Abstract—Extrinsic information transfer (EXIT) charts are a tool for predicting the convergence behavior of iterative processors for a variety of communication problems. A model is introduced that applies to decoding problems, including the iterative decoding of parallel concatenated (turbo) codes, serially concatenated codes, low-density parity-check (LDPC) codes, and repeat–accumulate (RA) codes. EXIT functions are defined using the model, and several properties of such functions are proved for erasure channels. One property expresses the area under an EXIT function in terms of a conditional entropy. A useful consequence of this result is that the design of capacity-approaching codes reduces to a curve-fitting problem for all the aforementioned codes. A second property relates the EXIT function of a code to its Helleseth–Kløve–Levenshtein information functions, and thereby to the support weights of its subcodes. The relation is via a refinement of information functions called split information functions, and via a refinement of support weights called split support weights. Split information functions are used to prove a third property that relates the EXIT function of a linear code to the EXIT function of its dual. Index Terms—Concatenated codes, duality, error-correction coding, iterative decoding, mutual information.

We study the convergence behavior of iterative decoding for a number of serially concatenated systems, such as a serially concatenated code, coded data transmission over an inter-symbol interference channel, bit-interleaved coded modulation, or trellis-coded modulation. We rederive an existing analysis technique called EXIT chart, simplify its construction, and construct simple irregular codes to improve the convergence of iterative decoding. An efficient and optimal optimization algorithm yields systems, which approach information theoretic limits very closely. However, these systems exhibit their performance only for very long block lengths. To overcome this problem, we optimize the decoding convergence after a fixed, finite amount of iterations yielding systems, which perform very well for short block lengths, too. As an example, optimal system configurations for communication over an additive white Gaussian noise channel are presented.

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Recent results indicate that the same turbo principle which delivers near to optimal strategies for channel coding, can be used to obtain very efficient source coding schemes. We investigate this issue applying ten Brink's EXIT chart analysis and show how this technique can be used to select the most efficient match of component codes and puncturing matrices to compress discrete memoryless sources. Aiming at perfect reconstruction at the decoder, i.e. lossless source coding, we present an encoding algorithm, which gradually removes the redundancy while checking the decodability of the compressed bit stream. This concept of decremental redundancy is dual to the principle of incremental redundancy that characterizes hybrid ARQ (Type II) communication protocols. Both principles can be combined when the channel is noisy.

This overview talk shows that the so-called turbo codes(decoders) entail a much broader principle. It discusses how the feedback of extrinsic information which we call the turbo principle can be used in many mobile communications receivers to improve performance through iterative processing. As an analysis and design tool the EXIT charts of mutual information transfer are used.

In this paper, we analyze the performance of Low Density Parity Check (LDPC) codes on memoryless channels. We use a recently proposed analysis technique for iterative decoding based on EXtrinsic Information Transfer (EXIT) charts. We show that, based on this technique, the predicted performance of an LDPC code does not depend on the specific memoryless channel, but only on the mutual information (MI) between the input and the output of the channel. As a validation of this conjecture, we evaluate the performance of some LDPC codes over five representative memoryless channels and we compare them, obtaining results in excellent agreement with our conjecture. 1.

Reduced latency versions of iterative decoders of low-density parity-check codes are analyzed in this paper. The proposed schemes converge faster than standard approaches.

We study the convergence behavior of iterative decoding of various serially concatenated systems such as a concatenated code, coded transmission over a channel introducing inter-symbol interference, bitinterleaved coded modulation, trellis coded modulation, a.s.o.

In this paper we consider iterative channel estimation, equalization, and decoding, or adaptive Turbo equalization, as a receiver technology for digital communication systems where the channel imposes time-varying intersymbol interference. We show how a semianalytical technique called EXIT charts, originally developed by S. ten Brink for analysis of Turbo codes, can be used to predict the performance of the iterative receiver for such systems. To demonstrate the usefulness of the technique, we use EXIT charts to address interesting questions about adaptive Turbo equalization for time-varying channels: Which pattern of training sequences should be used, what is the performance difference between optimal MAP equalization and suboptimal linear equalization, and between the case of a known channel and the case of an estimated channel, and what can be gained by using a recursive precoder in conjunction with the symbol mapper.

We consider the problem of coded data transmission over an inter-symbol interference (ISI) channel with unknown and possibly time-varying parameters. We propose a low-complexity algorithm for joint equalization, estimation, and decoding using an estimator, which is separate from the equalizer. Based on existing techniques for analyzing the convergence of iterative decoding algorithms, we show how to find powerful system configurations. This includes the use of recursive precoders in the transmitter. We derive novel a-posteriori probability equalization algorithms for imprecise knowledge of the channel parameters. We show that the performance loss implied by not knowing the parameters of the ISI channel is entirely a loss in signal-to-noise ratio for which a suitably designed iterative receiver algorithm converges.