The coded modulation scheme proposed in this paper has a simple construction: an integer sequence, representing the information, is convolved with a fixed, continuous-valued, finite impulse response (FIR) filter to generate the codeword - a lattice point. Due to power constraints, the code construction includes a shaping mechanism inspired by precoding techniques such as the Tomlinson-Harashima filter. We naturally term these codes “convolutional lattice codes” or alternatively “signal codes” due to the signal processing interpretation of the code construction. Surprisingly, properly chosen short FIR filters can generate good codes with large minimal distance. Decoding can be done efficiently by sequential decoding or for better performance by bidirectional sequential decoding. Error analysis and simulation results indicate that for the additive white Gaussian noise (AWGN) channel, convolutional lattice codes with computationally reasonable decoders can achieve low error rate close to the channel capacity.

Most of the existing methods that are used to solve the closest lattice point problem are based on an efficient search of the lattice points. In this paper a novel alternative approach is suggested where the closest point to a given vector is found by calculating which Voronoi cell contains this vector in an iterative manner. Each iteration is made of simple “slicing” operations, using a list of the Voronoi relevant vectors that define the basic Voronoi cell of the lattice. The algorithm is guaranteed to converge to the closest lattice point in a finite number of steps. The method is suitable, for example, for decoding of multi-input multi-output (MIMO) communication problems. The average computational complexity of the proposed method is comparable to that of the efficient variants of the sphere decoder, but its computational variability is smaller.

Low-density lattice codes (LDLC) are novel lattice codes that can be decoded efficiently and approach the capacity of the additive white Gaussian noise (AWGN) channel. In LDLC a codeword x is generated directly at the n-dimensional Euclidean space as a linear transformation of a corresponding integer message vector b, i.e., x = Gb-1, where H = G-1is restricted to be sparse. The fact that H is sparse is utilized to develop a linear-time iterative decoding scheme which attains, as demonstrated by simulations, good error performance within ~0.5 dB from capacity at block length of n =100,000 symbols. The paper also discusses convergence results and implementation considerations.

Most of the existing methods to solve the closest lattice point problem are based on an efficient search of the lattice points. In this paper, a novel alternative approach is suggested where the closest point to a given vector is found by calculating which Voronoi cell contains this vector in an iterative manner. Each iteration is made of simple "slicing" operations, using a list of the Voronoi relevant vectors that define the basic Voronoi cell of the lattice. The algorithm is guaranteed to converge to the closest lattice point in a finite number of steps. The method is suitable, for example, for decoding of multi-input multi-output (MIMO) communication problems. The average computational complexity of the proposed method is comparable to that of the efficient variants of the sphere decoder, but its computational variability is smaller.

Low density lattice codes (LDLC) are novel lattice codes that can approach the capacity of the additive white Gaussian noise (AWGN) channel and be decoded efficiently. In LDLC a codeword x is generated directly at the n-dimensional Euclidean space as a linear transformation of a corresponding integer message vector b, i.e., x = Gb, where H = G-1is restricted to be sparse. The fact that H is sparse is utilized to develop a linear-time iterative decoding scheme which attains, as demonstrated by simulations, good error performance within ~ 0.5 dB from capacity at block length of n = 100,000 symbols. The paper also discusses convergence results and implementation considerations

The problem of finding the closest lattice point arises in several communication problems, and is known to be NP-hard. Existing methods to solve the problem are based on the sphere decoder, which searches for all the lattice points in a sphere around the received point. The sphere decoder is general and does not exploit the noise properties of the communication channel. In this paper we suggest to use sequential decoding algorithms for this problem. In particular, we propose an algorithm based on the well known Fano algorithm that naturally exploits the noise structure, hence offers a significant complexity reduction with respect to the sphere decoder with only a small penalty in error performance. Two further improvements are suggested. The first is bidirectional stack decoding, where the stack is implemented using a heap data structure to avoid sorting. The second is interleaved decoding, where the possibility to choose an arbitrary search order along the lattice coordinates is used to interleave noise bursts at the receiver. Finally, a lower bound is found for the computational cutoff rate of sequential lattice decoding

Motivated by signal processing, we present a new class of channel codes, called signal codes, for continuous-alphabet channels. We analyze the codes and provide simulation results indicating that these codes can be practical and are an attractive alternative to trellis-code techniques.

The computational complexity of classical time domain gradient-based echo cancellation algorithms might be prohibitively high, due to the very long response of the acoustic transfer functions involved. A reduction in computational complexity can be achieved by using frequency domain or subband algorithms. However, these algorithms introduce an inherent delay in the signal path. The delayed echo has an annoying psychoacoustic effect. Additionally, the delay prevents natural, full-duplex conversation. Moreover, when operated in practical scenarios, using speech signals in actual room acoustic environments, the convergence and tracking properties of the frequency domain algorithms do not compare favorably with those of the NLMS algorithm. This is because the range of values of the convergence constant that support a stable filter is more restrictive for the frequency domain algorithms. In this study we introduce a new algorithm termed delayless frequency domain (DLFD). The DLFD exhibits performance comparable to that of the NLMS algorithm with a computational complexity comparable to that of standard frequency domain algorithms and without the processing delay.

We consider the problem of estimating the parameters of an unknown discrete linear system driven by a sequence of independent identically distributed (i.i.d.) random variables whose probability density function (PDF) may be non-Gaussian. We assume a general system structure that may contain causal and noncausal poles and zeros. The parameters characterizing the input PDF may also be unknown. We derive an asymptotic expression for the Cramer-Rao lower bound, and show that it is the highest (worst) in the Gaussian case, indicating that the estimation accuracy can only be improved when the input PDF is non-Gaussian. It is further shown that the asymptotic error variance in estimating the system parameters is unaffected by lack of knowledge of the PDF parameters, and vice verse. Computationally efficient gradient-based algorithms for finding the maximum likelihood estimate of the unknown system and PDF parameters, which incorporate backward filtering for the identification of non-causal parameters, are presented. The dual problem of blind deconvolution/equalization is considered, and asymptotically attainable lower bounds on the equalization performance are derived. These bounds imply that it is preferable to work with compact equalizer structures characterized by a small number of parameters as the attainable performance depend only on the total number of equalizer parameters.>

A class of iterative methods for solving the blind deconvolution problem, i.e. for recovering the input of an unknown possibly nonminimum-phase linear system by observation of its output, is presented. These methods are universal do not require prior knowledge of the input distribution, are computationally efficient and statistically stable, and converge to the desired solution regardless of initialization at a very fast rate. The effects of finite length of the data, finite length of the equalizer, and additive noise in the system on the attainable performance (intersymbol interference) are analyzed. It is shown that in many cases of practical interest the performance of the proposed methods is far superior to linear prediction methods even for minimum phase systems. Recursive and sequential algorithms are also developed, which allow real-time implementation and adaptive equalization of time-varying systems.>

A necessary and sufficient condition for blind deconvolution (without observing the input) of nonminimum-phase linear time-invariant systems (channels) is derived. Based on this condition, several optimization criteria are proposed, and their solution is shown to correspond to the desired response. These criteria involve the computation only of second- and fourth-order moments, implying a simple tap update procedure. The proposed methods are universal in the sense that they do not impose any restrictions on the probability distribution of the (unobserved) input sequence. It is shown that in several important cases (e.g. when the additive noise is Gaussian), the proposed criteria are essentially unaffected.>