Publications by Rüdiger Urbanke

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We introduce a technique for the analysis of general spatially coupled systems that are governed by scalar recursions. Such systems can be expressed in variational form in terms of a potential function. We show, under mild conditions, that the potential fu ...

Cryptographic key exchange protocols traditionally rely on computational conjectures such as the hardness of prime factorization(1) to provide security against eavesdropping attacks. Remarkably, quantum key distribution protocols such as the Bennett-Brassa ...

We consider the primitive relay channel, where the source sends a message to the relay and to the destination, and the relay helps the communication by transmitting an additional message to the destination via a separate channel. Two well-known coding tech ...

The placement of replicas across storage nodes in a replication-based storage system is known to affect rebuild times and therefore system reliability. Earlier work has shown that, for a replication factor of two, the reliability is essentially unaffected ...

Polarization codes were recently introduced by Ar\i kan. They are explicit code constructions which achieve the capacity of arbitrary symmetric binary-input discrete memoryless channels (and even extensions thereof) under a low complexity successive decodi ...

We consider a collection of Curie-Weiss (CW) spin systems, possibly with a random field, each of which is placed along the positions of a one-dimensional chain. The CW systems are coupled together by a Kac-type interaction in the longitudinal direction of ...

In this paper, we consider the problem of decoding Reed-Muller (RM) codes in binary erasure channel. We propose a novel algorithm, which exploits several techniques, such as list recursive (successive cancellation) decoding based on Plotkin decomposition, ...

We explore the relationship between polar and RM codes and we describe a coding scheme which improves upon the performance of the standard polar code at practical block lengths. Our starting point is the experimental observation that RM codes have a smalle ...

We consider communication over binary-input memoryless output-symmetric channels using low-density parity-check codes and message-passing decoding. The asymptotic (in the length) performance of such a combination for a fixed number of iterations is given b ...

Polar codes were recently introduced by Arikan. They achieve the capacity of arbitrary symmetric binary-input discrete memoryless channels under a low complexity successive cancellation decoding strategy. The original polar code construction is closely rel ...

For any prime power q, Mori and Tanaka introduced a family of q-ary polar codes based on the q x q Reed-Solomon polarization kernels. For transmission over a q-ary erasure channel, they also derived a closed-form recursion for the erasure probability of ea ...

Mobile users are increasing fast in numbers, new types of services and applications become available, and new mobile systems (e.g., for intelligent transportation) emerge. Meanwhile, the need for securing communication in such large scale, highly dynamic systems grows. But the organizational complexity and operational costs make traditional security solutions hard to deploy at the rate new mobile applications are rolled out. The challenge that lies ahead is how to provide versatile security compatible with

We consider the problem of determining the tradeoff between the rate and the block-length of polar codes for a given block error probability when we use the successive cancellation decoder. We take the sum of the Bhattacharyya parameters as a proxy for the ...

Convolutional LDPC ensembles, introduced by Felstrom and Zigangirov, have excellent thresholds and these thresholds are rapidly increasing as a function of the average degree. Several variations on the basic theme have been proposed to date, all of which s ...

Reed-Muller (RM) codes have undergone significant analytical advancements over the past decade, particularly for binary memoryless symmetric (BMS) channels. We extend the scope of RM codes development and analysis to multiple-access channels (MACs) and quantum Pauli channels, leveraging a unified approach. Specifically, we first derive the achievable rate region for RM codes on so-called Q-MACs, a class of MACs with additive correlated noise. This is achieved via a generalization of the bending and boosting

We consider communication over binary-input memoryless output-symmetric channels using low-density parity-check codes under MP decoding. The asymptotic (in the length) performance of such a combination for a fixed number of iterations is given by density e ...

We provide upper and lower bounds on the escape rate of the Bhattacharyya process corresponding to polar codes where transmission takes place over the the binary erasure channel. More precisely, we bound the exponent of the number of sub-channels whose Bha ...

Good quantum error-correcting codes that fulfill practical considerations, such as simple encoding circuits and efficient decoders, are essential for functional quantum information processing systems. Quantum polar codes satisfy some of these requirements but lack certain critical features, thereby hindering their widespread use. Existing constructions either require entanglement assistance to produce valid quantum codes, suffer from poor finite-size performance, or fail to tailor polar codes to the underly

The class of bilinear time-frequency representations (BTFR's) that are invariant (or covariant) to time shifts, frequency shifts, and time-frequency scalings. This shift-scale invariant class is the intersection of the classical shift-invariant (Cohen) class and the recently defined affine class. The mathematical description of shift-scale invariant BTFR's is in terms of a 1-D kernel and is thus particularly simple. The paper concentrates on the time-frequency localization properties of shift-scale invarian

There are two main attack models considered in the adversarial robustness literature: black-box and white-box. We consider these threat models as two ends of a fine-grained spectrum, indexed by the number of queries the adversary can ask. Using this point ...

Rüdiger Urbanke

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Displacement Convexity in Spatially Coupled Scalar Recursions

Experimental quantum key distribution certified by Bell's theorem

A New Coding Paradigm for the Primitive Relay Channel

Reliability of clustered vs. declustered replica placement in data storage systems

Polar Codes: Characterization of Exponent, Bounds, and Constructions

Chains of mean-field models

Permutation-based Decoding of Reed-Muller Codes in Binary Erasure Channel

From Polar to Reed-Muller Codes: a Technique to Improve the Finite-Length Performance

Exchange of Limits: Why Iterative Decoding Works

Polar Codes: Characterization of Exponent, Bounds, and Constructions

Near-Optimal Finite-Length Scaling for Polar Codes Over Large Alphabets

A Mobile World of Security

Universal bounds on the scaling behavior of polar codes

Threshold saturation via spatial coupling: Why convolutional LDPC ensembles perform so well over the BEC

Reed-Muller Codes for Quantum Pauli and Multiple Access Channels

Exchange of Limits: Why Iterative Decoding Works

On the scaling of polar codes: II. The behavior of un-polarized channels

Interpolation of Quantum Polar Codes and Quantum Reed-Muller Codes

Bilinear time-frequency representation of signals: The shift-scale invariant class

Query Complexity of Adversarial Attacks