Title: DoDo-Code: an Efficient Levenshtein Distance Embedding-based Code for 4-ary IDS Channel
Venue: NeurIPS 2025
Accepted: yes
Keywords: combinatorial code

error correcting code

synchronization error correcting
Abstract: With the emergence of new storage and communication methods, the insertion, deletion, and substitution (IDS) channel has attracted considerable attention. However, many topics on the IDS channel and the associated Levenshtein distance remain open, making the invention of a novel IDS-correcting code a hard task. Furthermore, current studies on single-IDS-correcting code misalign with the requirements of applications which necessitates the correcting of multiple errors. Compromise solutions have involved shortening codewords to reduce the chance of multiple errors. However, the code rates of existing codes are poor at short lengths, diminishing the overall storage density. In this study, a novel method is introduced for designing high-code-rate single-IDS-correcting codewords through deep Levenshtein distance embedding. A deep learning model is utilized to project the sequences into embedding vectors that preserve the Levenshtein distances between the original sequences. This embedding space serves as a proxy for the complex Levenshtein domain, within which algorithms for codeword search and segment correcting is developed. While the concept underpinning this approach is straightforward, it bypasses the mathematical challenges typically encountered in code design. The proposed method results in a code rate that outperforms existing combinatorial solutions, particularly for designing short-length codewords.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper introduces a novel algorithm for designing high-code-rate single-IDS-correcting codewords through a deep Levenshtein distance embedding. The method is composed from a CNN based Siamese neural network that embeds symbol sequences in a Euclidian sub-space. The embedding is trained to preserve the Levenshtein distance between the original sequences.\n\nThe learned embeddings offer a solution for IDS channels decoding in two main aspects:\n\n1. The proposed DoDo-Code achieves a code rate that surpasses the state-of-the-art and shows characteristics of “optimality” when code length n is small.\n\n2. With one edit operation corrupted codewords can be firmly corrected, the computational complexity is effectively reduced to O(n) of the decoder to correct IDS errors.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n1. The paper is well written and easy to understand.\n2. The proposed DoDo-Code achieves a state-of-the-art code rate compared to existing methods in the literature.\n2. The learned Levenshtein distance embedding enables a K-d tree–based segment correction procedure. This procedure has a time complexity between O(n) and O(n^2), depending on the number of queries, offering a performance advantage over existing methods.\n3. The reported experiments validate the code rate and correction time complexity claims for small code length (n). \n  \nWeaknesses:\n\n1. From a ML and deep learning perspective, the work presents no methodological advancements.\n2. The empirical evaluation of the correction capabilities and time complexity of the DoDo-Code are very limited, and is applied only on segments obtained by randomly one edit modification on the codewords. No evaluations on real world data sequences/segments were provided.\n3. Space complexity is not addressed, as the proposed method require storing the K-d tree and trained NNs together with the DoDo-Code code book.\n4. The use of the DoDo-Code for larger values of n is not discussed.\n5. The claim for \"minimal redundancy achievable\" is not formally proved.\n\nQUESTIONS:\n1. At what code length n does the DoDo-Code become computationally impractical? Have you conducted experiments for larger values of n, and does the performance advantage over existing methods persist at those scales?\n\nLIMITATIONS:\nThe overhead in terms of space is not addressed.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}

comments: SUMMARY:
This paper deals with coding for DNA storage. This problem is very popular in the research community as DNA based storage has a huge capacity. Sequencing operation is error prone and the errors which we can observe are not usual substitution errors but insertions and deletions. So, in order to deal with such errors new coding methods are required. Actually, such errors were already considered in the literature by Varshamov, Tenengoltz, Levenstein and others, these errors are a particular case of so-called asymmetric errors. But the problem is solved only for insertion or deletion of 1 symbol. The authors address the problem and propose new codes and embedding-based decoders that can deal with insertions, deletions and substitutions (IDS).

STRENGTHS AND WEAKNESSES:
The paper is well-written, clear and proposes rather interesting approach.

The main weaknesses are as follows. The usual coding task is to construct exponential number of codewords, e.g. $2^{100}$. Here the number of codewords is small (such that we can perform brute force search).

The rate comparison is not clear for me. The VT codes are optimal codes that are guaranteed to correct one error. You perform comparison in different conditions (probabilistic ones). This should be mentioned explicitly.

QUESTIONS:
- What is the memory complexity of K-d tree?
- Please mention the numbers of codewords in the constructed codes.
- What about long IDS correcting codes? Can the proposed approach be useful for this task?

