Abstract—This paper introduces the Modified Adaptive Belief Propagation (m-ABP) algorithm, an innovative method for the turbo decoding of product codes based on BCH component codes. The Adaptive Belief Propagation algorithm of Jiang and Narayanan is simplified by moving the matrix adaptation step

-limit performance of "Turbo Codes" --- codes whose decoding algorithm is equivalent to loopy belief propagation in a chain-structured Bayesian network. In this paper we ask: is there something special about the error-correcting code context, or does loopy propagation work as an approximate

/convolutional component codes, interleaver sizes less than 1000 and for three to six iterations. Index Terms- Concatenated codes, product codes, iterative decoding, “soft-inlsoft-out ” decoder, “turbo ” (de)coding.

be derived as specific instances of the sum-product algorithm, including the forward/backward algorithm, the Viterbi algorithm, the iterative "turbo" decoding algorithm, Pearl's belief propagation algorithm for Bayesian networks, the Kalman filter, and certain fast Fourier transform algorithms.

with the task of fusing and propagating the impacts of new information through the networks in such a way that, when equilibrium is reached, each proposition will be assigned a measure of belief consistent with the axioms of probability theory. It is shown that if the network is singly connected (e.g. tree

case of belief-propagation decoders, we provide an effective algorithm to determine the corresponding capacity to any desired degree of accuracy. The ideas presented in this paper are broadly applicable and extensions of the general method to low-density parity-check codes over larger alphabets, turbo

. The decoding of both codes can be tackled with a practical sum-product algorithm. We prove that these codes are "very good," in that sequences of codes exist which, when optimally decoded, achieve information rates up to the Shannon limit. This result holds not only for the binary-symmetric channel

Iterative decoding techniques have become a viable alternative for constructing high performance coding systems. In particular, the recent success of turbo codes indicates that performance close to the Shannon limit may be achieved. In this thesis, it is showed that many iterative decoding

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A new learning algorithm for multilayer feedforward networks, RPROP, is proposed. To overcome the inherent disadvantages of pure gradient-descent, RPROP performs a local adaptation of the weight-updates according to the behaviour of the errorfunction. In substantial difference to other adaptive