Adapting pretrained image-based diffusion models to generate temporally consistent videos has become an impactful generative modeling research direction. Training-free noise-space manipulation has proven to be an effective technique, where the challenge is to preserve the Gaussian white noise distribution while adding in temporal consistency. Recently, Chang et al. (2024) formulated this problem using an integral noise representation with distribution-preserving guarantees, and proposed an upsampling-based algorithm to compute it. However, while their mathematical formulation is advantageous, the algorithm incurs a high computational cost. Through analyzing the limiting-case behavior of their algorithm as the upsampling resolution goes to infinity, we develop an alternative algorithm that, by gathering increments of multiple Brownian bridges, achieves their infinite-resolution accuracy while simultaneously reducing the computational cost by orders of magnitude. We prove and experimentally validate our theoretical claims, and demonstrate our method's effectiveness in real-world applications. We further show that our method can readily extend to the 3-dimensional space.

A new transimpedance amplifier (TIA) design procedure using stagger tuning with inverted transformer coils is described in this paper. A broadband TIA, realized using the proposed staggered design technique that enhances the transimpedance limit and the bandwidth while only adding small passband gain ripple, was implemented in a 0.13-μm standard CMOS process. The TIA achieves a 3-dB bandwidth of 33 GHz with a 150 fF photodiode capacitance. The TIA transimpedance gain is 43.8 dBQ with ±8 ps group-delay variation over the entire bandwidth. The circuit occupies an active area of 250 μm × 260 μm and consumes 9 mW from a 2 V supply. Despite operating with much larger photodiode capacitance, the TIA achieves the highest figure of merit, and occupies smaller area while consuming the least amount of power among previously published TIAs designed for the same data rate in similar technologies.

A CMOS wide-bandwidth first-order current-mode all-pass filter (APF) is discussed. The circuit consists of one transistor, a resistor, a grounded inductor, and a load. When used with a current mirror as the load, the current-mode filter exhibits a high output impedance, which is advantageous from an integration point of view and enables this configuration to be cascaded with current-mode circuits. The operation of the proposed circuit is experimentally validated. The APF implemented in IBM 0.13-μm CMOS was measured to have the pole-zero pair located at 8.32 GHz and to achieve a 55 ps group delay while consuming 19 mW from a 1.5-V supply. This paper experimentally demonstrates a CMOS APF that operates at multi-GHz frequencies and achieves the highest delay-bandwidth products of the published CMOS first-order APFs known to the authors.

We propose a new graph representation for ISI channels that can be used for combined equalization and decoding by linear programming (LP) or iterative message-passing (IMP) decoding algorithms. We derive this graph representation by linearizing the ML detection metric, which transforms the equalization problem into a classical decoding problem. We observe that the performance of LP and IMP decoding on this model are very similar in the uncoded case, while IMP decoding significantly outperforms LP decoding when low-density parity-check (LDPC) codes are used. In particular, in the absence of coding, for certain classes of channels, both LP and IMP algorithms always find the exact ML solution using the proposed graph representation, without complexity that is exponential in the size of the channel memory. This applies even to certain two-dimensional ISI channels. However, for some other channel impulse responses, both decoders have nondiminishing probability of failure as SNR increases. We provide analytical explanations for many of these observations. In addition, we study the error events of LP decoding in the uncoded case, and derive a measure that can be used to classify ISI channels in terms of the performance of the proposed detection scheme.

While linear programming (LP) decoding provides more flexibility for finite-length performance analysis than iterative message-passing (IMP) decoding, it is computationally more complex to implement in its original form, due to both the large size of the relaxed LP problem and the inefficiency of using general-purpose LP solvers. This paper explores ideas for fast LP decoding of low-density parity-check (LDPC) codes. By modifying the previously reported Adaptive LP decoding scheme to allow removal of unnecessary constraints, we first prove that LP decoding can be performed by solving a number of LP problems that each contains at most one linear constraint derived from each of the parity-check constraints. By exploiting this property, we study a sparse interior-point implementation for solving this sequence of linear programs. Since the most complex part of each iteration of the interior-point algorithm is the solution of a (usually ill-conditioned) system of linear equations for finding the step direction, we propose a preconditioning algorithm to facilitate solving such systems iteratively. The proposed preconditioning algorithm is similar to the encoding procedure of LDPC codes, and we demonstrate its effectiveness via both analytical methods and computer simulation results.

Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we make a first step in studying this method, and show that by starting from a simple LP problem and adaptively adding the necessary constraints, the complexity of LP decoding can be significantly reduced. In particular, we observe that with adaptive LP decoding, the sizes of the LP problems that need to be solved become practically independent of the density of the parity-check matrix. We further show that adaptively adding extra constraints, such as constraints based on redundant parity checks, can provide large gains in the performance.

