number of matrices in the constellation is less than the ratio of the number of time samples to the number of transmit antennas, the rate-optimal cutoff rate attaining constellation is a set of equiprobable mutually orthogonal unitary matrices. When the signal-to-noise ratio (SNR) is below a specified threshold, the matrices in the constellation are rank one and the cutoff rate is achieved by applying all transmit power to a single antenna and using orthogonal signaling. Finally, we derive recursive necessary conditions and sufficient conditions for a constellation to lie in the feasible set     

Channel combining and splitting for cutoff rate improvement

The cutoff rate R₀(W) of a discrete memoryless channel (DMC) W is often used as a figure of merit alongside the channel capacity C(W). If a channel W is split into two possibly correlated subchannels W₁, W₂, the capacity function always satisfies C(W₁)+C(W₂)lesC(W), while there are examples for which R₀(W₁)+R₀(W₂ )>R₀(W). The fact that cutoff rate can be "created" by channel splitting was noticed by Massey in his study of an optical modulation system. This paper gives a general framework for achieving similar gains in the cutoff rate of arbitrary DMCs by methods of channel combining and splitting. The emphasis is on simple schemes that can be implemented in practice. We give several examples that achieve significant gains in cutoff rate at little extra system complexity. Theoretically, as the complexity grows without bound, the proposed framework is capable of boosting the cutoff rate of a channel to arbitrarily close to its capacity in a sense made precise in the paper. Apart from Massey's work, the methods studied here have elements in common with Forney's concatenated coding idea, a method by Pinsker for cutoff rate improvement, and certain coded-modulation techniques, namely, Ungerboeck's set-partitioning idea and Imai-Hirakawa multilevel coding; these connections are discussed in the paper     

Satellite constellation design for telecommunication in Antarctica

This paper addresses the problem of designing a small satellite constellation suitable for communications in Antarctica. This study has been motivated by the increasing international interests in having permanent bases in Antarctica to perform experiments in physics, atmospheric sciences, geology, and biology to name a few key areas. The existing and planned scientific expeditions in Antarctica require continuous and reliable communication services, especially during emergencies. Geostationary Earth orbit satellites do not cover this high latitude adequately, and constellations using circular orbits would require too many satellites to provide continuous regional coverage, thus increasing cost prohibitively. A three‐satellite constellation using elliptical orbits is proposed to address this issue. The critical inclination has been selected to predominantly keep the satellites over Antarctica, where the satellites will dwell most of the time. This configuration has been obtained by using the two‐dimensional lattice flower constellation design theory: a minimum parameter design methodology that enforces all three satellites in the same trajectory as seen from the Earth rotating frame. This aspect provides the continuous coverage necessary for reliable communications using only a small number of satellites. Copyright © 2015 John Wiley & Sons, Ltd.     

Capacity and cutoff rate calculations for a concatenated codingsystem

A model is developed for a concatenated coding system, and from it the overall channel cutoff rate and capacity is found using random coding arguments. The effects of interleaving between the inner and outer codes and of the availability of side information to the outer decoder are considered. The performance of several specific concatenated coding systems is calculated and used for comparison with the random coding result. From the analysis, a number of general conclusions regarding the design of concatenated coding systems are presented. All the results are derived assuming a block inner code     

MPSK modulated constellation design for differential space-time modulation

The constellation design for differential space-time modulation usually requires to construct L (constellation size) unitary matrices making the design complexity increasing rapidly with L. In this correspondence, we propose a new construction technique, which exploits the rotational invariance of unitary matrices and the property of MPSK modulation. The proposed constellations are derivable from a smaller set of D = L/M unitary matrices (via rotations defined by an M-ary PSK symbol) which, in turn, are parameterized by two unitary matrices U₁ and U₂. They share some good property of group constellations thereby considerably simplifying the optimization of U₁ and U₂. They also possess other good properties which allow for simplified maximum likelihood (ML) decoding. Extensive numerical examples are presented to demonstrate that the proposed constellations in general have larger diversity products than other constellations and thus, better error performance.     

通信卫星星座优化设计综述

通信卫星星座优化设计是构建通信星座系统的关键环节。对通信卫星星座设计中的优化模型和优化算法进行了综述和展望。首先,建立了通信卫星星座设计的一般优化模型;然后,从覆盖性能、星间链路和系统成本三个方面对优化模型中优化变量、目标函数和约束条件的构建进行了综述;之后,介绍了卫星星座设计中常用的三大类多目标优化算法,归纳总结了4种主流算法的主要特征,并比较分析了它们应用于卫星星座设计的优缺点;最后,指出了现有通信卫星星座优化设计中存在的问题及发展趋势。     

可见光通信色移键控星座设计方法研究

本文提出一种基于色移键控(CSK)调制兼容照明的可见光通信(VLC)系统星座图设计方法,可实现多色光源在通信的同时保证色度和视觉亮度稳定.基于国际照明委员会(CIE)1931 XYZ色度系统,本文给出了色度和亮度约束在CSK星座布局优化问题的数学表达式.进一步的本文提出采用数值优化中的内点法对该问题进行求解.由于内点法...     

