Related papers: Pseudoredundancy for the Bit-Flipping Algorithm
Binary segmentation is the classic greedy algorithm which recursively splits a sequential data set by optimizing some loss or likelihood function. Binary segmentation is widely used for changepoint detection in data sets measured over space…
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…
Iterative decoding and linear programming decoding are guaranteed to converge to the maximum-likelihood codeword when the underlying Tanner graph is cycle-free. Therefore, cycles are usually seen as the culprit of low-density parity-check…
Recovering high-level type information in binaries is a key task in reverse engineering and binary analysis. Binaries contain very little explicit type information. The structure of binary code is incredibly flexible allowing for ad-hoc…
Consider binary linear codes obtained from bipartite graphs as follows. There are~\(k \geq 1\) left nodes each representing a message bit and there are~\(m = m(k)\) right nodes each representing a parity bit, generated from the…
Minimum distance is an important parameter of a linear error correcting code. For improved performance of binary Low Density Parity Check (LDPC) codes, we need to have the minimum distance grow fast with n, the codelength. However, the best…
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…
The minimum distance of a code is an important concept in information theory. Hence, computing the minimum distance of a code with a minimum computational cost is a crucial process to many problems in this area. In this paper, we present…
Linear algebra expressions, which play a central role in countless scientific computations, are often computed via a sequence of calls to existing libraries of building blocks (such as those provided by BLAS and LAPACK). A sequence…
Recently, a novel lookup table based decoding method for binary low-density parity-check codes has attracted considerable attention. In this approach, mutual-information maximizing lookup tables replace the conventional operations of the…
[Draft] In this paper, the redundancy of Slepian Wolf coding is revisited. Applying the random binning and converse technique in \cite{yang}, the same results in \cite{he} are obtained with much simpler proofs. Moreover, our results reflect…
Polar codes have attracted much attention in the past decade due to their capacity-achieving performance. The higher decoding capacity is required for 5G and beyond 5G (B5G). Although the cyclic redundancy check (CRC)- assisted successive…
Digital data transfer can be protected by means of suitable error correcting codes. Among the families of state-of-the-art codes, LDPC (Low Density Parity-Check) codes have received a great deal of attention recently, because of their…
The problem of error correction in both coherent and noncoherent network coding is considered under an adversarial model. For coherent network coding, where knowledge of the network topology and network code is assumed at the source and…
The relation between the girth and the guaranteed error correction capability of $\gamma$-left regular LDPC codes when decoded using the bit flipping (serial and parallel) algorithms is investigated. A lower bound on the size of variable…
In this paper, we use reinforcement learning to find effective decoding strategies for binary linear codes. We start by reviewing several iterative decoding algorithms that involve a decision-making process at each step, including…
In this paper, we consider the mismatched rate-distortion problem, in which the encoding is done using a codebook, and the encoder chooses the minimum-distortion codeword according to a mismatched distortion function that differs from the…
The Bit-Flipping (BF) decoder, thanks to its very low computational complexity, is widely employed in post-quantum cryptographic schemes based on Moderate Density Parity Check codes in which, ultimately, decryption boils down to syndrome…
Minimizing risk with fairness constraints is one of the popular approaches to learning a fair classifier. Recent works showed that this approach yields an unfair classifier if the training set is corrupted. In this work, we study the…
This paper investigates decoding of binary linear block codes over the binary erasure channel (BEC). Of the current iterative decoding algorithms on this channel, we review the Recovery Algorithm and the Guess Algorithm. We then present a…