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- Thomas J. Richardson, Rüdiger L. Urbanke
- IEEE Trans. Information Theory
- 2001

In this paper, we present a general method for determining the capacity of low-density parity-check (LDPC) codes under message-passing decoding when used over any binary-input memoryless channel with discrete or continuous output alphabets. Transmitting at rates below this capacity, a randomly chosen element of the given ensemble will achieve an arbitrarily… (More)

- Thomas J. Richardson, Amin Shokrollahi, Rüdiger L. Urbanke
- IEEE Trans. Information Theory
- 2001

We design low-density parity-check (LDPC) codes that perform at rates extremely close to the Shannon capacity. The codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides. Our theoretical analysis of the codes is based on [1]. Assuming that the underlying communication channel is symmetric, we prove that… (More)

Iterative techniques have revolutionized the theory and practice of coding and have been adopted in themajority of next-generation communications standards.Modern Coding Theory summarizes the state of the art in iterative coding, with particular emphasis on the underlying theory. Starting with Gallager’s original ensemble of low-density parity-check codes… (More)

- Sae-Young Chung, Thomas J. Richardson, Rüdiger L. Urbanke
- IEEE Trans. Information Theory
- 2001

Density evolution is an algorithm for computing the capacity of low-density parity-check (LDPC) codes under messagepassing decoding. For memoryless binary-input continuous-output additive white Gaussian noise (AWGN) channels and sum-product decoders, we use a Gaussian approximation for message densities under density evolution to simplify the analysis of… (More)

- Shrinivas Kudekar, Thomas J. Richardson, Rüdiger L. Urbanke
- IEEE Transactions on Information Theory
- 2010

Convolutional low-density parity-check (LDPC) ensembles, introduced by Felström and Zigangirov, have excellent thresholds and these thresholds are rapidly increasing functions of the average degree. Several variations on the basic theme have been proposed to date, all of which share the good performance characteristics of convolutional LDPC… (More)

- Thomas J. Richardson, Rüdiger L. Urbanke
- IEEE Trans. Information Theory
- 2001

Low-density parity-check (LDPC) codes can be considered serious competitors to turbo codes in terms of performance and complexity and they are based on a similar philosophy: constrained random code ensembles and iterative decoding algorithms. In this paper, we consider the encoding problem for LDPC codes. More generally, we consider the encoding problem for… (More)

- Changyan Di, David Proietti, Emre Telatar, Thomas J. Richardson, Rüdiger L. Urbanke
- IEEE Trans. Information Theory
- 2002

In this paper, we are concerned with the finite-length analysis of low-density parity-check (LDPC) codes when used over the binary erasure channel (BEC). The main result is an expression for the exact average bit and block erasure probability for a given regular ensemble of LDPC codes when decoded iteratively. We also give expressions for upper bounds on… (More)

- Bertrand M. Hochwald, Thomas L. Marzetta, Thomas J. Richardson, Wim Sweldens, Rüdiger L. Urbanke
- IEEE Trans. Information Theory
- 2000

We propose a systematic method for creating constellations of unitary space–time signals for multiple-antenna communication links. Unitary space–time signals, which are orthonormal in time across the antennas, have been shown to be well-tailored to a Rayleigh fading channel where neither the transmitter nor the receiver knows the fading coefficients. The… (More)

- Sae-Young Chung, G. David Forney, Thomas J. Richardson, Rüdiger L. Urbanke
- IEEE Communications Letters
- 2001

We develop improved algorithms to construct good low-density parity-check codes that approach the Shannon limit very closely. For rate 1/2, the best code found has a threshold within 0.0045 dB of the Shannon limit of the binary-input additive white Gaussian noise channel. Simulation results with a somewhat simpler code show that we can achieve within 0.04… (More)

- Abdelaziz Amraoui, Andrea Montanari, Thomas J. Richardson, Rüdiger L. Urbanke
- IEEE Transactions on Information Theory
- 2009

We investigate the behavior of iteratively decoded low-density parity-check (LDPC) codes over the binary erasure channel in the so-called ldquowaterfall region.rdquo We show that the performance curves in this region follow a simple scaling law. We conjecture that essentially the same scaling behavior applies in a much more general setting and we provide… (More)