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36
Extrinsic information transfer functions: Model and erasure channel properties,” 2004
 IEEE Trans. Inform. Theory. Available
, 2004
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EXIT charts of irregular codes
, 2002
"... We study the convergence behavior of iterative decoding of a serially concatenated code. We rederive a existing analysis technique called EXIT chart [15] and show that for certain decoders the construction of an EXIT chart simplifies tremendously. The findings are extended such that simple irregula ..."
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Cited by 76 (7 self)
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We study the convergence behavior of iterative decoding of a serially concatenated code. We rederive a existing analysis technique called EXIT chart [15] and show that for certain decoders the construction of an EXIT chart simplifies tremendously. The findings are extended such that simple irregular codes can be constructed, which can be used to improve the converence of the iterative decoding algorithm significantly. An efficient and optimal optiamization algorithm is presented. Finally, some results on thresholds on the decoding convergence are outlined.
Design of Serially Concatenated Systems Depending on the Block Length
 IEEE Trans. Commun
, 2004
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Design methods for irregular repeat accumulate codes
, 2002
"... We optimize the randomlike ensemble of Irregular Repeat Accumulate (IRA) codes for binaryinput symmetric channels in the large blocklength limit. Our optimization technique is based on approximating the Evolution of the Densities (DE) of the messages exchanged by the BeliefPropagation (BP) messa ..."
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Cited by 37 (5 self)
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We optimize the randomlike ensemble of Irregular Repeat Accumulate (IRA) codes for binaryinput symmetric channels in the large blocklength limit. Our optimization technique is based on approximating the Evolution of the Densities (DE) of the messages exchanged by the BeliefPropagation (BP) messagepassing decoder by a onedimensional dynamical system. In this way, the code ensemble optimization can be solved by linear programming. We propose four such DE approximation methods, and compare the performance of the obtained code ensembles over the binary symmetric channel (BSC) and the binaryantipodal input additive white Gaussian channel (BIAWGNC). Our results clearly identify the best among the proposed methods and show that the IRA codes obtained by these methods are competitive with respect to the bestknown irregular LowDensity ParityCheck codes (LDPC). In view of this and the very simple encoding structure of IRA codes, they emerge as attractive design choices.
Convergence Prediction for Iterative Decoding of Threefold Concatenated Systems
 in Proc. IEEE Global Commun. Conf. (GLOBECOM '02
, 2002
"... We show how to use EXIT charts for convergence prediction of a threefold serially concatenated system. The corresponding chart has three dimensions and allows to appropriately select system parameters and to find an optimal schedule of decoding iterations between the three decoders of such a system. ..."
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Cited by 23 (1 self)
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We show how to use EXIT charts for convergence prediction of a threefold serially concatenated system. The corresponding chart has three dimensions and allows to appropriately select system parameters and to find an optimal schedule of decoding iterations between the three decoders of such a system. Convergence thresholds are obtained to determine the minimal signalto noise ratios for which convergence is possible. It turns out that threefold concatenated systems do not achieve any additional performance gain compared to suitably designed twofold systems. We conclude that a threefold concatenation should be considered only when the decoders cannot be chosen freely.
The EXIT Chart  Introduction to Extrinsic Information Transfer
 in Iterative Processing,” In Proc. 12th Europ. Signal Proc. Conf (EUSIPCO
, 2004
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Computation of SymbolWise Mutual Information in Transmission Systems with LogAPP Decoders and Application to EXIT Charts
, 2004
"... The symbolwise mutual information between the binary inputs of a channel encoder and the softoutputs of a LogAPP decoder, i.e., the aposteriori loglikelihood ratios (LLRs), is analyzed. This mutual information can be expressed as the expectation of a function of solely the absolute values of the ..."
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Cited by 20 (2 self)
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The symbolwise mutual information between the binary inputs of a channel encoder and the softoutputs of a LogAPP decoder, i.e., the aposteriori loglikelihood ratios (LLRs), is analyzed. This mutual information can be expressed as the expectation of a function of solely the absolute values of the aposteriori LLRs. This result provides a simple and elegant method for computing the mutual information by simulation. As opposed to the conventional method, explicit measurements of histograms of the softoutputs are not necessary. In fact, online estimation is possible, and bits having different statistical properties need not be treated separately. As a direct application, the computation of extrinsic information transfer (EXIT) charts is considered.
