Aleksandar Kavcic

Simulation-Based Computation of Information Rates for Channels With Memory

The information rate of finite-state source/channel models can be accurately estimated by sampling both a long channel input sequence and the corresponding channel output sequence, followed by a forward sum-product recursion on the joint source/channel trellis. This method is extended to compute upper and lower bounds on the information rate of very general channels with memory by means of finite-state approximations. Further upper and lower bounds can be computed by reduced-state methods

The Feasibility of Magnetic Recording at 10 Terabits Per Square Inch on Conventional Media

This paper proposes a new approach to magnetic recording based on shingled writing and two-dimensional readback and signal-processing. This approach continues the use of conventional granular media but proposes techniques such that a substantial fraction of one bit of information is stored on each grain. Theoretically, areal-densities of the order of 10 Terabits per square inch may be achievable. In this paper we examine the feasibility of this two-dimensional magnetic recording (TDMR) and identify the significant challenges that must be overcome to achieve this vision.

Equal-diagonal QR decomposition and its application to precoder design for successive-cancellation detection

In multiple-input multiple-output (MIMO) multiuser detection theory, the QR decomposition of the channel matrix H can be used to form the back-cancellation detector. In this paper, we propose an optimal QR decomposition, which we call the equal-diagonal QR decomposition, or briefly the QRS decomposition. We apply the decomposition to precoded successive-cancellation detection, where we assume that both the transmitter and the receiver have perfect channel knowledge. We show that, for any channel matrix H, there exists a unitary precoder matrix S, such that HS=QR, where the nonzero diagonal entries of the upper triangular matrix R in the QR decomposition of HS are all equal to each other. The precoder and the resulting successive-cancellation detector have the following properties. a) The minimum Euclidean distance between two signal points at the channel output is equal to the minimum Euclidean distance between two constellation points at the precoder input up to a multiplicative factor that equals the diagonal entry in the R-factor. b) The superchannel HS naturally exhibits an optimally ordered column permutation, i.e., the optimal detection order for the vertical Bell Labs layered space-time (V-BLAST) detector is the natural order. c) The precoder S minimizes the block error probability of the QR successive cancellation detector. d) A lower and an upper bound for the free distance at the channel output is expressible in terms of the diagonal entries of the R-factor in the QR decomposition of a channel matrix. e) The precoder S maximizes the lower bound of the channels free distance subject to a power constraint. f) For the optimal precoder S, the performance of the QR detector is asymptotically (at large signal-to-noise ratios (SNRs)) equivalent to that of the maximum-likelihood detector (MLD) that uses the same precoder. Further, We consider two multiplexing schemes: time-division multiple access (TDMA) and orthogonal frequency-division multiplexing (OFDM). We d

Binary intersymbol interference channels: Gallager codes, density evolution, and code performance bounds

We study the limits of performance of Gallager codes (low-density parity-check (LDPC) codes) over binary linear intersymbol interference (ISI) channels with additive white Gaussian noise (AWGN). Using the graph representations of the channel, the code, and the sum-product message-passing detector/decoder, we prove two error concentration theorems. Our proofs expand on previous work by handling complications introduced by the channel memory. We circumvent these problems by considering not just linear Gallager codes but also their cosets and by distinguishing between different types of message flow neighborhoods depending on the actual transmitted symbols. We compute the noise tolerance threshold using a suitably developed density evolution algorithm and verify, by simulation, that the thresholds represent accurate predictions of the performance of the iterative sum-product algorithm for finite (but large) block lengths. We also demonstrate that for high rates, the thresholds are very close to the theoretical limit of performance for Gallager codes over ISI channels. If C denotes the capacity of a binary ISI channel and if C/sub i.i.d./ denotes the maximal achievable mutual information rate when the channel inputs are independent and identically distributed (i.i.d.) binary random variables (C/sub i.i.d.//spl les/C), we prove that the maximum information rate achievable by the sum-product decoder of a Gallager (coset) code is upper-bounded by C/sub i.i.d./. The last topic investigated is the performance limit of the decoder if the trellis portion of the sum-product algorithm is executed only once; this demonstrates the potential for trading off the computational requirements and the performance of the decoder.

The Viterbi algorithm and Markov noise memory

This work designs sequence detectors for channels with intersymbol interference (ISI) and correlated (and/or signal-dependent) noise. We describe three major contributions. (i) First, by modeling the noise as a finite-order Markov process, we derive the optimal maximum-likelihood sequence detector (MLSD) and the optimal maximum a posteriori (MAP) sequence detector extending to the correlated noise case the Viterbi algorithm. We show that, when the signal-dependent noise is conditionally Gauss-Markov, the branch metrics in the MLSD are computed from the conditional second-order noise statistics. We evaluate the branch metrics using a bank of finite impulse response (FIR) filters. (ii) Second, we characterize the error performance of the MLSD and MAP sequence detector. The error analysis of these detectors is complicated by the correlation asymmetry of the channel noise. We derive upper and lower bounds and computationally efficient approximations to these bounds based on the banded structure of the inverses of Gauss-Markov covariance matrices. An experimental study shows the tightness of these bounds. (iii) Finally, we derive several classes of suboptimal sequence detectors, and demonstrate how these and others available in the literature relate to the MLSD. We compare their error rate performance and their relative computational complexity, and show how the structure of the MLSD and the performance evaluation guide us in choosing a best compromise between several types of suboptimal sequence detectors.

