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`Tree pruning (TP) is an algorithm for probabilistic inference on binary Markov random fields. It has been recently derived by Dror Weitz and used to construct the first fully polynomial approximation scheme for counting independent sets up to the `tree uniqueness threshold. It can be regarded as a clever method for pruning the belief propagation computation tree, in such a way to exactly account for the effect of loops. In this paper we generalize the original algorithm to make it suitable for decoding linear codes, and discuss various schemes for pruning the computation tree. Further, we present the outcomes of numerical simulations on several linear codes, showing that tree pruning allows to interpolate continuously between belief propagation and maximum a posteriori decoding. Finally, we discuss theoretical implications of the new method.
It is well known that for linear Gaussian channels, a nearest neighbor decoding rule, which seeks the minimum Euclidean distance between a codeword and the received channel output vector, is the maximum likelihood solution and hence capacity-achievin
We propose a binary message passing decoding algorithm for product codes based on generalized minimum distance decoding (GMDD) of the component codes, where the last stage of the GMDD makes a decision based on the Hamming distance metric. The propose
A product code with single parity-check component codes can be described via the tools of a multi-kernel polar code, where the rows of the generator matrix are chosen according to the constraints imposed by the product code construction. Following th
This paper presents new low-complexity lattice-decoding algorithms for noncoherent block detection of QAM and PAM signals over complex-valued fading channels. The algorithms are optimal in terms of the generalized likelihood ratio test (GLRT). The co
In multi-terminal communication systems, signals carrying messages meant for different destinations are often observed together at any given destination receiver. Han and Kobayashi (1981) proposed a receiving strategy which performs a joint unique de