# Hongchao Zhou's research while affiliated with California Institute of Technology and other places

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## Publications (23)

This work studies the Stopping-Set Elimination Problem, namely, given a stopping set, how to remove the fewest erasures so that the remaining erasures can be decoded by belief propagation in k iterations (including k =∞). The NP-hardness of the problem is proven. An approximation algorithm is presented for k = 1. And efficient exact algorithms are...

A memory device having a plurality of cells, each of which stores a value, where the values of the cells are mapped to discrete levels and the discrete levels represent data, is programmed by determining a maximum number of cell levels in the memory device, and determining the set of values that are associated with each of the cell levels. The maxi...

Stochastic switching circuits are relay circuits that
consist of stochastic switches called pswitches. The study of stochastic switching circuits has widespread applications in many fields of computer science, neuroscience, and biochemistry. In this paper, we discuss several properties of stochastic switching circuits, including robustness, express...

Generating random bits from a source of biased coins (the biased is unknown) is a classical question that was originally studied by von Neumann. There are a number of known algorithms that have asymptotically optimal information efficiency, namely, the expected number of generated random bits per input bit is asymptotically close to the entropy of...

Information-efficient approaches for extracting randomness from imperfect sources have been extensively studied, but simpler and faster ones are required in the high-speed applications of random number generation. In this paper, we focus on linear constructions, namely, applying linear transformation for randomness extraction. We show that linear t...

The construction of asymmetric error correcting codes is a topic that was
studied extensively, however, the existing approach for code construction
assumes that every codeword should tolerate $t$ asymmetric errors. Our main
observation is that in contrast to symmetric errors, asymmetric errors are
content dependent. For example, in Z-channels, the...

In this paper, we present a universal scheme for transforming an arbitrary
algorithm for biased 2-face coins to generate random bits from the general
source of an m-sided die, hence enabling the application of existing algorithms
to general sources. In addition, we study approaches of efficiently generating
a prescribed number of random bits from a...

A stochastic flow network is a directed graph with incoming edges (inputs) and outgoing edges (outputs), tokens enter through the input edges, travel stochastically in the network and can exit the network through the output edges. Each node in the network is a splitter, namely, a token can enter a node through an incoming edge and exit on one of th...

We study the problem of extracting a prescribed number of random bits by
reading the smallest possible number of symbols from non-ideal stochastic
processes. The related interval algorithm proposed by Han and Hoshi has
asymptotically optimal performance; however, it assumes that the distribution
of the input stochastic process is known. The motivat...

This paper presents a practical writing/reading scheme in nonvolatile
memories, called balanced modulation, for minimizing the asymmetric component
of errors. The main idea is to encode data using a balanced error-correcting
code. When reading information from a block, it adjusts the reading threshold
such that the resulting word is also balanced o...

Information-efficient approaches for extracting randomness from imperfect
sources have been extensively studied, but simpler and faster ones are required
in the high-speed applications of random number generation. In this paper, we
focus on linear constructions, namely, applying linear transformation for
randomness extraction. We show that linear t...

We study the problem of extracting a prescribed number of random bits by reading the smallest possible number of symbols from non-ideal stochastic processes. The related
interval algorithm proposed by Han and Hoshi has asymptotically optimal performance; however, it assumes that the distribution of the input stochastic process is known. The motivat...

Phase-change memory (PCM) is an emerging nonvolatile memory technology that promises very high performance.
It currently uses discrete cell levels to represent data, controlled
by a single amorphous/crystalline domain in a cell. To improve
data density, more levels per cell are needed. There exist a number of challenges, including cell programming...

Predetermined fixed thresholds are commonly used in nonvolatile memories for reading binary sequences, but they usually result in significant asymmetric errors after a long duration, due to voltage or resistance drift. This motivates us to construct error-correcting schemes with dynamic reading thresholds, so that the asymmetric component of errors...

Linear transformations have many applications in information theory, like data compression and error-correcting codes design. In this paper, we study the power of linear transformations in randomness extraction, namely linear extractors, as another important application. Comparing to most existing methods for randomness extraction, linear extractor...

For many nonvolatile memories, - including flash memories, phase-change memories, etc., - maximizing the storage capacity is a key challenge. The existing method is to use multilevel cells (MLC) of more and more levels. The number of levels supported by MLC is seriously constrained by the worst-case performance of cell-programming noise and cell he...

Schemes for probabilistic computation can exploit
physical sources to generate random values in the form of
bit streams. Generally, each source has a fixed bias and so
provides bits with a specific probability of being one. If many different probability values are required, it can be expensive to generate all of these directly from physical sources...

