On SOVA for nonbinary codes

For binary codes, Fossorier et al. (see ibid., vol.2, p.137-9, 1998) have shown that the soft-output Viterbi algorithm (SOVA) becomes equivalent to the max-log-maximum a posteriori (MAP) algorithm after a modification. In this letter, we generalize such modified SOVA to nonbinary cases, motivated by the fact that the performance gap between the original SOVA and the max-log-MAP algorithm broadens in these cases, The equivalence between the two algorithms is proved in a more compact form. The modified SOVA requires only add-compare-select operations and is well suited for high-speed parallel implementation     

On optimal linear filtering for edge detection

In this paper, we revisit the analytical expressions of the three Canny's (1983) criteria for edge detection quality: good detection, good localization, and low multiplicity of false detections. Our work differs from Canny's work on two essential points. Here, the criteria are given for discrete sampled signals, i.e., for the real, implemented filters. Instead of a single-step edge as input signal, we use pulses of various width. The proximity of other edges affects the quality of the detection process. This is taken into account in the new expressions of these criteria. We derive optimal filters for each of the criteria and for any combination of them. In particular, we define an original filter which maximizes detection and localization and a simple approximation of the optimal filter for the simultaneous maximization of the three criteria. The upper bounds of the criteria are computed which allow users to measure the absolute and relative performance of any filter (exponential, Deriche (1987), and first derivative of Gaussian filters are evaluated). Our criteria can also be used to compute the optimal value of the scale parameter of a given filter when the resolution of the detection is fixed.     

On a class of linear time-varying filters

This paper is devoted to a special class of linear time-varying filters, members of which are commonly employed in practice. It is shown that some of these filters share a number of desirable properties with linear stationary systems, the most important of which is the preservation of wide sense stationarity of stochastic inputs. An application to the problem of transmitting a continuous signal over a sampled data channel is included. Some results coincide with those for a multichannel system with simultaneous optimum stationary presampling and postsampling filters.     

两类最优跳频序列集的线性复杂度

利用有限域中的一类不同于幂置换的置换多项式,将两类具有低线性复杂度的跳频序列集变换为具有高线性复杂度的最优跳频序列集。通过理论证明给出了变换以后序列线性复杂度的精确值。所得到的两类新的跳频序列集不仅具有最优的Hamming相关值,而且相对于变换前的序列集具有大的线性复杂度,可以抵抗Berlekamp-Massey算法的攻击。     

On the realization of a class of linear systems

A technique for the realization of linear continuous time-invariant systems from the given transfer function matrix is proposed.     

On turbo decoding of nonbinary codes

Symbol-by-symbol maximum a posteriori (MAP) decoding algorithms for nonbinary block and convolutional codes over an extension field GF(p ^a) are presented. Equivalent MAP decoding rules employing the dual code are given which are computationally more efficient for high-rate codes. It is shown that these algorithms meet all requirements needed for iterative decoding as the output of the decoder can be split into three independent estimates: soft channel value, a priori term and extrinsic value. The discussed algorithms are then applied to a parallel concatenated coding scheme with nonbinary component codes in conjunction with orthogonal signaling     

新的三元零相关区二维阵列集

提出了一类新的三元零相关区二维阵列集的构造方法.新的阵列集可由任意一对Hadamard阵生成,并且在零相关区内,其周期相关函数和非周期相关函数都为0.构造的二维阵列集中包含的阵列数目接近Tang-Fan-Matsufuji界,其性能参数达到了近似理想的状态.     

On optimal signal sets for digital communications with finiteprecision and amplitude constraints

The maximum data rate that can be reliably communicated given a linear, time-invariant, dispersive channel, a receiver that samples the channel output to within an accuracy of ±d where d >0, and a transmitter with an output amplitude constraint is evaluated. For any dispersive channel the maximum rate depends on d and is finite. The transmitted waveforms must be designed so that two channel outputs associated with two distinct transmitted signals are separated in amplitude at a particular time by d. It is shown that given any channel impulse response with rational Laplace transform, there exists an optimal sets of inputs that are ±A everywhere where A is the maximum allowable amplitude. Furthermore, in any finite time interval, each input changes sign a finite number of times. If the channel impulse response is a single decaying exponential, it is shown that simple binary signaling, in which A or -A, depending on the current message bit, is transmitted during each symbol interval, maximizes the data rate     

On the optimal linear feature (Corresp.)

The problem of finding the linear scalar feature that minimizes the probability of error in discriminating between two Gaussian multivariate hypotheses is comidered. A one-dimensional search algorithm to solve this problem is given, improving upon a previous multidimentional theorem.     

