Related papers: List decoding of repeated codes
Reed-Muller (RM) and polar codes are a class of capacity-achieving channel coding schemes with the same factor graph representation. Low-complexity decoding algorithms fall short in providing a good error-correction performance for RM and…
Computation codes in network information theory are designed for the scenarios where the decoder is not interested in recovering the information sources themselves, but only a function thereof. K\"orner and Marton showed for distributed…
We present a new decoding algorithm based on error locating pairs and correcting an amount of errors exceeding half the minimum distance. When applied to Reed--Solomon or algebraic geometry codes, the algorithm is a reformulation of the…
In this paper, a derandomized algorithm for sampling decoding is proposed to achieve near-optimal performance in lattice decoding. By setting a probability threshold to sample candidates, the whole sampling procedure becomes deterministic,…
We present a low-complexity and low-latency decoding algorithm for a class of Reed-Muller (RM) subcodes that are defined based on the product of smaller RM codes. More specifically, the input sequence is shaped as a multi-dimensional array,…
We propose an alternative method for collaborative decoding of interleaved Reed-Solomon codes. Simulation results for a concatenated coding scheme using polar codes as inner codes are included.
Linearized Reed-Solomon (LRS) codes are sum-rank metric codes that fulfill the Singleton bound with equality. In the two extreme cases of the sum-rank metric, they coincide with Reed-Solomon codes (Hamming metric) and Gabidulin codes (rank…
We improve the method in \cite{Seidl:10} for increasing the finite-lengh performance of polar codes by protecting specific, less reliable symbols with simple outer repetition codes. Decoding of the scheme integrates easily in the known…
Polynomial remainder codes are a large class of codes derived from the Chinese remainder theorem that includes Reed-Solomon codes as a special case. In this paper, we revisit these codes and study them more carefully than in previous work.…
An efficient decoding algorithm for horizontally u-interleaved LRPC codes is proposed and analyzed. Upper bounds on the decoding failure rate and the computational complexity of the algorithm are derived. It is shown that interleaving…
A two-part successive syndrome-check decoding of polar codes is proposed with the first part successively refining the received codeword and the second part checking its syndrome. A new formulation of the successive-cancellation (SC)…
Regenerating codes provide an efficient way to recover data at failed nodes in distributed storage systems. It has been shown that regenerating codes can be designed to minimize the per-node storage (called MSR) or minimize the…
Due to the ability to provide superior error-correction performance, the successive cancellation list (SCL) algorithm is widely regarded as one of the most promising decoding algorithms for polar codes with short-to-moderate code lengths.…
This paper presents encoding and decoding algorithms for several families of optimal rank metric codes whose codes are in restricted forms of symmetric, alternating and Hermitian matrices. First, we show the evaluation encoding is the right…
The decoding of error syndromes of surface codes with classical algorithms may slow down quantum computation. To overcome this problem it is possible to implement decoding algorithms based on artificial neural networks. This work reports a…
We present a list decoding algorithm for quaternary negacyclic codes over the Lee metric. To achieve this result, we use a Sudan-Guruswami type list decoding algorithm for Reed-Solomon codes over certain ring alphabets. Our decoding…
In this paper, we extend the work of (Abbondati et al., 2024) on decoding simultaneous rational number codes by addressing two important scenarios: multiplicities and the presence of bad primes (divisors of denominators). First, we…
The new method for Reed-Solomon codes decoding is introduced. The method is based on the star trellis decoding of the binary image of Reed-Solomon codes.
The explosion of the amount of data stored in cloud systems calls for more efficient paradigms for redundancy. While replication is widely used to ensure data availability, erasure correcting codes provide a much better trade-off between…
List-decoding of Reed-Solomon (RS) codes beyond the so called Johnson radius has been one of the main open questions since the work of Guruswami and Sudan. It is now known by the work of Rudra and Wootters, using techniques from high…