LIMITATIONS:
The codes are short and contain small amount of codewords.
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-07-02

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces DoDo-Code, a novel method introduced for designing high-code-rate single-IDS-correcting codewords through using deep Levenshtein distance embedding. The method leverages a Siamese neural network to map sequences (codewords) into an embedding space that preserves Levenshtein distances, then uses this space as a proxy for complex distance computations in both codeword search and error correction. The approach targets short-length codewords where existing combinatorial methods have poor code rates.\nThe authors make three key contributions: (1) a deep embedding method that approximates Levenshtein distances using squared Euclidean distance in embedding space, (2) a greedy codeword search algorithm that selects sequences (codewords) with lowest probability density function values to maximize code rate, and (3) a fast error correction method using K-d tree search in embedding space. Experiments on 4-ary codes demonstrate superior code rates compared to state-of-the-art combinatorial methods for short codewords.\n\nSTRENGTHS AND WEAKNESSES:\nThe paper presents a creative approach using deep learning by mapping sequences to embedding vectors and leveraging this embedding space as a proxy for the complex Levenshtein domain. A novel codeword searching algorithm was introduced in the embedding space to maximize the codebook, thereby achieving high-code-rate. Additionally, a decoding algorithm was integrated into the Euclidean embedding space using a K-d tree rather than operating in the Levenshtein domain, thereby reducing computational complexity.\n\nWeaknesses: Some sections (e.g. 3.2) of the paper rely on concepts that are explained somewhat briefly. Providing more illustrative explanations or examples could improve clarity and make the overall approach easier to follow.\n\nQUESTIONS:\n1. The paper lacks clarity about the exact filtering criterion in the greedy search algorithm. In Section 3.2, you describe \"filtering out the neighboring sequences\" without specifying the distance threshold. However, examination of the code reveals that all sequences with Levenshtein distance ≤2 from each selected codeword are removed, not just distance-1 neighbors as the term \"neighboring sequences\" typically implies. This critical detail should be explicitly stated in the paper for algorithmic clarity.\n2. A pseudocode of the embedding-based greedy search algorithm may be included in the paper for better understanding.\n3. Table 1 demonstrates that the revised loss function yields larger codebooks compared to the original loss when used with embedding-based greedy search. However, the paper lacks a clear explanation connecting the loss function design to this improved performance. Could the authors explain how the revised loss function's approach affects the embedding space structure and subsequent PDF-based codeword selection, ultimately leading to the larger codebooks observed\n4. Could the authors provide more intuition behind the use of low probability density regions in the embedding space for codeword selection? A brief explanation how low-density embeddings correspond to fewer Levenshtein neighbors would make the strategy easier to understand.\n\nLIMITATIONS:\nYes, the authors do address the limitations.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces DoDo-Code, a deep learning–based method for constructing error-correcting codes over a 4-ary alphabet that are resilient to single insertion, deletion, or substitution errors. The core idea is to embed codewords into a continuous space where distances approximate the Levenshtein metric. This learned embedding enables efficient codeword construction through greedy search, and fast decoding using K-d trees. The motivation stems from the high computational complexity of directly computing Levenshtein distances in the discrete code space. By operating in a continuous proxy space learned by a neural encoder, the authors exploit the structured neighborhood geometry to select codewords more systematically, avoiding random or exhaustive search. For decoding, candidate codewords are first retrieved based on proximity in the embedding space, and then the exact Levenshtein distance is computed over this smaller subset to identify the closest match.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\n\n1. Application is niche but novel. Successfully addresses the practical problem that existing combinatorial codes have poor rates at short lengths. Specifically, exploiting the multivariate embedding to replace random search over the codeword space with a more structured tree-based greedy search for error correction is very interesting.\n\n2. Performance seems to be very good for short code lengths (N=10). While a code length of 10 is considered too small for general codes, within IDS codes it appears to be an acceptable choice for a small set of applications. Within this space, the practical performance (inference time for a given number of corrections) is impressive. \n\nWeaknesses \n\n1. Overly strong claims such as “...embedding vectors carry the properties of their original sequences from the Levenshtein distance domain...” are made without sufficient justification. Many such statements assume a high level of familiarity with the topic, making it difficult to fully appreciate the actual contributions.\n\n2. The overall research theme seems more suited to an information theory or wireless communication venue than NeurIPS. The contributions from a deep learning perspective are few to none, with most innovations stemming from the clever application of deep learning to solve error correction problems. For instance, there is a large body of work on \"neural channel codes,\" which similarly transform discrete codewords into continuous embeddings to improve error correction. Refer to [1], [2], [3].\n\nAgain, without detracting from the contributions of the paper, in my opinion, the work may be better appreciated by the coding theory community than the NeurIPS community, as the majority of the contributions lie in cleverly identifying the lack of structure needed for faster decoding of IDS codes in discrete space and bridging this gap by transforming the codes into continuous space using standard deep learning techniques.\n\n1. ProductAE: Toward Training Larger Channel Codes based on Neural Product Codes, ICC 2022\n\n2. DeepIC+: Learning Codes for Interference Channels, TWS 2023\n\n3. Generalized Concatenated Polar Auto-Encoder: A Deep Learning Based Polar Coding Scheme, GLOBECOM 2024\n\nQUESTIONS:\nNo specific questions\n\nLIMITATIONS:\nNone", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-04"}