arXiv subjects

Uri Erez

Publications and source records attributed to Uri Erez.

At least 19 recordsLinked to original sources

arXiv2026

A Note on Scaling in Randomly Rotated Quantization and Its Connection to the CDEF +1 Pythagorean Relation

Quantization schemes based on randomized rotations have recently received renewed attention, including the roles of MMSE and unbiased reconstruction scalings. In this note, we point out the connection to classical results in statistical signal processing and communication theory. Specifically, the two reconstruction scales used in the EDEN line of work admit a natural interpretation as finite-dimensional, realization-dependent counterparts of the Wiener and unbiased coefficients in the classical CDEF formulation. At finite blocklength, the CDEF +1 relation holds pointwise for each rotation realization as an exact geometric (Pythagorean) identity, but does not hold after averaging the distortions over the rotation. The classical SNR relation $\sf{SNR}_{\rm MMSE}=\sf{SNR}_{\rm MMSE,U}+1$ is recovered as $d\to\infty$: once the overall scale is handled separately, the empirical coordinate statistics of a randomly rotated vector approach their i.i.d. Gaussian counterparts, and the rotation-dependent quantities concentrate. Importantly, EDEN goes beyond this classical correspondence: for every finite $d$, its Haar-rotation formulation guarantees exact conditional unbiasedness, a stronger property than the second-order notion of unbiasedness in CDEF. We further comment on two distinct roles random rotations play in quantization: one is approximate Gaussianization of the coordinates; the other is decorrelation of reconstruction errors across quantization branches.

cs.IT↗

arXiv2026

Stochastic Chase Decoding for BMS Channels via Rate Distortion Theory

This work develops a rate-distortion-based approach to stochastic Chase decoding of algebraic codes over binary memoryless symmetric (BMS) channels, replacing the heuristics traditionally used to determine flip probabilities with information-theoretically grounded flipping rules. In particular, we reinterpret stochastic Chase decoding as a random-coding construction for error-pattern covering codes. Our approach builds on the framework of Nguyen et al., who introduced a rate-distortion formulation of multiple-attempt decoding for Reed-Solomon codes over nonbinary channels. In their formulation, erasure patterns are generated so as to align with, and thereby mask, hard-decision errors. We adapt this framework to the design of bit-flip probabilities for Chase decoding over BMS channels. This yields an explicit characterization of the asymptotically optimal bit-flipping rule, together with the expected list size required to ensure that the transmitted codeword appears in the decoding list with high probability. Moreover, for binary and quaternary symmetric channels, we demonstrate that the optimal bit-flipping rule, determined by exhaustive search, closely matches the information-theoretic rule even at short block lengths.

cs.IT↗

arXiv2025

Extension of the Poltyrev Bound to Binary Memoryless Symmetric Channels

The Poltyrev bound provides a very tight upper bound on the decoding error probability when using binary linear codes for transmission over the binary symmetric channel and the additive white Gaussian noise channel, making use of the code's weight spectrum. In the present work, the bound is extended to memoryless symmetric channels with a discrete output alphabet. The derived bound is demonstrated on a hybrid BSC-BEC channel. Additionally, a reduced-complexity bound is introduced at the cost of some loss in tightness.

cs.IT↗

arXiv2024

Design of Threshold-Constrained Indirect Quantizers

We address the problem of indirect quantization of a source subject to a mean-squared error distortion constraint. A well-known result of Wolf and Ziv is that the problem can be reduced to a standard (direct) quantization problem via a two-step approach: first apply the conditional expectation estimator, obtaining a ``new'' source, then solve for the optimal quantizer for the latter source. When quantization is implemented in hardware, however, invariably constraints on the allowable class of quantizers are imposed, typically limiting the class to \emph{time-invariant} scalar quantizers with contiguous quantization cells. In the present work, optimal indirect quantization subject to these constraints is considered. Necessary conditions an optimal quantizer within this class must satisfy are derived, in the form of generalized Lloyd-Max conditions, and an iterative algorithm for the design of such quantizers is proposed. Furthermore, for the case of a scalar observation, we derive a non-iterative algorithm for finding the optimal indirect quantizer based on dynamic programming.

