arXiv subjects

Yajuan Liu

Publications and source records attributed to Yajuan Liu.

6 recordsLinked to original sources

arXiv2026

One Burst of t-Deletion and One Burst of t-Substitution Error-Correcting Codes

Synchronization errors, including insertions, deletions, and substitutions, may occur in bursts in communication systems such as DNA data storage, file synchronization, and magnetic recording. In this paper, we study an error model con?sisting of one burst of t-deletions and one burst of t-substitutions. By reformulating the original sequence into a matrix form, we propose an explicit construction of error-correcting codes capable of correcting one burst of t-deletions and one burst of t-substitutions with O(log n) redundancy.

cs.IT↗

arXiv2026

Error-Correcting Codes for Two Bursts of t1-Deletion-t2-Insertion with Reduced Complexity

Burst errors involving simultaneous insertions, deletions, and substitutions occur in practical scenarios, including DNA data storage and document synchronization, motivating the development of channel codes that can correct such errors. In this paper, we construct error-correcting codes (ECCs) capable of handling multiple bursts of t1-deletion-t2-insertion ((t1, t2)-DI) errors, where each burst consists of t1 deletions followed by t2 insertions in a binary sequence. We make three key contributions: First, we establish the fundamental equivalence among (i) ECCs correcting two bursts of (t1, t2)-DI errors, (ii) ECCs correcting two bursts of (t2, t1)-DI errors, and (iii) ECCs correcting one burst of (t1, t2)-DI together with one burst of (t2, t1)-DI errors. Then, we derive lower and upper bounds on the code size of two-burst (t1, t2)-DI ECCs, which can naturally be extended to the case of multiple bursts. Finally, we present constructions of ECCs correcting two bursts of (t1, t2)-DI errors. Compared with codes obtained via the direct application of the syndrome compression technique, the proposed constructions achieve substantially improved computational efficiency.

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arXiv2025

Error Correcting Codes for Segmented Burst-Deletion Channels

We study segmented burst-deletion channels motivated by the observation that synchronization errors commonly occur in a bursty manner in real-world settings. In this channel model, transmitted sequences are implicitly divided into non-overlapping segments, each of which may experience at most one burst of deletions. In this paper, we develop error correction codes for segmented burst-deletion channels over arbitrary alphabets under the assumption that each segment may contain only one burst of t-deletions. The main idea is to encode the input subsequence corresponding to each segment using existing one-burst deletion codes, with additional constraints that enable the decoder to identify segment boundaries during the decoding process from the received sequence. The resulting codes achieve redundancy that scales as O(log b), where b is the length of each segment.

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arXiv2025

Constrained Error-Correcting Codes for Efficient DNA Synthesis

DNA synthesis is considered as one of the most expensive components in current DNA storage systems. In this paper, focusing on a common synthesis machine, which generates multiple DNA strands in parallel following a fixed supersequence,we propose constrained codes with polynomial-time encoding and decoding algorithms. Compared to the existing works, our codes simultaneously satisfy both l-runlength limited and ε-balanced constraints. By enumerating all valid sequences, our codes achieve the maximum rate, matching the capacity. Additionally, we design constrained error-correcting codes capable of correcting one insertion or deletion in the obtained DNA sequence while still adhering to the constraints.

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arXiv2025

A New Cooperative Repair Scheme with Small Finite Field for Distributed Storage Systems

In this paper, we consider the multiple failures in the distributed storage systems under the cooperative repair model. We introduce a new cooperative repair scheme for the (n,k,d,N) minimum storage regenerating (MSR) codes proposed by Ye and Barg (IEEE Transactions on Information Theory, vol. 64, no. 4, 2017), which is capable of repairing any h failed nodes by connecting any k \le d \le n - h helper nodes. Compared to prior cooperative repair schemes for (n,k,d,N) MSR codes, which require a finite field F_q with q \ge (d - k + 1)n, the proposed approach reduces the field size to q \ge n + 1.

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arXiv2022

A New Cooperative Repair Scheme with k + 1 Helper Nodes for (n, k) Hadamard MSR codes with Small Sub-packetization

Cooperative repair model is an available technology to deal with multiple node failures in distributed storage systems. Recently, explicit constructions of cooperative MSR codes were given by Ye (IEEE Transactions on Information Theory, 2020) with sub-packetization level $(d-k+h)(d-k+1)^n$. Specifically, the sub-packetization level is $(h+1)2^n$ when $d=k+1$. In this paper, we propose a new cooperative repair scheme by means of the inter-instance and intra-instance pairing inherited from the perfect code which reduces the sub-packetization to $2^n$ when $(h+1)|2^n$ and $(2\ell+1)2^n$ when $h+1=(2\ell+1)2^m$ for $m\ge 0$, $\ell\ge 1$ with $d=k+1$ helper nodes. That is to say, the sub-packetization is $h + 1 $ times or $2^m$ times less than Ye's. It turned out to be the best result so far known.

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