Related papers: Efficient Scheduling of Serial Iterative Decoding …
We define a class of multi--hop erasure networks that approximates a wireless multi--hop network. The network carries unicast flows for multiple users, and each information packet within a flow is required to be decoded at the flow…
Finite alphabet iterative decoders (FAID) with multilevel messages that can surpass BP in the error floor region for LDPC codes on the BSC were previously proposed. In this paper, we propose decimation-enhanced decoders. The technique of…
We detail a novel Fourier-based approach (IterativeFT) for identifying deterministic network structure in the presence of both edge pruning and Gaussian noise. This technique involves the iterative execution of forward and inverse 2D…
Polar codes asymptotically achieve the symmetric capacity of memoryless channels, yet their error-correcting performance under successive-cancellation (SC) decoding for short and moderate length codes is worse than that of other modern…
We present a new algorithm, Fractional Decomposition Tree (FDT) for finding a feasible solution for an integer program (IP) where all variables are binary. FDT runs in polynomial time and is guaranteed to find a feasible integer solution…
An algorithm of improving the performance of iterative decoding on perpendicular magnetic recording is presented. This algorithm follows on the authors' previous works on the parallel and serial concatenated turbo codes and low-density…
For lossy image compression systems, we develop an algorithm, iterative refinement, to improve the decoder's reconstruction compared to standard decoding techniques. Specifically, we propose a recurrent neural network approach for…
We consider the design and analysis of coding schemes for the binary input two way relay channel with erasure noise. We are particularly interested in reliable physical layer network coding in which the relay performs perfect error…
We give a recursive decoding algorithm for projective Reed-Muller codes making use of a decoder for affine Reed-Muller codes. We determine the number of errors that can be corrected in this way, which is the current highest for decoders of…
Topological quantum codes, such as toric and surface codes, are excellent candidates for hardware implementation due to their robustness against errors and their local interactions between qubits. However, decoding these codes efficiently…
Luby Transform (LT) codes are a class of fountain codes that have proved to perform very efficiently over the erasure channel. These codes are rateless in the sense that an infinite stream of encoded symbols can be generated on the fly.…
Efficient and realistic error decoding is crucial for fault-tolerant quantum computation (FTQC) on near-term devices. While decoding is a classical post-processing task, its effectiveness depends on accurately modeling quantum noise, which…
Fast decoding algorithms are decisive for real-time quantum error correction and for analyzing properties of error correction codes. Here, we develop variants of the union-find decoder that simplify its implementation and provide potential…
Cryptographic check values (digital signatures, MACs and H-MACs) are useful only if they are free of errors. For that reason all of errors in cryptographic check values should be corrected after the transmission over a noisy channel before…
We provide a rigorous mathematical analysis of two communication strategies: soft decode-and-forward (soft-DF) for relay channels, and soft partial interference-cancelation (soft-IC) for interference channels. Both strategies involve soft…
Non-binary low-density parity-check (LDPC) codes have some advantages over their binary counterparts, but unfortunately their decoding complexity is a significant challenge. The iterative hard- and soft-reliability based majority-logic…
The article presents a computationally effective algorithm for calculating the multiresolution discrete Fourier transform (MrDFT). The algorithm is based on the idea of reducing the computational complexity which was introduced by Wen and…
It was estimated that the world produced $59 ZB$ ($5.9 \times 10^{13} GB$) of data in 2020, resulting in the enormous costs of both data storage and transmission. Fortunately, recent advances in deep generative models have spearheaded a new…
Surface codes reach high error thresholds when decoded with known algorithms, but the decoding time will likely exceed the available time budget, especially for near-term implementations. To decrease the decoding time, we reduce the…
In this paper, we propose a Gradient Descent Bit-Flipping (GDBF) decoding with momentum, which considers past updates to provide inertia to the decoding process. We show that GDBF or randomized GDBF decoders with momentum may closely…