Related papers: Weight vs Magnetization Enumerator for Gallager Co…
The performance of low-density parity-check (LDPC) codes at high signal-to-noise ratios (SNRs) is known to be limited by the presence of certain sub-graphs that exist in the Tanner graph representation of the code, for example trapping sets…
Gravitational-wave parameter estimation for compact binary signals typically relies on sequential estimation of the properties of the detector Gaussian noise and of the binary parameters. This procedure assumes that the noise variance,…
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…
Moderate Density Parity Check (MDPC) codes are defined here as codes which have a parity-check matrix whose row weight is $O(\sqrt{n})$ where $n$ is the length $n$ of the code. They can be decoded like LDPC codes but they decode much less…
In this paper, we leverage polar codes and the well-established channel polarization to design capacity-achieving codes with a certain constraint on the weights of all the columns in the generator matrix (GM) while having a low-complexity…
This work considers the problem of estimating the parameters of negative mixture models, i.e. mixture models that possibly involve negative weights. The contributions of this paper are as follows. (i) We show that every rational probability…
We present an analytic method of assessing the typical performance of low-density parity-check codes on finite-state Markov channels. We show that this problem is similar to a spin-glass model on a `small-world' lattice. We apply our…
We present a nonintrusive method for reliably estimating the noise level during quantum computation and quantum communication protected by quantum error-correcting codes. As preprocessing of quantum error correction, our scheme estimates…
Departing from traditional communication theory where decoding algorithms are assumed to perform without error, a system where noise perturbs both computational devices and communication channels is considered here. This paper studies…
We discuss the performance of Low-Density-Parity-Check (LDPC) codes decoded by means of Linear Programming (LP) at moderate and large Signal-to-Noise-Ratios (SNR). Utilizing a combination of the previously introduced pseudo-codeword-search…
This study focuses on the efficiency of message-passing-based decoding algorithms for polar and low-density parity-check (LDPC) codes. Both successive cancellation (SC) and belief propagation (BP) decoding algorithms are studied {in} the…
Recently, it was shown that if multiplicative weights are assigned to the edges of a Tanner graph used in belief propagation decoding, it is possible to use deep learning techniques to find values for the weights which improve the…
The number-theoretic codes are a class of codes defined by single or multiple congruences. These codes are mainly used for correcting insertion and deletion errors, and for correcting asymmetric errors. This paper presents a formula for a…
The syndrome decoding problem has been proposed as a computational hardness assumption for code based cryptosystem that are safe against quantum computing. The problem has been reduced to finding the codeword with the smallest non-zero…
A product code with single parity-check component codes can be described via the tools of a multi-kernel polar code, where the rows of the generator matrix are chosen according to the constraints imposed by the product code construction.…
While quantum weight enumerators establish some of the best upper bounds on the minimum distance of quantum error-correcting codes, these bounds are not optimized to quantify the performance of quantum codes under the effect of arbitrary…
We consider decoding of binary Tanner codes using message-passing iterative decoding and linear programming (LP) decoding in MBIOS channels. We present new certificates that are based on a combinatorial characterization for local-optimality…
A quantum error correcting protocol can be substantially improved by taking into account features of the physical noise process. We present an efficient decoder for the surface code which can account for general noise features, including…
Weight-only quantization is widely used to mitigate the memory-bound nature of LLM inference. Codebook-based methods extend this trend by achieving strong accuracy in the extremely low-bit regime (e.g., 2-bit). However, current kernels rely…
A new construction for moderate density parity-check (MDPC) codes using finite geometry is proposed. We design a parity-check matrix for this family of binary codes as the concatenation of two matrices: the incidence matrix between points…