On a class of signals and matrices giving very fast algorithms for linear problems

In this paper is presented a class of stochastic signals and of correlation matrices introducing very fast algorithms for solving linear problems. These signals are derived from white noise by using three kinds of operations combined in various orders: summation, difference and instantaneous modulation. The discrete time Brownian motion is a particular example of such signals.     

一类低相关序列集的线性复杂度研究

在密码系统和通信系统中使用大线性复杂度的低相关序列能有效地提高数据的安全性,设计大线性复杂度的二元低相关序列是一个重要的研究问题.使用d-齐次函数是构造低相关序列集的一种有效途径,Key方法可以确定这些序列的线性复杂度.对正偶数n和与2n/2-1互素的任意正整数r,提出了一类周期为2n-1的2n条序列组成的二元序列集S(r).对某些适当选取的参数r,S(r)中序列的线性复杂度为n2n/2-3,或n2n.2-4.参数n可以取任意正偶数,所构造的具有大线性复杂度的序列具有广泛的使用范围.     

Cost-effective LFSR synthesis for optimal pseudoexhaustive BISTtest sets

The generation of pseudoexhaustive test sets for the built-in self-test (BIST) of combinational circuits is addressed, using as a test pattern generator a simple linear feedback register (LFSR), structure, known as LFSR/SR. It is shown that particular orderings of the LFSR cells can significantly reduce the test set size. In addition, it is shown that an LFSR/SK designed with a particular cell ordering and the allowance of a marginal number of additional cells guarantees pseudoexhaustive test sets of the minimum size 2^w, where w is the maximum input dependency limit of the circuit under test. Extensive experimentation on benchmark circuits and comparisons with the hardware overhead of other methods indicate the advantage of this approach     

On a simple method for detecting synchronization errors in coded messages

We investigate the problem of designing pairs (p,s) of words with the property that, if each word of a coded message is prefixed by p and suffixed by s, the resulting set of coded messages is error detecting with finite delay. We consider (combinatorial) channels permitting any combination of the substitution, insertion, and deletion (SID) error types, and address the cases of both scattered and burst errors. A pair (p,s) with the above property is evaluated in terms of three parameters: redundancy, delay of decoding, and frequency of the detectable errors. In the case of SID channels with burst errors, we provide a complete and explicit characterization of their error-detecting pairs (p,s), which involves the period of the word sp.     

A fast algorithm for optimal linear interpolation

A fast algorithm for computing the optimal linear interpolation filter is developed. The algorithm is based on the Sherman-Morrison inversion formula for symmetric matrices. The relationship between the derived algorithm and the Levinson algorithm is illustrated. It is shown that the new algorithm, in comparison with the well-known algorithms, requires fewer multiplications and hence is of lower complexity     

On a class of random processes exhibiting optimal nonlinear one-step predictors (Corresp.)

Two classes of random processes that exhibit one-step predictors with optimal nonlinear minimum mean-squared error (MMSE) are discussed, and conditions for membership to one of these classes are given. Examples of each class are presented, and the optimal one-step predictors are given.     

Formulas for linear optimal control over a finite or infinite interval

Algebraic expressions are given for the solution of the optimal-linear-regulator problem for a constant plant and quadratic performance index. They enable the time-varying or constant feedback gains and the resulting plant trajectories to be found.     

非二进制LDPC码编码调制在光纤通信中的应用

为满足100Gb/s光纤通信的需求,提出了非二进制LDPC码编码调制(NB-LDPC-CM)方案.该方案通过使用频谱效率调制以及非二进制前向纠错LDPC码,提供了一种在高总比特率下实现可靠通信的前向纠错机制.与现有的BI-LDPC-CM方案相比,该方案在误比特率(BER)为10-7的情况下,采用16点、32点、和64点四维星座图时,额外提供的净编码增益分别为0.26dB、1.14dB和2.14dB.     

Improved algorithm for optimal stabilisation of linear systems

An algorithm for the optimal stabilisation of linear systems is proposed, based on the dyadic decomposition of the plant matrix. The algorithm is superior to others that have been given.     

On the error matrix in optimal linear filtering of stationary processes

The error covariance matrix corresponding to optimal linear causal filtering of second-order stationary processes in additive noise is considered. Formulas expressing this error matrix in terms of the optimal transfer function are established, and in the nonsingular case the optimal transfer function is expressed in terms of the spectral densities. These are straightforward generalizations of previously published scalar results, and the derivation is similarly based on Hardy space theory. Explicit bounds on the minimal error (i.e., the trace of the optimal error covariance matrix) are obtained for filtering in white noise. Furthermore, an explicit expression for the error covariance matrix is derived for the case of transmitting the same signal over several white-noise channels.