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Motivated by the significant performance gains which polar codes experience when they are decoded with successive cancellation list decoders, we study how the scaling exponent changes as a function of the list size L. In particular, we fix the block error ...
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 the asymptotic behavior of the polarization process in the large block-length regime when transmission takes place over a binary-input memoryless symmetric channel W. In particular, we study the asymptotics of the cumulative distribution, P(Z(n ...
Consider a receiver that observes multiple interfering codewords. The compute-and-forward technique makes it possible for the receiver to directly decode linear combinations of the codewords. Previous work has focused on compute-and-forward for linear Gaus ...
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 polarization phenomenon in a special sense is shown for an arbitrary discrete memoryless channel (DMC) by imposing a quasigroup structure on the input alphabet. The same technique is used to derive a polarization theorem for an arbitrary multiple access ...
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 ...
Polar codes are constructed for arbitrary channels by imposing an arbitrary quasigroup structure on the input alphabet. The block error probability under successive cancellation decoding decays exponentially with the square root of the block length. It is ...
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
A challenging problem related to the design of polar codes is "robustness against channel parameter variations'', as stated in Arıkan's original work. In this paper, we describe how the problem of robust polar code design can be viewed as a mismatch decodi ...
