11 research outputs found
New constructions of WOM codes using the Wozencraft ensemble
In this paper we give several new constructions of WOM codes. The novelty in
our constructions is the use of the so called Wozencraft ensemble of linear
codes. Specifically, we obtain the following results.
We give an explicit construction of a two-write Write-Once-Memory (WOM for
short) code that approaches capacity, over the binary alphabet. More formally,
for every \epsilon>0, 0<p<1 and n =(1/\epsilon)^{O(1/p\epsilon)} we give a
construction of a two-write WOM code of length n and capacity
H(p)+1-p-\epsilon. Since the capacity of a two-write WOM code is max_p
(H(p)+1-p), we get a code that is \epsilon-close to capacity. Furthermore,
encoding and decoding can be done in time O(n^2.poly(log n)) and time
O(n.poly(log n)), respectively, and in logarithmic space.
We obtain a new encoding scheme for 3-write WOM codes over the binary
alphabet. Our scheme achieves rate 1.809-\epsilon, when the block length is
exp(1/\epsilon). This gives a better rate than what could be achieved using
previous techniques.
We highlight a connection to linear seeded extractors for bit-fixing sources.
In particular we show that obtaining such an extractor with seed length O(log
n) can lead to improved parameters for 2-write WOM codes. We then give an
application of existing constructions of extractors to the problem of designing
encoding schemes for memory with defects.Comment: 19 page
Using Short Synchronous WOM Codes to Make WOM Codes Decodable
In the framework of write-once memory (WOM) codes, it is important to
distinguish between codes that can be decoded directly and those that require
that the decoder knows the current generation to successfully decode the state
of the memory. A widely used approach to construct WOM codes is to design first
nondecodable codes that approach the boundaries of the capacity region, and
then make them decodable by appending additional cells that store the current
generation, at an expense of a rate loss. In this paper, we propose an
alternative method to make nondecodable WOM codes decodable by appending cells
that also store some additional data. The key idea is to append to the original
(nondecodable) code a short synchronous WOM code and write generations of the
original code and of the synchronous code simultaneously. We consider both the
binary and the nonbinary case. Furthermore, we propose a construction of
synchronous WOM codes, which are then used to make nondecodable codes
decodable. For short-to-moderate block lengths, the proposed method
significantly reduces the rate loss as compared to the standard method.Comment: To appear in IEEE Transactions on Communications. The material in
this paper was presented in part at the 2012 IEEE International Symposium on
Information Theory, Cambridge, MA, July 201
SoK: Plausibly Deniable Storage
Data privacy is critical in instilling trust and empowering the societal pacts of modern technology-driven democracies. Unfortunately, it is under continuous attack by overreaching or outright oppressive governments, including some of the world\u27s oldest democracies. Increasingly-intrusive anti-encryption laws severely limit the ability of standard encryption to protect privacy. New defense mechanisms are needed.
Plausible deniability (PD) is a powerful property, enabling users to hide the existence of sensitive information in a system under direct inspection by adversaries. Popular encrypted storage systems such as TrueCrypt and other research efforts have attempted to also provide plausible deniability. Unfortunately, these efforts have often operated under less well-defined assumptions and adversarial models. Careful analyses often uncover not only high overheads but also outright security compromise. Further, our understanding of adversaries, the underlying storage technologies, as well as the available plausible deniable solutions have evolved dramatically in the past two decades. The main goal of this work is to systematize this knowledge. It aims to:
- identify key PD properties, requirements, and approaches;
- present a direly-needed unified framework for evaluating security and performance;
- explore the challenges arising from the critical interplay between PD and modern system layered stacks;
- propose a new trace-oriented PD paradigm, able to decouple security guarantees from the underlying systems and thus ensure a higher level of flexibility and security independent of the technology stack.
This work is meant also as a trusted guide for system and security practitioners around the major challenges in understanding, designing, and implementing plausible deniability into new or existing systems
Capacity-Achieving Coding Mechanisms: Spatial Coupling and Group Symmetries
The broad theme of this work is in constructing optimal transmission mechanisms for a wide variety of communication systems. In particular, this dissertation provides a proof of threshold saturation for spatially-coupled codes, low-complexity capacity-achieving coding schemes for side-information problems, a proof that Reed-Muller and primitive narrow-sense BCH codes achieve capacity on erasure channels, and a mathematical framework to design delay sensitive communication systems.
Spatially-coupled codes are a class of codes on graphs that are shown to achieve capacity universally over binary symmetric memoryless channels (BMS) under belief-propagation decoder. The underlying phenomenon behind spatial coupling, known as âthreshold saturation via spatial couplingâ, turns out to be general and this technique has been applied to a wide variety of systems. In this work, a proof of the threshold saturation phenomenon is provided for irregular low-density parity-check (LDPC) and low-density generator-matrix (LDGM) ensembles on BMS channels. This proof is far simpler than published alternative proofs and it remains as the only technique to handle irregular and LDGM codes. Also, low-complexity capacity-achieving codes are constructed for three coding problems via spatial coupling: 1) rate distortion with side-information, 2) channel coding with side-information, and 3) write-once memory system. All these schemes are based on spatially coupling compound LDGM/LDPC ensembles.
Reed-Muller and Bose-Chaudhuri-Hocquengham (BCH) are well-known algebraic codes introduced more than 50 years ago. While these codes are studied extensively in the literature it wasnât known whether these codes achieve capacity. This work introduces a technique to show that Reed-Muller and primitive narrow-sense BCH codes achieve capacity on erasure channels under maximum a posteriori (MAP) decoding. Instead of relying on the weight enumerators or other precise details of these codes, this technique requires that these codes have highly symmetric permutation groups. In fact, any sequence of linear codes with increasing blocklengths whose rates converge to a number between 0 and 1, and whose permutation groups are doubly transitive achieve capacity on erasure channels under bit-MAP decoding. This pro-vides a rare example in information theory where symmetry alone is suïŹcient to achieve capacity.
While the channel capacity provides a useful benchmark for practical design, communication systems of the day also demand small latency and other link layer metrics. Such delay sensitive communication systems are studied in this work, where a mathematical framework is developed to provide insights into the optimal design of these systems
Eastern Illinois University Undergraduate Catalog 2003 - 2004
This Catalog lists available courses for the 2003-2004 term.https://thekeep.eiu.edu/eiu_catalogs/1017/thumbnail.jp
Eastern Illinois University Undergraduate Catalog 2003 - 2004
This Catalog lists available courses for the 2003-2004 term.https://thekeep.eiu.edu/eiu_catalogs/1017/thumbnail.jp
Eastern Illinois University Undergraduate Catalog 1993 - 1994
This Catalog lists available courses for the 1993-1994 term.https://thekeep.eiu.edu/eiu_catalogs/1031/thumbnail.jp