Jonathan S. Yedidia

Rateless codes on noisy channels

This paper studies the performance of two classes of rateless codes (LTand Raptor codes) on noisy channels such as the BSC and the AWGNC. We find that Raptor codes outperform LT codes, and have good performance on a wide variety of noisy channels.

Performance of Fountain Codes in Collaborative Relay Networks

Cooperative communications, where parallel relays forward information to a destination node, can greatly improve the energy efficiency and latency in ad-hoc networks. However, current networks do not fully exploit its potential as they only use traditional energy-accumulation, which is often used in conjunction with repetition coding or cooperative space-time codes. In this paper, we show that the concept of mutual- information-accumulation can be realized with the help of fountain codes, and leads to a lower energy expenditure and a lower transmission time than energy accumulation. We then provide an analysis of the performance of mutual information accumulation in relay networks with N relay nodes. We first analyze the quasi-synchronuous scenario where the source stops transmitting and the relay nodes start transmitting after L relay nodes have successfully decoded the source data. We show that an optimum L exists, and is typically on the order of 3 or 4. We also give closed-form equations for the energy savings that can be achieved by the use of mutual-information-accumulation at the receiver. We then analyze and provide bounds for an alternate scenario where each relay node starts its transmission to the destination as soon as it has decoded the source data, independent of the state of the other relay nodes. This approach further reduces the transmission time, because the transmission by the relay nodes helps the other relay nodes that are still receiving.

Tangible interaction + graphical interpretation: a new approach to 3D modeling

Construction toys are a superb medium for geometric models. We argue that such toys, suitably instrumented or sensed, could be the inspiration for a new generation of easy-to-use, tangible modeling systems—especially if the tangible modeling is combined with graphical-interpretation techniques for enhancing nascent models automatically. The three key technologies needed to realize this idea are embedded computation, vision-based acquisition, and graphical interpretation. We sample these technologies in the context of two novel modeling systems: physical building blocks that self-describe, interpret, and decorate the structures into which they are assembled; and a system for scanning, interpreting, and animating clay figures.

Using Distributed Source Coding to Secure Fingerprint Biometrics

We describe a method to encode fingerprint biometrics securely for use, e.g., in encryption or access control. The system is secure because the stored data does not suffice to recreate the original fingerprint biometric. Therefore, a breach in database security does not lead to the loss of biometric data. At the same time the stored data suffices to validate a probe fingerprint. Our approach is based on the use of distributed source coding techniques implemented with graph-based codes. We present a statistical model of the relationship between the enrollment biometric and the (noisy) biometric measurement taking during authentication. We describe how to validate or reject a candidate biometric probe given the probe and the stored encoded data. We report the effectiveness of our method as tested on a database consisting of 579 data sets, each containing roughly 15 measurements of a single finger. We thereby demonstrate a working secure biometric system for fingerprints.

Feature extraction for a Slepian-Wolf biometric system using LDPC codes

We present an information-theoretically secure biometric storage system using graph-based error correcting codes in a Slepian-Wolf coding framework. Our architecture is motivated by the noisy nature of personal biometrics and the requirement to provide security without storing the true biometric at the device. The principal difficulty is that real biometric signals, such as fingerprints, do not obey the i.i.d. or ergodic statistics that are required for the underlying typicality properties in the Slepian-Wolf coding framework. To meet this challenge, we propose to transform the biometric data into binary feature vectors that are i.i.d. Bernoulli(0.5), independent across different users, and related within the same user through a BSC-p channel with small p< 0.5. Since this is a standard channel model for LDPC codes, the feature vectors are now suitable for LDPC syndrome coding. The syndromes serve as secure biometrics for access control. Experiments on a fingerprint database demonstrate that the system is information-theoretically secure, and achieves very low false accept rates and low false reject rates.

Construction of high-girth QC-LDPC codes

We describe a hill-climbing algorithm that constructs high-girth quasi-cyclic low-density parity check (QC-LDPC) codes. Given a desired girth, the algorithm can find QC-LDPC codes of shorter block-length in much less time compared with the previously proposed ldquoguess-and-testrdquo algorithm. An analysis is also provided to explain when guess-and-test would be expected to perform well or badly.

Building virtual structures with physical blocks

We describe a tangible interface for building virtual structures using physical building blocks. We demonstrate two applications of our system. In one version, the blocks are used to construct geometric models of objects and structures for a popular game, Quake II™. In another version, buildings created with our blocks are rendered in different styles, using intelligent decoration of the building model.

Cooperative relay networks using fountain codes

We investigate a cooperative communications scheme with N parallel relays, where both the transmissions from the source to the relays and from the relays to the destination use fountain codes. Receivers for fountain codes can accumulate mutual information, while traditional energy collection methods, such as repetition or cooperative space-time codes, only accumulate energy. As a consequence, using fountain codes can reduce the total energy required for transmitting data from the source to the destination. We first analyze the scenario where the source stops transmitting and the relay nodes start transmitting after L relay nodes have successfully decoded the source data. We optimize L, and also give closed-form equations for the energy savings that can be achieved by the use of mutual-information-collection at the receiver instead of traditional energy-collection methods. We then analyze an alternate scenario where each relay node starts its transmission to the destination as soon as it has decoded the source data, and helps the other relay nodes that are still in reception mode. Doing so further reduces the total transmission time and energy consumption.

Hierarchical and High-Girth QC LDPC Codes

We present an approach to designing capacity-approaching high-girth low-density parity-check (LDPC) codes that are friendly to hardware implementation, and compatible with some desired input code structure defined using a protograph. The approach is based on a mapping of any class of codes defined using a protograph into a family of hierarchical quasi-cyclic (HQC) LDPC codes. Whereas the parity check matrices of standard quasi-cyclic (QC) LDPC codes are composed of circulant submatrices, those of HQC LDPC codes are composed of a hierarchy of circulant submatrices that are, in turn, constructed from circulant submatrices, and so on, through some number of levels. Next, we present a girth-maximizing algorithm that optimizes the degrees of freedom within the family of codes to yield a high-girth HQC LDPC code, subject to bounds imposed by the fact that HQC codes are still quasi-cyclic. Finally, we discuss how certain characteristics of a code protograph will lead to inevitable short cycles and show that these short cycles can be eliminated using a “squashing” procedure that results in a high-girth QC LDPC code, although not a hierarchical one. We illustrate our approach with three design examples of QC LDPC codes-two girth-10 codes of rates 1/3 and 0.45 and one girth-8 code of rate 0.7-all of which are obtained from protographs of one-sided spatially coupled codes.

Distributed source coding using serially-concatenated-accumulate codes

We describe a practical method for distributed compression of q-ary sources using multi-level serially concatenated-accumulate codes. Our approach works well at high compression rates, and allows for graceful and incremental rate-adaptivity. Simulations show that the compression efficiency is near the information-theoretic limits for correlations between sources that obey a Gaussian or Laplacian distribution.