The capacity of low-density parity-check codes under message-passing decoding

By T. Richardson, Rüdiger L. Urbanke. IEEE Transactions on Information Theory, 2001

3,268 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/f2b32222ec8955c4378fd2804757f4f8449d9241

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Citations in the corpus

Performance analysis and code optimization of low density parity-check codes on Rayleigh fading channels (2001, methodology): “With iterative message passing decoders, LDPC codes exhibit an interesting threshold effect [1][3]: if the noise level of the channel is smaller than a certain threshold, the bit error probability goes to zero as the block size goes to infinity; if the noise level is above the threshold, the probabi”
Designing Iterative Decoding Schemes with the Extrinsic Information Transfer Chart (2001, background): “In [10] the authors propose a density evolution algorithm to calculate convergence thresholds for randomly constructed irregular low–density parity–check (LDPC) codes on the additive white Gaussian noise (AWGN) chan-”
Analyzing the turbo decoder using the Gaussian approximation (2000, methodology): “Table IV shows the convergence thresholds for several LDPC codes obtained through our technique and the density evolution technique [ 10 ], respectively.”
Turbo equalization: principles and new results (2002, methodology): “The algorithms for the approximate MMSE LE’s (I) and (II) can be implemented in the frequency domain [30], which further decreases the computational load for specific systems.”
Irregular repeat accumulate codes (2000, methodology): “After defining the codes in Section 2, and observing that they have a simple linear-time encoding algorithm, in Section 3, using the powerful Richarson-Urbanke method [ 2 ], we will prove rigorously that IRA codes solve the final problem for the binary erasure channel.”
Information Theory, Inference, and Learning Algorithms (2004, methodology): “Thresholds fmax for regular low-density parity-check codes, assuming sum–product decoding algorithm, from Richardson and Urbanke (2001a). The Shannon limit for rate-1/2 codes is fmax = 0.”
Extrinsic information transfer functions: model and erasure channel properties (2004, background): “Such a code is often represented by a bipartite graph whose left vertices are called variable nodes and whose right vertices are called check nodes (see [4]).”
A new look at survey propagation and its generalizations (2004, background): “This equivalence is important because belief propagation is a message-passing algorithm—widely used and studied in various areas, including coding theory [35, 24, 44], computer vision [17, 11] and artificial intelligence [34, 45]—-for computing approximations to marginal distributions in Markov rand”
Efficient encoding of low-density parity-check codes (2001, background): “It was then shown in [ 11 ] that similar analytic tools can be used to study the asymptotic behavior of a very broad class of message-passing algorithms for a wide class of channels and it was demonstrated in [12] that LDPC codes can come extremely close to capacity on many channels.”
On the Effectiveness of OTFS for Joint Radar Parameter Estimation and Communication (2020, methodology): “…node x i the message Notice that all the variable nodes and the function nodes can be activated in alternative rounds and, in each round, all the nodes of the same type can be activated in parallel, e.g., adopting the same ﬂooding schedule used for low-density parity check (LDPC) decoding [45].”
Capacity-approaching protograph codes (2009, background): “After 1993 there have been many contributions to the design and analysis of LDPC codes; see for example [4], [5], [6], [7], [8], [9], and references therein.”
Spatially coupled ensembles universally achieve capacity under belief propagation (2012, background): “In the ﬁrst 50 years, coding theory focused on the construction of algebraic coding schemes and algorithms that were capable of exploiting the algebraic structure.”
Bit-Interleaved Coded Modulation (2008, methodology): “Fortunately, a powerful set of rather general results come to rescue [22, 60, 96, 97].”
On interleave-division multiple-access (2004, methodology): “Second, we will develop a semi-analytical technique based on the SNR density evolution technique [9], [20]-[22] to estimate the bit-error-rate (BER) performance of these algorithms.”