The iterative turbo decoding algorithm has fixed points

Duan, Long; Rimoldi, Bixio

doi:10.1109/18.959276

Cited by 15 publications

(4 citation statements)

References 11 publications

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“…At a low SNR, the opposite is true although the estimation errors are not as serious. If the turbo decoding is terminated after iteration , the BER can be estimated by BER (7) where and are the mean and variance of the systematic part of , respectively, and denote, respectively, the and from iteration , and is the CDF for the Gaussian distribution with zero mean and unity variance.…”

Section: Gaussian Approximations For Turbo Decodingmentioning

confidence: 99%

“…Using geometrical analysis, [4] is able to reveal a number of dynamic behaviors of turbo decoding, including the existence of fixed points and some conditions for the uniqueness and stability of fixed points. The existence of fixed points is also proved in [7] using a somewhat simpler but also deterministic approach. However, the existence of a fixed point does not imply anything about the convergence of turbo decoding, as the system may exhibit multiple fixed points or even limit cycles.…”

Section: Introductionmentioning

confidence: 99%

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Stochastic Analysis of Turbo Decoding

2005

IEEE Trans. Inform. Theory

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This paper proposes a stochastic framework for dynamic modeling and analysis of turbo decoding. By modeling the input and output signals of a turbo decoder as random processes, we prove that these signals become ergodic when the block size of the code becomes very large. This basic result allows us to easily model and compute the statistics of the signals in a turbo decoder. Using the ergodicity result and the fact that a sum of lognormal distributions is well approximated using a lognormal distribution, we show that the input-output signals in a turbo decoder, when expressed using log-likelihood ratios (LLRs), are well approximated using Gaussian distributions. Combining the two results above, we can model a turbo decoder using two input parameters and two output parameters (corresponding to the means and variances of the input and output signals). Using this model, we are able to reveal the whole dynamics of a decoding process. We have discovered that a typical decoding process is much more intricate than previously known, involving two regions of attraction, several fixed points, and a stable equilibrium manifold at which all decoding trajectories converge. Some applications of the stochastic framework are also discussed, including a fast decoding scheme. Index Terms-Iterative decoding, maximum a posteriori probability (MAP) decoding, soft decoding, turbo codes, turbo decoding.

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Section: Gaussian Approximations For Turbo Decodingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stochastic Analysis of Turbo Decoding

2005

IEEE Trans. Inform. Theory

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“…By iteratively solving the set of fixed point equations, the algorithm converges to one fixed point. In general there exists not necessarily only one fixed point, i.e., one solution to the set of fixed point equations, see [27] for a corresponding discussion on Turbo decoding. However, one solution of this set of fixed point equations corresponds to the solution of the genuine optimization problem in (5.5).…”

Section: Principle Of Iterative Code-aided Synchronized Detectionmentioning

confidence: 99%

On the Achievable Rate of Stationary Fading Channels

Dörpinghaus

2011

Foundations in Signal Processing, Communications and Networking

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“…A whole range of phenomena known to occur in nonlinear systems, such as existence of multiple fixed points, oscillatory behavior, bifurcations, chaos, and transient chaos are found in iterative decoding algorithms [11] [12].…”

Section: Nonlinear Dynamics Of Iterative Decodingmentioning

confidence: 99%

A Perturbation Method for Decoding LDPC Concatenated with CRC

Xiao

Lu²,

Lin³

et al. 2007

2007 IEEE Wireless Communications and Networking Conference

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In this paper, a novel decoding algorithm using perturbation techniques for LDPC concatenated with CRC (LDPC-CRC) is proposed. The CRC is used to check the residual error of the BP algorithm, while a new parameter is introduced to LDPC decoding to describe the reliability of each bit in the iterative decoding algorithm. Upon an error is detected, redecoding process with perturbation method will be aroused. Simulation results show that this method lowers the error floor for codeword length of several hundred bits effectively. Index Terms− LDPC, BP, reliability, Chaos, error floor

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The iterative turbo decoding algorithm has fixed points

Cited by 15 publications

References 11 publications

Stochastic Analysis of Turbo Decoding

Stochastic Analysis of Turbo Decoding

On the Achievable Rate of Stationary Fading Channels

A Perturbation Method for Decoding LDPC Concatenated with CRC

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