cs.IT↗

arXiv2024

Lower Bounds on Mutual Information for Linear Codes Transmitted over Binary Input Channels, and for Information Combining

It has been known for a long time that the mutual information between the input sequence and output of a binary symmetric channel (BSC) is upper bounded by the mutual information between the same input sequence and the output of a binary erasure channel (BEC) with the same capacity. Recently, Samorodintsky discovered that one may also lower bound the BSC mutual information in terms of the mutual information between the same input sequence and a more capable BEC. In this paper, we strengthen Samordnitsky's bound for the special case where the input to the channel is distributed uniformly over a linear code. Furthermore, for a general (not necessarily binary) input distribution $P_X$ and channel $W_{Y|X}$, we derive a new lower bound on the mutual information $I(X;Y^n)$ for $n$ transmissions of $X\sim P_X$ through the channel $W_{Y|X}$.

cs.IT↗

arXiv2020

Incremental Refinements and Multiple Descriptions with Feedback

It is well known that independent (separate) encoding of K correlated sources may incur some rate loss compared to joint encoding, even if the decoding is done jointly. This loss is particularly evident in the multiple descriptions problem, where the sources are repetitions of the same source, but each description must be individually good. We observe that under mild conditions about the source and distortion measure, the rate ratio Rindependent(K)/Rjoint goes to one in the limit of small rate/high distortion. Moreover, we consider the excess rate with respect to the rate-distortion function, Rindependent(K, M) - R(D), in M rounds of K independent encodings with a final distortion level D. We provide two examples - a Gaussian source with mean-squared error and an exponential source with one-sided error - for which the excess rate vanishes in the limit as the number of rounds M goes to infinity, for any fixed D and K. This result has an interesting interpretation for a multi-round variant of the multiple descriptions problem, where after each round the encoder gets a (block) feedback regarding which of the descriptions arrived: In the limit as the number of rounds M goes to infinity (i.e., many incremental rounds), the total rate of received descriptions approaches the rate-distortion function. We provide theoretical and experimental evidence showing that this phenomenon is in fact more general than in the two examples above.

cs.IT↗

arXiv2020

An Orthogonality Principle for Select-Maximum Estimation of Exponential Variables

It was recently proposed to encode the one-sided exponential source X via K parallel channels, Y1, ..., YK , such that the error signals X - Yi, i = 1,...,K, are one-sided exponential and mutually independent given X. Moreover, it was shown that the optimal estimator \hat{Y} of the source X with respect to the one-sided error criterion, is simply given by the maximum of the outputs, i.e., \hat{Y} = max{Y1,..., YK}. In this paper, we show that the distribution of the resulting estimation error X - \hat{Y} , is equivalent to that of the optimum noise in the backward test-channel of the one-sided exponential source, i.e., it is one-sided exponentially distributed and statistically independent of the joint output Y1,...,YK.

cs.IT↗

arXiv2019

Super-Nyquist Rateless Coding for Intersymbol Interference Channels

A rateless transmission architecture is developed for communication over Gaussian intersymbol interference channels, based on the concept of super-Nyquist (SNQ) signaling. In such systems, the signaling rate is chosen significantly higher than the Nyquist rate of the system. We show that such signaling, when used in conjunction with good "off-the-shelf" base codes, simple linear redundancy, and minimum mean-square error decision feedback equalization, results in capacity-approaching, low-complexity rateless codes for the time-varying intersymbol-interference channel. Constructions for both single-input / single-output (SISO) and multi-input / multi-output (MIMO) ISI channels are developed.

cs.IT↗

arXiv2019

On General Lattice Quantization Noise

The problem of constructing lattices such that their quantization noise approaches a desired distribution is studied. It is shown that asymptotically is the dimension, lattice quantization noise can approach a broad family of distribution functions with independent and identically distributed components.

cs.IT↗

arXiv2019

Simple Bounds for the Symmetric Capacity of the Rayleigh Fading Multiple Access Channel

