Related papers: On Hard-Decision Decoding of Product Codes
Polar codes are one of the most recent advancements in coding theory and they have attracted significant interest. While they are provably capacity achieving over various channels, they have seen limited practical applications.…
We study low-complexity iterative decoding algorithms for product codes. We revisit two algorithms recently proposed by the authors based on bounded distance decoding (BDD) of the component codes that improve the performance of conventional…
Cooperative optimization is a new way for finding global optima of complicated functions of many variables. It has some important properties not possessed by any conventional optimization methods. It has been successfully applied in solving…
Polar codes are a new class of capacity-achieving error-correcting codes with low encoding and decoding complexity. Their low-complexity decoding algorithms rendering them attractive for use in software-defined radio applications where…
The development of practical, high-performance decoding algorithms reduces the resource cost of fault-tolerant quantum computing. Here we propose a decoder for the surface code that finds low-weight correction operators for errors produced…
This paper presents a generalized construction of RS-SPC product codes. A low-complexity joint-decoding scheme is proposed for these codes, in which a BP-based iterative decoding is performed based on the binary expansion of the whole…
A new permutation decoding approach for polar codes is presented. The complexity of the algorithm is similar to that of a successive cancellation list (SCL) decoder, while it can be implemented with the latency of a successive cancellation…
With the success of transformer architectures across diverse applications, the error correction code transformer (ECCT) has gained significant attention for its superior decoding performance. In spite of its advantages, the error floor…
We propose a novel soft-aided iterative decoding algorithm for product codes (PCs). The proposed algorithm, named iterative bounded distance decoding with combined reliability (iBDD-CR), enhances the conventional iterative bounded distance…
The advancement of deep learning has led to the development of neural decoders for low latency communications. However, neural decoders can be very complex which can lead to increased computation and latency. We consider iterative pruning…
We introduce a novel algorithm for decoding binary linear codes by linear programming. We build on the LP decoding algorithm of Feldman et al. and introduce a post-processing step that solves a second linear program that reweights the…
We combine two approaches to optimize the iterative decoding of product codes with precoded polar component codes. On one side, we generate bitwise soft messages based on the codebook probability, an approximation of an auxiliary quantity…
Decoders that provide an estimate of the probability of a logical failure conditioned on the error syndrome ("soft-output decoders") can reduce the overhead cost of fault-tolerant quantum memory and computation. In this work, we construct…
Staircase codes (SCCs) are typically decoded using iterative bounded-distance decoding (BDD) and hard decisions. In this paper, a novel decoding algorithm is proposed, which partially uses soft information from the channel. The proposed…
A novel SC decoding method of polar codes is proposed in $d$-deletion channels, where a new pruning strategy is designed to reduce decoding complexity. Considering the difference of the scenario weight distributions, pruning thresholds for…
The successive cancellation list decoding algorithm for polar codes yields near-optimal decoding performance at the cost of high implementation complexity. The successive cancellation stack algorithm has been shown to provide similar…
In the search for highly efficient decoders for short LDPC codes approaching maximum likelihood performance, a relayed decoding strategy, specifically activating the ordered statistics decoding process upon failure of a neural min-sum…
We develop a simple and general post-selection strategy for high-rate quantum codes that is transferrable across decoders. After an initial baseline run, the decoder is re-run once per logical observable, and forced in these latter runs to…
Fast SC decoding overcomes the latency caused by the serial nature of the SC decoding by identifying new nodes in the upper levels of the SC decoding tree and implementing their fast parallel decoders. In this work, we first present a novel…
This work introduces a decoding strategy for binary self-dual codes possessing an automorphism of a specific type. The proposed algorithm is a hard decision iterative decoding scheme. The enclosed experiments show that the new decoding…