We propose an approximation of maximum-likelihood detection in ISI channels based on linear programming or message passing. We convert the detection problem into a binary decoding problem, which can be easily combined with LDPC decoding. We show that, for a certain class of channels and in the absence of coding, the proposed technique provides the exact ML solution without an exponential complexity in the size of channel memory, while for some other channels, this method has a non-diminishing probability of failure as SNR increases. Some analysis is provided for the error events of the proposed technique under linear programming.

The multivariate interpolation decoding (MID) algorithm for certain Reed-Solomon codes was recently introduced by Parvaresh and Vardy. The MID algorithm attempts to list-decode up to ntauMID= n (1 -RM(M+1)/) errors, in a Reed-Solomon code of length n and rate R, using (M+1)-variate polynomial interpolation. This improves on the Guruswami-Sudan decoding radius of tauGS= 1 - radicR by a large margin, especially for high-rate codes. The problem is that successful decoding is not guaranteed: there are certain patterns of less than ntauMIDerrors which the MID algorithm fails to decode. Nevertheless, simulations show that the actual performance of the MID decoder is very close to what one would expect if all patterns of up to ntauMIDerrors were corrected. On the other hand, analysis of the failure probability for the MID algorithm is extremely difficult, and there were no analytic results so far to confirm this empirically observed behavior. In this work, we provide such analytic results: we present a detailed analysis of the probability of failure in the MID algorithm for the special case where M = 2 and the interpolation multiplicity is m = 1. In this case, the MID algorithm attempts to correct up to ntau2,1errors, where tau2,1= 1 -3radic6R2. We consider the situation where symbol values received from the channel at the erroneous positions are distributed uniformly at random (a version of the q-ary symmetric channel). We show that, with high probability, the performance of the MID algorithm is very close to the optimum in this case. Specifically, we prove that if the fraction of positions in error is at most tau2,1-O(R5/3), then the probability of failure in the MID algorithm is at most n-Omega(n). Thus the probability of failure is, indeed, negligible for large n in this case

The ability of linear programming (LP) decoding to detect failures, and its potential for improvement by the addition of new constraints, motivates the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we show that the application of such adaptive methods can significantly reduce the complexity of the LP decoding algorithm, which, in the standard formulation, is exponential in the maximum row weight of the parity-check matrix. We further show that adaptively adding new constraints, e.g. by combining parity checks, can provide large gains in LP decoder performance

Previous results suggest that the crosstalk produced by the fiber nonlinearity in a WDM system imposes a severe limit to the capacity of optical fiber channels, since the interference power increases faster than the signal power, thereby limiting the maximum achievable signal-to-interference-plus-noise ratio (SINR). We study this system in the weakly nonlinear regime as a multiple-access channel, and show that by optimally using the information from all the channels for detection, the change in the capacity region due to the nonlinear effect is minimal. On the other hand, if the receiver uses the output of only one wavelength channel, the capacity is significantly reduced due to the nonlinearity, and saturates as the interference power becomes comparable to the noise, which is consistent with earlier results. The results hold in channels with or without memory. Every point in the capacity region can be achieved without knowledge of the nonlinearity parameters at the transmitters. The structures of optimal/suboptimal receivers are briefly discussed

A single-user receiver structure for space-time coded CDMA downlink is studied in a multiuser frequency selective channel. The proposed scheme is a two dimensional decision feedback equalizer (2D-DFE), whose filters are optimized based on the MMSE criterion to cancel noise, ISI, and MUI with a reasonable complexity. By modeling the spreading codes of the interfering users as random sequences, system performance has been evaluated using the Gaussian approximation. Two models for the desired user's spreading sequence have been considered and compared. Our numerical results show that in both cases the 2D-DFE exhibits significant performance improvement and capacity enhancement over the standard space-time coded RAKE structure, especially in interference-limited conditions.

In this paper, two single-antenna receiver structures for multiuser space-time coded wideband CDMA downlink are studied in frequency selective fading channels. The first structure is the standard space-time coded RAKE receiver, while in the second structure, we have proposed a two dimensional decision feedback equalizer (2D-DFE), whose filters are optimized to jointly cancel noise, ISI, and MUI based on the MMSE criterion. For this receiver, by modeling the spreading sequences of the interfering users as random sequences, system bit error probability has been calculated using the Gaussian approximation. Our numerical results show that the 2D-DFE exhibits significant performance improvement over the space-time coded RAKE structure, especially in the interference-limited conditions.