Communication over the i.i.d. Rayleigh slow-fading MAC is considered, where all terminals are equipped with a single antenna. Further, a communication protocol is considered where all users transmit at (just below) the symmetric capacity (per user) of the channel, a rate which is fed back (dictated) to the users by the base station. Tight bounds are established on the distribution of the rate attained by the protocol. In particular, these bounds characterize the probability that the dominant face of the MAC capacity region contains a symmetric rate point, i.e., that the considered protocol strictly attains the sum capacity of the channel. The analysis provides a non-asymptotic counterpart to the diversity-multiplexing tradeoff of the multiple access channel. Finally, a practical scheme based on integer-forcing and space-time precoding is shown to be an effective coding architecture for this communication scenario.

cs.IT↗

arXiv2019

A Simple Receive Diversity Technique for Distributed Beamforming

A simple method is proposed for use in a scenario involving a single-antenna source node communicating with a destination node that is equipped with two antennas via multiple single-antenna relay nodes, where each relay is subject to an individual power constraint. Furthermore, ultra-reliable and low-latency communication are desired. The latter requirement translates to considering only schemes that make use of local channel state information. Whereas for a receiver equipped with a single antenna, distributed beamforming is a well known and adequate solution, no straightforward extension is known. In this paper, a scheme is proposed based on a space-time diversity transformation that is applied as a front-end operation at the destination node. This results in an effective unitary channel matrix replacing the scalar coefficient corresponding to each user. Each relay node then inverts its associated channel matrix, which is the generalization of undoing the channel phase in the classical case of distributed beamforming to a single-antenna receiver, and then repeats the message over the resulting "gain-only" channel. In comparison to a single-antenna destination node, the method doubles the diversity order without requiring any channel state information at the receiver while at the same time retaining the array gain offered by the relays.

cs.IT↗

arXiv2019

Eliminating Interference in LOS Massive Multi-User MIMO with a Few Transceivers

Wireless cellular communication networks are bandwidth and interference limited. An important means to overcome these resource limitations is the use of multiple antennas. Base stations equipped with a very large (massive) number of antennas have been the focus of recent research. A bottleneck in such systems is the limited number of transmit/receive chains. In this work, a line-of-sight (LOS) channel model is considered. It is shown that for a given number of interferers, it suffices that the number of transmit/receive chains exceeds the number of desired users by one, assuming a sufficiently large antenna array. From a theoretical point of view, this is the first result proving the near-optimal performance of antenna selection, even when the total number of signals (desired and interfering) is larger than the number of receive chains. Specifically, a single additional chain suffices to reduce the interference to any desired level. We prove that using the proposed selection, a simple linear receiver/transmitter for the uplink/downlink provides near-optimal rates. In particular, in the downlink direction, there is no need for complicated dirty paper coding; each user can use an optimal code for a single user interference-free channel. In the uplink direction, there is almost no gain in implementing joint decoding. The proposed approach is also a significant improvement both from system and computational perspectives. Simulation results demonstrating the performance of the proposed method are provided.

eess.SP↗

arXiv2019

The Interference Channel Revisited: Aligning Interference by Adjusting Receive Antenna Separation

It is shown that a receiver equipped with two antennas may null an arbitrary large number of spatial directions to any desired accuracy, while maintaining the interference-free signal-to-noise ratio, by judiciously adjusting the distance between the antenna elements. The main theoretical result builds on ergodic theory. The practicality of the scheme in moderate signal-to-noise systems is demonstrated for a scenario where each transmitter is equipped with a single antenna and each receiver has two receive chains and where the desired spacing between antenna elements is achieved by selecting the appropriate antennas from a large linear antenna array. We further extend the proposed scheme to show that interference can be eliminated also in specular multipath channels as well as multiple-input multiple-output interference channels where a single extra receiver suffices to align all interferers into a one-dimensional subspace. To demonstrate the performance of the scheme, we show significant gains for interference channels with four as well as six users, at low to moderate signal-to-noise ratios (0-20 dB). The robustness of the proposed technique to small channel estimation errors is also explored.

cs.IT↗

arXiv2019

On the Importance of Asymmetry and Monotonicity Constraints in Maximal Correlation Analysis

