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We describe a successive-cancellation \emph{list} decoder for polar codes, which is a generalization of the classic successive-cancellation decoder of Ar{\i}kan. In the proposed list decoder, up to $L...
An open question about Gabidulin codes is whether polynomial-time list decoding beyond half the minimum distance is possible or not. In this contribution, we give a lower and an upper bound on the lis...
When binary linear error-correcting codes are used over symmetric channels, a relaxed version of the maximum likelihood decoding problem can be stated as a linear program (LP). This LP decoder can be ...
We reformulate a recently introduced interpolation-based unique decoding algorithm of algebraic geometry codes using the theory of Gr\"obner bases of modules on the coordinate ring of the base curve. ...
A variety of low-density parity-check (LDPC) ensembles have now been observed to approach capacity with message-passing decoding. However, all of them use soft (i.e., non-binary) messages and a poster...
We prove the following results concerning the combinatorics of list decoding, motivated by the exponential gap between the known upper bound (of $O(1/\gamma)$) and lower bound (of $\Omega_p(\log (1/\g...
Abstract: We present a family of constant-dimension codes for random linear network coding called spread codes. This is a family of optimal codes with maximum minimum distance. A spread code is constr...
Abstract: The work identifies the first lattice decoding solution that achieves, in the general outage-limited MIMO setting and in the high-rate and high-SNR limit, both a vanishing gap to the error-p...
Abstract: Mathematical programming is a branch of applied mathematics and has recently been used to derive new decoding approaches, challenging established but often heuristic algorithms based on iter...
Abstract: Applying the max-product (and belief-propagation) algorithms to loopy graphs is now quite popular for best assignment problems. This is largely due to their low computational complexity and ...
Abstract: Low density parity-check (LDPC) codes are a class of linear block codes that are decoded by running belief propagation (BP) algorithm or log-likelihood ratio belief propagation (LLR-BP) over...
Abstract: We present a new combinatorial characterization for local-optimality of a codeword in irregular Tanner codes. This characterization is a generalization of [Arora, Daskalakis, Steurer; 2009] ...
Abstract: We study a noncoherent multiple-input multiple-output (MIMO) fading multiple-access channel (MAC), where the transmitters and the receiver are aware of the statistics of the fading, but not ...
Abstract: We propose a decoding algorithm for the $(u\mid u+v)$-construction that decodes up to half of the minimum distance of the linear code. We extend this algorithm for a class of matrix-product ...
Abstract: This paper considers the multiple-input-single-output interference channel (MISO-IC) with interference decoding capability (IDC), so that the interference signal can be decoded and subtracte...

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