Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Elements of information theory
Elements of information theory
Analysis of low density codes and improved designs using irregular graphs
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Turbo codes: principles and applications
Turbo codes: principles and applications
Turbo Coding, Turbo Equalisation and Space-Time Coding for Transmission over Fading Channels
Turbo Coding, Turbo Equalisation and Space-Time Coding for Transmission over Fading Channels
Turbo Coding
Unveiling turbo codes: some results on parallel concatenated coding schemes
IEEE Transactions on Information Theory
Iterative decoding of binary block and convolutional codes
IEEE Transactions on Information Theory
Cross-entropy and iterative decoding
IEEE Transactions on Information Theory
Good error-correcting codes based on very sparse matrices
IEEE Transactions on Information Theory
The geometry of turbo-decoding dynamics
IEEE Transactions on Information Theory
Factor graphs and the sum-product algorithm
IEEE Transactions on Information Theory
Analyzing the turbo decoder using the Gaussian approximation
IEEE Transactions on Information Theory
The turbo decoding algorithm and its phase trajectories
IEEE Transactions on Information Theory
Low-density parity-check codes based on finite geometries: a rediscovery and new results
IEEE Transactions on Information Theory
Information geometry of turbo and low-density parity-check codes
IEEE Transactions on Information Theory
Turbo decoding as an instance of Pearl's “belief propagation” algorithm
IEEE Journal on Selected Areas in Communications
Iterative decoding of compound codes by probability propagation in graphical models
IEEE Journal on Selected Areas in Communications
Analysis, design, and iterative decoding of double serially concatenated codes with interleavers
IEEE Journal on Selected Areas in Communications
Iterative turbo decoder analysis based on density evolution
IEEE Journal on Selected Areas in Communications
Turbo equalization: adaptive equalization and channel decoding jointly optimized
IEEE Journal on Selected Areas in Communications
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The turbo decoding algorithm of a decade ago constituted a milestone in error-correction coding for digital communications, and has inspired extensions to generalized receiver topologies, including turbo equalization, turbo synchronization, and turbo CDMA, among others. Despite an accrued understanding of iterative decoding over the years, the "turbo principle" remains elusive to master analytically, thereby inciting interest from researchers outside the communications domain. In this spirit, we develop a tutorial presentation of iterative decoding for parallel and serial concatenated codes, in terms hopefully accessible to a broader audience. We motivate iterative decoding as a computationally tractable attempt to approach maximum-likelihood decoding, and characterize fixed points in terms of a "consensus" property between constituent decoders. We review how the decoding algorithm for both parallel and serial concatenated codes coincides with an alternating projection algorithm, which allows one to identify conditions under which the algorithm indeed converges to a maximum-likelihood solution, in terms of particular likelihood functions factoring into the product of their marginals. The presentation emphasizes a common framework applicable to both parallel and serial concatenated codes.