On the capacity of Markov sources over noisy channels

We present an expectation-maximization method for optimizing Markov process transition probabilities to increase the mutual information rate achievable when the Markov process is transmitted over a noisy finite-state machine channel. The method provides a tight lower bound on the achievable information rate of a Markov process over a noisy channel and it is conjectured that it actually maximizes this information rate. The latter statement is supported by empirical evidence (not shown in this paper) obtained through brute-force optimization methods on low-order Markov processes. The proposed expectation-maximization procedure can be used to find tight lower bounds on the capacities of finite-state machine channels (say, partial response channels) or the noisy capacities of constrained (say, run-length limited) sequences, with the bounds becoming arbitrarily tight as the memory-length of the input Markov process approaches infinity. The method links the Arimoto-Blahut algorithm to Shannons noise-free entropy maximization by introducing the noisy adjacency matrix.

Iterative timing recovery

The last decade has seen the development of iteratively decodable error-control codes of unprecedented power, whose large coding gains enable reliable communication at very low signal-to-noise ratio (SNR). A by-product of this trend is that timing recovery must be performed at an SNR lower than ever before. Conventional timing recovery ignores the presence or error-control coding and thus doomed to fail when the SNR is low enough. This article describes the iterative timing recovery, a method for implementing timing recovery in cooperation with iterative error-control decoding so as to approximate a more complicated receiver that jointly solves the timing recovery and decoding problems.

UWB delay profile models for residential and commercial indoor environments

We present models for the ultrawideband (UWB) channel delay profile in indoor environments, based on the processing of two large sets of measured data. Both measurement sets are for a center frequency of 5 GHz, but the bandwidths are very different-1.25 GHz and 6 GHz. We model both line-of-sight (LOS) and nonline-of-sight (NLOS) paths, and do so for both single-family homes and commercial buildings. Also, we consider both the profile at a receiver point, which we call the multipath intensity profile (MIP), and the locally spatially averaged profile, which we call the power delay profile (PDP). For both cases, we find that the profile for NLOS paths can be modeled as a decaying exponential times a noise-like variation with lognormal statistics and that, for LOS paths, the profile has the same form plus a strong component at the minimum delay. The model consists of statistical descriptions of the parameters of these functions, including the effects of transmit-receive (T--R) distance and of variations from building to building. We show simulation results for a few cases to demonstrate that the model accurately predicts key properties of the measured channels, such as the distribution of rms delay spread.

UWB indoor path loss model for residential and commercial buildings

We present a statistical model for the path loss of ultra-wideband channels in indoor environments. In contrast to previous measurements, the data reported here are for a bandwidth of 6 GHz rather than 1.25 GHz; they encompass commercial buildings in addition to single-family homes (20 of each); and local spatial averaging is included. As before, the center frequency is 5.0 GHz. Separate models are given for commercial and residential environments and-within each category-for line-of-sight (LOS) and non-line-of-sight (NLS) paths. All four models have the same mathematical structure, differing only in their numerical parameters. The two new models (LOS and NLS) for residences closely match those derived from the previous measurements, thus affirming the stability of our path loss modeling. For greater accuracy, we therefore pool the two data sets in our final models for residences. We find that the path loss statistics for the two categories of buildings are quite similar.

A Generalization of the Blahut–Arimoto Algorithm to Finite-State Channels

The classical Blahut-Arimoto algorithm (BAA) is a well-known algorithm that optimizes a discrete memoryless source (DMS) at the input of a discrete memoryless channel (DMC) in order to maximize the mutual information between channel input and output. This paper considers the problem of optimizing finite-state machine sources (FSMSs) at the input of finite-state machine channels (FSMCs) in order to maximize the mutual information rate between channel input and output. Our main result is an algorithm that efficiently solves this problem numerically; thus, we call the proposed procedure the generalized BAA. It includes as special cases not only the classical BAA but also an algorithm that solves the problem of finding the capacity-achieving input distribution for finite-state channels with no noise. While we present theorems that characterize the local behavior of the generalized BAA, there are still open questions concerning its global behavior; these open questions are addressed by some conjectures at the end of the paper. Apart from these algorithmic issues, our results lead to insights regarding the local conditions that the information-rate-maximizing FSMSs fulfill; these observations naturally generalize the well-known Kuhn-Tucker conditions that are fulfilled by capacity-achieving DMSs at the input of DMCs.