Spatially coupled ensembles universally achieve capacity under belief propagation
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The contribution of this thesis is twofold. In the first part, we generalize and analyze two classes of error correcting codes: LDPC codes and product codes. We generalize graphical codes by considering checks being arbitrary codes instead of single pariti ...
EPFL2013
Spatially coupled low-density parity-check codes show an outstanding performance under the low-complexity belief propagation (BP) decoding algorithm. They exhibit a peculiar convergence phenomenon above the BP threshold of the underlying non-coupled ensemb ...
A new iterative low complexity algorithm has been presented for computing the Walsh-Hadamard transform (WHT) of an N dimensional signal with a K-sparse WHT, where N is a power of two and K = O(N^α), scales sub- linearly in N for some 0 < α < 1. Assuming a ...
2013
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We investigate spatially coupled code ensembles. For transmission over the binary erasure channel, it was recently shown that spatial coupling increases the belief propagation threshold of the ensemble to essentially the maximum a priori threshold of the u ...
Institute of Electrical and Electronics Engineers2013
We prove that channel combining and splitting via Arikan's polarization transformation improves Gallager's reliability function E-0 for binary input channels. In this sense, polarization creates E-0. This observation gives yet another justification as to w ...
We consider single-hop broadcast erasure channels (BEC) with degraded message sets and instantaneous feedback regularly available from all receivers, and demonstrate that the main principles of the virtual queue-based algorithms in [1], which were proposed ...
Spatial coupling has recently emerged as a powerful paradigm to construct graphical models that work well under low-complexity message-passing algorithms. Although much progress has been made on the analysis of spatially coupled models under message passin ...
Spatially coupled codes have been of interest recently owing to their superior performance over memoryless binary-input channels. The performance is good both asymptotically, since the belief propagation thresholds approach the Shannon limit, as well as fo ...
We consider single-hop broadcast packet erasure channels (BPEC) with degraded message sets and instantaneous feedback regularly available from all receivers, and demonstrate that the main principles of the virtual-queue-based algorithms in [1], which were ...
Convolutional low-density parity-check (LDPC) ensembles, introduced by Felstrom and Zigangirov, have excellent thresholds and these thresholds are rapidly increasing functions of the average degree. Several variations on the basic theme have been proposed ...