The maximal correlation coefficient is a well-established generalization of the Pearson correlation coefficient for measuring non-linear dependence between random variables. It is appealing from a theoretical standpoint, satisfying R\'enyi's axioms for a measure of dependence. It is also attractive from a computational point of view due to the celebrated alternating conditional expectation algorithm, allowing to compute its empirical version directly from observed data. Nevertheless, from the outset, it was recognized that the maximal correlation coefficient suffers from some fundamental deficiencies, limiting its usefulness as an indicator of estimation quality. Another well-known measure of dependence is the correlation ratio which also suffers from some drawbacks. Specifically, the maximal correlation coefficient equals one too easily whereas the correlation ratio equals zero too easily. The present work recounts some attempts that have been made in the past to alter the definition of the maximal correlation coefficient in order to overcome its weaknesses and then proceeds to suggest a natural variant of the maximal correlation coefficient as well as a modified conditional expectation algorithm to compute it. The proposed dependence measure at the same time resolves the major weakness of the correlation ratio measure and may be viewed as a bridge between these two classical measures.

cs.IT↗

arXiv2017

Achievability Performance Bounds for Integer-Forcing Source Coding

Integer-forcing source coding has been proposed as a low-complexity method for compression of distributed correlated Gaussian sources. In this scheme, each encoder quantizes its observation using the same fine lattice and reduces the result modulo a coarse lattice. Rather than directly recovering the individual quantized signals, the decoder first recovers a full-rank set of judiciously chosen integer linear combinations of the quantized signals, and then inverts it. It has been observed that the method works very well for "most" but not all source covariance matrices. The present work quantifies the measure of bad covariance matrices by studying the probability that integer-forcing source coding fails as a function of the allocated rate, %in excess of the %Berger-Tung benchmark, where the probability is with respect to a random orthonormal transformation that is applied to the sources prior to quantization. For the important case where the signals to be compressed correspond to the antenna inputs of relays in an i.i.d. Rayleigh fading environment, this orthonormal transformation can be viewed as being performed by nature. Hence, the results provide performance guarantees for distributed source coding via integer forcing in this scenario.

cs.IT↗

arXiv2017

Diversity Combining via Universal Orthogonal Space-Time Transformations

Receiver diversity combining methods play a key role in combating the detrimental effects of fadingin wireless communication and other applications. A novel diversity combining method is proposedwhere a universal, i.e., channel independent, orthogonal dimension-reducing space-time transformationis applied prior to quantization of the signals. The scheme may be considered as the counterpart ofAlamouti modulation, and more generally of orthogonal space-time block codes.

cs.IT↗

arXiv2017

Comments on Downlink Non-Orthogonal Multiple Access: Relative Gain Subject to Near Sum-Rate Optimality

Non-orthogonal access techniques have recently gained renewed interest in the context of next generation wireless networks. As the relative gain, with respect to traditionally employed orthogonal-access techniques depends on many factors, it is of interest to obtain insights by considering the simplest scenario, the two-user downlink (broadcast) channel where all nodes are equipped with a single antenna. Further, we focus on rate pairs that are in the vicinity of sum-rate optimalilty with respect to the capacity region of the broadcast channel. A simple and explicit characterization of the relative gain of non-orthogonal transmission with respect to orthogonal transmission is obtained under these conditions as an immediate consequence of the capacity regions of the two.

cs.IT↗

arXiv2017

Explicit Lower Bounds on the Outage Probability of Integer Forcing over Nrx2 Channels

The performance of integer-forcing equalization for communication over the compound multiple-input multipleoutput channel is investigated. An upper bound on the resulting outage probability as a function of the gap to capacity has been derived previously, assuming a random precoding matrix drawn from the circular unitary ensemble is applied prior to transmission. In the present work a simple and explicit lower bound on the worst-case outage probability is derived for the case of a system with two transmit antennas and two or more receive antennas, leveraging the properties of the Jacobi ensemble. The derived lower bound is also extended to random space-time precoding, and may serve as a useful benchmark for assessing the relative merits of various algebraic space-time precoding schemes. We further show that the lower bound may be adapted to the case of a $1 \times N_t$ system. As an application of this, we derive closed-form bounds for the symmetric-rate capacity of the Rayleigh fading multiple-access channel where all terminals are equipped with a single antenna. Lastly, we demonstrate that the integer-forcing equalization coupled with distributed space-time coding is able to approach these bounds.

cs.IT↗