Design of LDPC Codes: A Survey and New Results
"... Abstract — This survey paper provides fundamentals in the design of LDPC codes. To provide a target for the code designer, we first summarize the EXIT chart technique for determining (near)optimal degree distributions for LDPC code ensembles. We also demonstrate the simplicity of representing codes ..."
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Cited by 11 (2 self)
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Abstract — This survey paper provides fundamentals in the design of LDPC codes. To provide a target for the code designer, we first summarize the EXIT chart technique for determining (near)optimal degree distributions for LDPC code ensembles. We also demonstrate the simplicity of representing codes by protographs and how this naturally leads to quasicyclic LDPC codes. The EXIT chart technique is then extended to the special case of protographbased LDPC codes. Next, we present several design approaches for LDPC codes which incorporate one or more accumulators, including quasicyclic accumulatorbased codes. The second half the paper then surveys several algebraic LDPC code design techniques. First, codes based on finite geometries are discussed and then codes whose designs are based on ReedSolomon codes are covered. The algebraic designs lead to cyclic, quasicyclic, and structured codes. The masking technique for converting regular quasicyclic LDPC codes to irregular codes is also presented. Some of these results and codes have not been presented elsewhere. The paper focuses on the binaryinput AWGN channel (BIAWGNC). However, as discussed in the paper, good BIAWGNC codes tend to be universally good across many channels. Alternatively, the reader may treat this paper as a starting point for extensions to more advanced channels. The paper concludes with a brief discussion of open problems. I.
An MSE based transfer chart to analyze iterative decoding schemes
 42nd Allerton Conference on Communications, Control and Computing
, 2004
"... An alternative to extrinsic information transfer (EXIT) charts called mean squared error (MSE) charts that use a measure related to the MSE instead of mutual information is proposed. Using the relationship between mutual information and minimum mean squared error (MMSE), a relationship between the r ..."
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Cited by 10 (0 self)
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An alternative to extrinsic information transfer (EXIT) charts called mean squared error (MSE) charts that use a measure related to the MSE instead of mutual information is proposed. Using the relationship between mutual information and minimum mean squared error (MMSE), a relationship between the rate of any code and the area under a plot of MSE versus signal to noise ratio (SNR) is obtained, when the log likelihood ratio’s (LLR) can be assumed to be from a Gaussian channel. Using this result, a theoretical justification is provided for designing concatenated codes by matching the EXIT charts of the inner and outer decoders, when the LLRs are Gaussian which is typically assumed for code design using EXIT charts. Finally, for the special case of AWGN channel it is shown that any capacity achieving code has an EXIT curve that is flat. This extends Ashikhmin et al’s results for erasure channels to the Gaussian channel.
Performance Evaluation of Linear Turbo Receivers Using Analytical Extrinsic Information Transfer Functions
 EURASIP JOURNAL ON APPLIED SIGNAL PROCESSING 2005:6, 892–905
, 2005
"... Turbo receivers reduce the effect of the interferencelimited propagation channels through the iterative exchange of information between the frontend receiver and the channel decoder. Such an iterative (turbo) process is difficult to describe in a closed form so the performance evaluation is often ..."
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Cited by 9 (5 self)
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Turbo receivers reduce the effect of the interferencelimited propagation channels through the iterative exchange of information between the frontend receiver and the channel decoder. Such an iterative (turbo) process is difficult to describe in a closed form so the performance evaluation is often done by means of extensive numerical simulations. Analytical methods for performance evaluation have also been proposed in the literature, based on Gaussian approximation of the output of the linear signal combiner. In this paper, we propose to use mutual information to parameterize the logarithmiclikelihood ratios (LLRs) at the input/output of the decoder, casting our approach into the framework of extrinsic information transfer (EXIT) analysis. We find the EXIT functions of the frontend (FE) receiver analytically, that is, using solely the information about the channel state. This is done, decomposing the FE receiver into elementary blocks described independently. Our method gives an insight into the principle of functioning of the linear turbo receivers, allows for an accurate calculation of the expected bit error rate in each iteration, and is more flexible than the one previously used in the literature, allowing us to analyze the performance for various FE structures. We compare the proposed analytical method with the results of simulated data transmission in case of multiple antennas transceivers.