Related papers: On Pseudocodewords and Decision Regions of Linear …
We develop a framework for linear-programming (LP) decoding of non-binary linear codes over rings. We prove that the resulting LP decoder has the `maximum likelihood certificate' property, and we show that the decoder output is the lowest…
In order to understand the performance of a code under maximum-likelihood (ML) decoding, it is crucial to know the minimal codewords. In the context of linear programming (LP) decoding, it turns out to be necessary to know the minimal…
In order to understand the performance of a code under maximum-likelihood (ML) decoding, one studies the codewords, in particular the minimal codewords, and their Hamming weights. In the context of linear programming (LP) decoding, one's…
A framework for linear-programming (LP) decoding of nonbinary linear codes over rings is developed. This framework facilitates linear-programming based reception for coded modulation systems which use direct modulation mapping of coded…
Just as the Hamming weight spectrum of a linear block code sheds light on the performance of a maximum likelihood decoder, the pseudo-weight spectrum provides insight into the performance of a linear programming decoder. Using properties of…
We analyze Linear Programming (LP) decoding of graphical binary codes operating over soft-output, symmetric and log-concave channels. We show that the error-surface, separating domain of the correct decoding from domain of the erroneous…
In this paper, we present an improved union bound on the Linear Programming (LP) decoding performance of the binary linear codes transmitted over an additive white Gaussian noise channels. The bounding technique is based on the second-order…
Message-passing iterative decoders for low-density parity-check (LDPC) block codes are known to be subject to decoding failures due to so-called pseudo-codewords. These failures can cause the large signal-to-noise ratio performance of…
While low-density parity-check (LDPC) codes are near capacity-achieving when paired with iterative decoders, these decoders may not output a codeword due to the existence of pseudocodewords. Thus, pseudocodewords have been studied to give…
In his Ph.D. disseration, Feldman and his collaborators define the linear programming decoder for binary linear codes, which is a linear programming relaxation of the maximum-likelihood decoding problem. This decoder does not, in general,…
Belief Propagation (BP) and Linear Programming (LP) decodings of Low Density Parity Check (LDPC) codes are discussed. We summarize results of instanton/pseudo-codeword approach developed for analysis of the error-floor domain of the codes.…
In Linear Programming (LP) decoding of a Low-Density-Parity-Check (LDPC) code one minimizes a linear functional, with coefficients related to log-likelihood ratios, over a relaxation of the polytope spanned by the codewords \cite{03FWK}. In…
A new approach for decoding binary linear codes by solving a linear program (LP) over a relaxed codeword polytope was recently proposed by Feldman et al. In this paper we investigate the structure of the polytope used in the LP relaxation…
Maximum Likelihood (ML) decoding is the optimal decoding algorithm for arbitrary linear block codes and can be written as an Integer Programming (IP) problem. Feldman et al. relaxed this IP problem and presented Linear Programming (LP)…
This paper tackles two problems that fall under the study of coding for insertions and deletions. These problems are motivated by several applications, among them is reconstructing strands in DNA-based storage systems. Under this paradigm,…
We propose several improvements for Linear Programming (LP) decoding algorithms for High Density Parity Check (HDPC) codes. First, we use the automorphism groups of a code to create parity check matrix diversity and to generate valid cuts…
Linear programming (LP) decoding approximates maximum-likelihood (ML) decoding of a linear block code by relaxing the equivalent ML integer programming (IP) problem into a more easily solved LP problem. The LP problem is defined by a set of…
In this paper, the linear programming (LP) decoder for binary linear codes, introduced by Feldman, et al. is extended to joint-decoding of binary-input finite-state channels. In particular, we provide a rigorous definition of LP…
Decoding quantum error-correcting codes is a key challenge in enabling fault-tolerant quantum computation. In the classical setting, linear programming (LP) decoders offer provable performance guarantees and can leverage fast practical…
Surface codes exploit topological protection to increase error resilience in quantum computing devices and can in principle be implemented in existing hardware. They are one of the most promising candidates for active error correction, not…