Related papers: Efficient Decoding of Insertion and Deletion Error…
We study codes that can detect the exact number of deletions and insertions in concatenated binary strings. We construct optimal codes for the case of detecting up to $\del$ deletions. We prove the optimality of these codes by deriving a…
Modern program verifiers use logic-based encodings of the verification problem that are discharged by a back end reasoning engine. However, instances of such encodings for large programs can quickly overwhelm these back end solvers. Hence,…
Error correction codes are a crucial part of the physical communication layer, ensuring the reliable transfer of data over noisy channels. The design of optimal linear block codes capable of being efficiently decoded is of major concern,…
Turbo codes and CRC codes are usually decoded separately according to the serially concatenated inner codes and outer codes respectively. In this letter, we propose a hybrid decoding algorithm of turbo-CRC codes, where the outer codes, CRC…
We first give a construction of binary $t_1$-deletion-$t_2$-insertion-burst correcting codes with redundancy at most $\log(n)+(t_1-t_2-1)\log\log(n)+O(1)$, where $t_1\ge 2t_2$. Then we give an improved construction of binary codes capable…
Interior-point algorithms constitute a very interesting class of algorithms for solving linear-programming problems. In this paper we study efficient implementations of such algorithms for solving the linear program that appears in the…
A novel permutation decoding method for Reed-Muller codes is presented. The complexity and the error correction performance of the suggested permutation decoding approach are similar to that of the recursive lists decoder. It is…
In a digital communication system, information is sent from one place to another over a noisy communication channel. It may be possible to detect and correct errors that occur during the transmission if one encodes the original information…
Polar codes have emerged as the most favorable channel codes for their unique capacity-achieving property. To date, numerous works have been reported for efficient design of polar codes decoder. However, these prior efforts focused on…
We present many new results related to reliable (interactive) communication over insertion-deletion channels. Synchronization errors, such as insertions and deletions, strictly generalize the usual symbol corruption errors and are much…
A new class of exact-repair regenerating codes is constructed by combining two layers of erasure correction codes together with combinatorial block designs, e.g., Steiner systems, balanced incomplete block designs and t-designs. The…
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…
In this work, we present hardware and software implementations of flexible polar systematic encoders and decoders. The proposed implementations operate on polar codes of any length less than a maximum and of any rate. We describe the…
This paper gives a brief survey of binary single-deletion-correcting codes. The Varshamov-Tenengolts codes appear to be optimal, but many interesting unsolved problems remain. The connections with shift-register sequences also remain…
This work is on fast encoding and decoding of polar codes. We propose and detail 8-bit and 16-bit parallel decoders that can be used to reduce the decoding latency of the successive-cancellation decoder. These decoders are universal and can…
In this paper, we propose a partitioning technique that decomposes a pair of sequences with overlapping $t$-deletion $s$-substitution balls into sub-pairs, where the $^{\leq}t$-burst-deletion balls of each sub-pair intersect. This…
We propose a novel decoding algorithm for staircase codes which reduces the effect of undetected component code miscorrections. The algorithm significantly improves performance, while retaining a low-complexity implementation suitable for…
When digital data are transmitted over a noisy channel, it is important to have a mechanism allowing recovery against a limited number of errors. Normally, a user string of 0's and 1's, called bits, is encoded by adding a number of…
Correcting insertions/deletions as well as substitution errors simultaneously plays an important role in DNA-based storage systems as well as in classical communications. This paper deals with the fundamental task of constructing codes that…
The so-called fast polar decoding schedules are meant to improve the decoding speed of the sequential-natured successive cancellation list decoders. The decoding speedup is achieved by replacing various parts of the serial decoding process…