Related papers: Algebraic matching techniques for fast decoding of…
In this paper, we introduce a new coding and decoding structure for enhancing the reliability and performance of polar codes, specifically at low error rates. We achieve this by concatenating two polar codes in series to create robust…
We show that locally repairable codes (LRCs) can be list decoded efficiently beyond the Johnson radius for a large range of parameters by utilizing the local error correction capabilities. The new decoding radius is derived and the…
It is well known that to fulfill their full potential, the design of polar codes must be tailored to their intended decoding algorithm. While for successive cancellation (SC) decoding, information theoretically optimal constructions are…
The root finding step of the Guruswami-Rudra list decoding algorithm for folded Reed-Solomon codes is considered. It is shown that a multivariate generalization of the Roth-Ruckenstein algorithm can be used to implement it. This leads to an…
We investigate the decoding region for Algebraic Soft-Decision Decoding (ASD) of Reed-Solomon codes in a discrete, memoryless, additive-noise channel. An expression is derived for the error correction radius within which the soft-decision…
Product codes are widespread in optical communications, thanks to their high throughput and good error-correction performance. Systematic polar codes have been recently considered as component codes for product codes. In this paper, we…
Polar codes are able to achieve the capacity of memoryless channels under successive cancellation (SC) decoding. Soft Cancellation (SCAN) is a soft-output decoder based on the SC schedule, useful in iterative decoding and concatenation of…
A new Chase-type soft-decision decoding algorithm for Reed-Solomon codes is proposed, referred to as tree-based Chase-type algorithm}. The proposed tree-based Chase-type algorithm takes the set of all vectors as the set of testing patterns,…
Polar codes under cyclic redundancy check aided successive cancellation list (CA-SCL) decoding can outperform the turbo codes and the LDPC codes when code lengths are configured to be several kilobits. In order to reduce the decoding…
We exploit the redundancy of the language-based source to help polar decoding. By judging the validity of decoded words in the decoded sequence with the help of a dictionary, the polar list decoder constantly detects erroneous paths after…
Polar-coded multiple-input multiple-output systems are investigated. An advanced receiver implementing joint list decoding of polar codes and QR- and MMSE-based detectors is proposed. The approximate and exact path metrics are derived for…
It is shown how to combine ordered statistics decoding (OSD) with CRC-aided belief propagation list (CBPL) decoding of polar codes. Even when the reprocessing order of the OSD is as low as one, the new decoder is shown to significantly…
In this paper, we study polar codes from a practical point of view. In particular, we study concatenated polar codes and rate-compatible polar codes. First, we propose a concatenation scheme including polar codes and Low-Density…
This work studies several decoding algorithms for hyperbolic codes. We use some previous ideas to describe how to decode a hyperbolic code using the largest Reed-Muller code contained in it or using the smallest Reed-Muller code that…
A transform that enables generator-matrix-based Reed-Solomon (RS) coded data to be recovered under interpolation-based list decoding is presented. The transform matrix needs to be computed only once and the transformation of an element from…
Polar codes with large kernels achieve optimal error exponents but are difficult to construct when low decoding complexity is also required. We address this challenge under recursive maximum likelihood decoding (RMLD) using a rein-forcement…
Reed-Solomon (RS) codes are an important class of non-binary error-correction codes. They are particularly competent in correcting burst errors, being widely applied in modern communications and data storage systems. This also thanks to…
Gabidulin codes are the rank-metric analogs of Reed-Solomon codes and have a major role in practical error control for network coding. This paper presents new encoding and decoding algorithms for Gabidulin codes based on low-complexity…
Polar codes are a new family of error correction codes for which efficient hardware architectures have to be defined for the encoder and the decoder. Polar codes are decoded using the successive cancellation decoding algorithm that includes…
A novel search method for large polarization kernels is proposed. The algorithm produces a kernel with given partial distances by employing the depth-first search combined with the computation of coset leaders weight tables and sufficient…