Codes that correct asymmetric errors have important applications in storage systems, including optical disks and Read Only Memories. The construction of asymmetric error correcting codes is a topic that was studied extensively, however, the existing approach for code construction assumes that every codeword could sustain t asymmetric errors. Our ma...

We propose variable-level cell, a new data representation scheme, for nonvolatile memories (including flash memories, phase-change memories, etc.). We derive its storage capacity, and analyze its performance on rewriting data.

The problem of random number generation from an uncorrelated random source (of unknown probability distribution) dates back to von Neumann's 1951 work. Elias (1972) generalized von Neumann's scheme and showed how to achieve optimal efficiency in unbiased random bits generation. Hence, a natural question is what if the sources are correlated? Both E...

The problem of random number generation from an uncorrelated random source (of unknown probability distribution) dates back to von Neumann's 1951 work. Elias (1972) generalized von Neumann's scheme and showed how to achieve optimal efficiency in unbiased random bits generation. Hence, a natural question is what if the sources are correlated? Both E...

Stochastic switching circuits are relay circuits that consist of stochastic switches (that we call pswitches). We study the expressive power of these circuits; in particular, we address the following basic question: given an arbitrary integer q, and a pswitch set {1/q, 2/q, ..., q-1/q}, can we realize any rational probability with denominator q^n (...

Many natural systems, including chemical and biological systems, can be modeled using stochastic switching circuits. These circuits consist of stochastic switches, called pswitches, which operate with a fixed probability of being open or closed. We study the effect caused by introducing an error of size. to each pswitch in a stochastic circuit. We...

## Citations

... In recent works (including results from the authors of this work), machine learning and algorithmic techniques have been used to exploit NR to correct errors in data [21], [22], [23], [27], [33], [48], [49], [53], [54]. This work studies the Representation-Oblivious scheme for the first time, and also presents new theoretical analysis for the Representation-Aware scheme. ...

... Furthermore, the authors also investigated new approaches for efficiently generating a prescribed number of random bits from an arbitrary biased coin. In [21] the problem of extracting a prescribed number of random bits was addressed by reading the smallest possible number of symbols from a source whose statistical behaviour is not fully specified. The related interval algorithm proposed by Han and Hoshi [9] has asymptotically optimal performance, however it assumes that the distribution of the input stochastic process is known. ...

... Although some asymmetric codes have been proposed (e.g. [15], [24], [37]), channel inputs are equiprobable for most practical codes. The mutual information between the input and the output is then given by ...

Reference: Adaptive read thresholds for NAND flash

... The detector resilience to unknown mismatch by drift can be improved in various ways, for example, by employing coding techniques. Balanced codes [6,7,8,9] and composition check codes [10,11], in conjunction with Slepian's optimal detection [12] offer excellent resilience in the face of channel mismatch on a block of symbols basis. These coding and signal processing techniques are often considered too expensive in terms of code redundancy and hardware, in particular when high-speed applications are considered. ...

... Note that this model also includes the so-called Z-channel where q = 0 such that only 1 → 0 errors occur. The Z-channel captures the fact that in applications q is often significantly smaller than p [14,53]. ...

... Doing so can introduce additional problems [56]. However, von Neumann's algorithm has been generalized to provide conditioning and randomness extraction for biased, correlated sequences [57]. We note that hashing [58] is a powerful operation for extracting maximal-entropy bits from partially-unpredictable ones [59]. ...

... The Zhou-Bruck algorithm was introduced in [2] and later analysed in [3]. It allows the safe application of the Peres [14] algorithm to a biased dice. ...

... Our approach is a systematic implementation of probabilistic switching circuits, using DNA strand displacement reactions. Unlike the theory of the original switching circuits proposed by Shannon (20), wherein signals arriving at the input terminal of a deterministic switch always reach the output terminal if the switch is ON and always stop flowing if the switch is OFF, the theory of probabilistic switching circuits allows the signals to flow through a switch with a specified probability (21,22). Exploiting the intrinsic stochasticity of molecular interactions, in our implementation, each input DNA signal is designed to bind to a DNA switch and release an output signal with a one-half probability. ...

Reference: Probabilistic switching circuits in DNA

... The statement proved by R. L. Skhirtladze in [15] is written in our notation as W {∧,∨, } (p) = [0, 1] for p ∈ (0, 1). This was generalized by the author in [16] to 1] was also later independently proved by H. Zhou, P. Loh and J. Bruck in [17]. The following statement is a direct consequence of these observations. ...

... Even in current state-of-the-art 19nm NAND, noise is significant towards the end of life of the drive. One way to recover host data in the presence of noise is to use advanced signal processing algorithms [1], [2], [3], [4], but excessive re-reads and post-read signal processing could jeopardize the advantages brought by this technology. ...

Reference: Adaptive Read Thresholds for NAND Flash