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Serially Concatenated Systems: An Iterative Decoding Approach with Application to Continuous Phase Modulation
, 1999
"... Iterative methods for concatenated coding and modulation in digital communication systems are considered. It is assumed that the code and modulation can be described by finitestate machines (FSM). An iterative decoder for such a system typically consists of a posteriori probability (APP) algorithms ..."
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Iterative methods for concatenated coding and modulation in digital communication systems are considered. It is assumed that the code and modulation can be described by finitestate machines (FSM). An iterative decoder for such a system typically consists of a posteriori probability (APP) algorithms for the constituent FSMs. Starting with a detailed examination of these algorithms, it is found that their initialization values can be formally justified. Then, possible iterative methods such as fixpoint iteration, Jacobi overrelaxation, damped substitution, and Newton's method are presented and evaluated. The result is that fixpoint iteration seems to be the best choice in most situations. As an
The performance of serial turbo codes does not concentrate
 in "IEEE Transactions on Information Theory", 2011, accepted, http://hal.inria.fr/hal00641106/en. 28 Activity Report INRIA 2011
"... Abstract—Minimum distances and maximum likelihood error probabilities of serial turbo codes with uniform interleaver are analyzed. It is shown that, for a fraction of interleavers approaching one as the blocklength grows large, the minimum distance of serial turbo codes grows as a positive power ..."
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Abstract—Minimum distances and maximum likelihood error probabilities of serial turbo codes with uniform interleaver are analyzed. It is shown that, for a fraction of interleavers approaching one as the blocklength grows large, the minimum distance of serial turbo codes grows as a positive power of their blocklength, while their error probability decreases exponentially fast in some positive power of their blocklength, on sufficiently good memoryless channels. Such a typical code behavior contrasts the performance of the average serial turbo code, whose error probability is dominated by an asymptotically negligible fraction of poorly performing interleavers, and decays only as a negative power of the blocklength. The analysis proposed in this paper relies on precise bounds of the minimum distance of the typical serial turbo code, whose scaling law is shown to depend both on the free distance of its outer constituent encoder, which determines the exponent of its sublinear growth in the blocklength, and on the effective free distance of its inner constituent encoder. The latter is defined as the smallest weight of codewords obtained when the input word of the inner encoder has weight two, and appears as a linear scaling factor for the minimum distance of the typical serial turbo code. Hence, despite the lack of concentration of the maximum likelihood error probability around its expected value, the main design parameters suggested by the averagecode analysis turn out to characterize also the performance of the typical serial turbo code. By showing for the first time that the typical serial turbo code’s minimum distance scales linearly in the effective free distance of the inner constituent encoder, the presented results generalize, and improve upon, the probabilistic bounds of Kahale and Urbanke, as well as the deterministic upper bound of Bazzi, Mahdian, and Spielman, where only the dependence on the outer encoder’s free distance was proved. Index Terms—Error probability, minimum distance, serially concatenated codes, turbo codes, typical code analysis. I.
An APP Algorithm for Fading Channels using ForwardOnly Prediction
"... A multipleantenna receiver is proposed for achieving a diversity effect that partly overcomes the severity of continuoustime frequencyflat Rayleigh fading channels, and fast fading channels in particular. The error performance is further improved by bit interleaving and channel coding, where the ..."
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A multipleantenna receiver is proposed for achieving a diversity effect that partly overcomes the severity of continuoustime frequencyflat Rayleigh fading channels, and fast fading channels in particular. The error performance is further improved by bit interleaving and channel coding, where the encoders/channel is viewed as a serially concatenated system: a convolutional code (CC) constitutes the outer code, whereas a differential encoder and the fading channel (having truncated memory) form a joint inner code. In order to obtain a feasible detector structure, it is desirable to perform iterative decoding, which implies the need for an APP (a posteriori probability) algorithm that can operate over fading channels. For this purpose, the wellknown BCJR algorithm (due to Bahl, Cocke, Jelinek, Raviv [1]) is generalized to handle channels having memory. Numerical results indicate that iterative decoding becomes more powerful when the exploited channel memory depth is extended, but the chief performance gain is due to space diversity provided by the multiple antennas.