Related papers: On Unique Decoding from Insertions and Deletions
We initiate the probabilistic analysis of linear programming (LP) decoding of low-density parity-check (LDPC) codes. Specifically, we show that for a random LDPC code ensemble, the linear programming decoder of Feldman et al. succeeds in…
Polar codes are a family of capacity-achieving codes that have explicit and low-complexity construction, encoding, and decoding algorithms. Decoding of polar codes is based on the successive-cancellation decoder, which decodes in a bit-…
Because of its high data density and longevity, DNA is emerging as a promising candidate for satisfying increasing data storage needs. Compared to conventional storage media, however, data stored in DNA is subject to a wider range of errors…
DNA as a data storage medium has several advantages, including far greater data density compared to electronic media. We propose that schemes for data storage in the DNA of living organisms may benefit from studying the reconstruction…
Quantum synchronisation errors are a class of quantum errors that change the number of qubits in a quantum system. The classical error correction of synchronisation errors has been well-studied, including an insertion-deletion equivalence…
Motivated by applications in DNA-based storage and communication systems, we study deletion and insertion errors simultaneously in a burst. In particular, we study a type of error named $t$-deletion-$s$-insertion-burst ($(t,s)$-burst for…
Permutation codes were extensively studied in order to correct different types of errors for the applications on power line communication and rank modulation for flash memory. In this paper, we introduce the neural network decoders for…
Language model (LM) decoding is based on the next-token prediction (NTP) probability distribution. For neural LMs (e.g., Transformer-based), NTP distribution is essentially a softmax-regularized dot product between an encoded input context…
In this paper, a novel decoding algorithm for low-density parity-check (LDPC) codes based on convex optimization is presented. The decoding algorithm, called interior point decoding, is designed for linear vector channels. The linear vector…
In this paper, we present a novel communication channel, called the absorption channel, inspired by information transmission in neurons. Our motivation comes from in-vivo nano-machines, emerging medical applications, and brain-machine…
We study a minimal model for genome evolution whose elementary processes are single site mutation, duplication and deletion of sequence regions and insertion of random segments. These processes are found to generate long-range correlations…
We consider the topic of universal decoding with a decoder that does not have direct access to the codebook, but only to noisy versions of the various randomly generated codewords, a problem motivated by biometrical identification systems.…
We study near optimal error correction codes for real-time communication. In our setup the encoder must operate on an incoming source stream in a sequential manner, and the decoder must reconstruct each source packet within a fixed playback…
An indel refers to a single insertion or deletion, while an edit refers to a single insertion, deletion or substitution. In this paper, we investigate codes that combat either a single indel or a single edit and provide linear-time…
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 develop several analytical lower bounds on the capacity of binary insertion and deletion channels by considering independent uniformly distributed (i.u.d.) inputs and computing lower bounds on the mutual information between the input and…
In this paper, we study achievable rates of concatenated coding schemes over a deoxyribonucleic acid (DNA) storage channel. Our channel model incorporates the main features of DNA-based data storage. First, information is stored on many,…
We present the first known efficient decoding algorithm for correcting multiple insertion-deletion errors in Helberg codes and their non-binary generalizations, extending a known algorithm for correcting multiple deletion errors.
DNA data storage systems encode digital data into DNA strands, enabling dense and durable storage. Efficient data retrieval depends on coverage depth, a key performance metric. We study the random access coverage depth problem and focus on…
The errors occurring in DNA-based storage are correlated in nature, which is a direct consequence of the synthesis and sequencing processes. In this paper, we consider the memory-$k$ nanopore channel model recently introduced by Hamoum et…