Optimization of a lattice-based constellation for signaling over apartial response channel

This article discusses the problem of optimizing a lattice-based signal constellation for signaling over a partial response channel. The objective is to minimize the probability of error which is determined by the combined effects of the additive Gaussian noise and channel memory     

On the generalized symmetric cutoff rate for finite-state channels

Finite-state discrete-time channels with equiprobable M-ary inputs are considered. The generating function bound, which is ubiquitously applied to upper-bound the error probability of uncoded signaling over these channels, is used here to lower-bound the corresponding generalized symmetric cutoff rate, which lower-bounds the practically achievable rates and error exponents in these channels with symmetric signaling. The bound accounts for general additive metrics. For the special case of the optimal maximum-likelihood metric, the corresponding bound is shown to be asymptotically tight in the region where the symmetric cutoff rate approaches its maximum value of log₂ M (bits-per-channel use). For a finite-state additive white Gaussian noise (AWGN) channel this feature is used to relate the minimum Euclidean distance of an uncoded symmetric system to the corresponding symmetric cutoff rate. The results are demonstrated for AWGN channels corrupted by linear and nonlinear intersymbol interference. They are also used to assess the efficiency of concatenated coding over the 4-ary AWGN channel where the finite-state mechanism is defined by simple rate 1/2, four-state Ungerboeck 4-AM trellis code     

Generalized cutoff rate of time- and frequency-selective fadingchannels

The generalized cutoff rate of time- and frequency-selective fading channels is evaluated for M-ary frequency-shift keying (MFSK) and M-ary differential phase-shift keying (MDPSK) modulation with soft decoding. The optimal signaling rate and code rate for dispersive channels are evaluated. The guard time effect, is used in multipath spread channels, is evaluated for frequency-selective channels, and the optimal combination of signaling rate, code rate, and guard time is presented. Special attention is given to CCIR (International Radio Consultative Committee) HF channel models     

Properties of cutoff corrugated surfaces for corrugated horn design

Corrugated horns involve a junction between the corrugated surface and a conducting groundplane. Proper horn design requires an understanding of the electromagnetic properties of the corrugated surface and this junction. An integral equation solution has been used to study the influence of corrugation density and tooth thickness on the power loss, surface current, and the scattering from a groundplane-corrugated surface junction.     

Optimum asymmetric constellation design for trellis-coded modulation over gaussian channels

This letter studies the optimization of asymmetric constellations for trellis-coded modulation (TCM). Unlike the conventional criterion of maximizing the free Euclidean distance, the criterion here is to minimize the bit error rate (BER) of TCM systems. The letter presents an easy way to derive the BER upper bound for any TCM codes, and proposes the method for designing optimum asymmetric constellations by minimizing the bound. The given method can be applied to TCM systems with arbitrary state numbers. Numerical results verify that all the codes designed by the proposed method achieve better BER performance than symmetric ones.     

Bounds on the symmetric binary cutoff rate for dispersive Gaussianchannels

Bounds on the symmetric binary cutoff rate for a pulse amplitude modulated (PAM) signaling over dispersive Gaussian channels are evaluated and discussed. These easily calculable bounds can be used to estimate the reliable rate of information transmission and the error exponent behavior for binary (two-level) PAM schemes, operating through a prefiltered additive white Gaussian channel, the memory of which is long enough to make the exact evaluation of the cutoff rate formidable. The core of the bounding technique relies on a probabilistic interpretation of a fundamental theorem in matrix theory, regarding the logarithm of the largest eigenvalue of a nonnegative primitive matrix, commonly applied in large deviation problems. These bounds are calculated for some examples and their respective tightness is considered. Further potential applications of the proposed bounding technique are pointed out     

Evaluation of bit error rate for packet combining with constellation rearrangement

In this paper, we propose a method for evaluation of the bit error rate (BER) for packet combining based on constellation rearrangement (CoRe). Such mapping diversity scheme, adopted in the high speed downlink packet access (HSDPA), uses Gray‐mapped constellations and is based on suboptimal accumulation of the reliability metrics generated in each of the transmissions. We present an exact model for the logarithmic likelihood ratios (LLR) obtained by means of the so‐called max‐log approximation, and we show that their conditional probability density functions (pdf) are piecewise Gaussian. We then present the derivation of the uncoded BER and illustrate it with simulation results that confirm our formulation. Finally, we propose simplifications which significantly reduce the complexity of the evaluation method and provide results with a very good accuracy; an extension to transmissions over faded channel is also presented. Copyright © 2007 John Wiley & Sons, Ltd.