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We present new lower and upper bounds for the compression rate of binary prefix codes optimized over memoryless sources according to two related exponential codeword length objectives. The objectives explored here are exponential-average…
Hybrid variational quantum algorithms (VQAs) are promising for solving practical problems such as combinatorial optimization, quantum chemistry simulation, quantum machine learning, and quantum error correction on noisy quantum computers.…
In this paper we analyze a specific class of rateless codes, called LT codes with unequal recovery time. These codes provide the option of prioritizing different segments of the transmitted data over other. The result is that segments are…
This paper presents a general approach for optimizing the number of symbols in increments (packets of incremental redundancy) in a feedback communication system with a limited number of increments. This approach is based on a tight normal…
A pruned variant of polar coding is reinvented for all binary erasure channels. For small $\varepsilon>0$, we construct codes with block length $\varepsilon^{-5}$, code rate $\text{Capacity}-\varepsilon$, error probability $\varepsilon$,…
The residual vector quantization (RVQ) technique plays a central role in recent advances in neural audio codecs. These models effectively synthesize high-fidelity audio from a limited number of codes due to the hierarchical structure among…
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…
In this paper, we assume an error such that a single insertion occurs and then a single deletion occurs. Under such an error model, this paper provides a decoding algorithm for non-binary quantum codes constructed by Matsumoto and Hagiwara.
We study two basic problems regarding edit error, i.e. document exchange and error correcting codes for edit errors (insdel codes). For message length $n$ and edit error upper bound $k$, it is known that in both problems the optimal sketch…
A permutationally invariant n-bit code for quantum error correction can be realized as a subspace stabilized by the non-Abelian group S_n. The code corresponds to bases for the trivial representation, and all other irreducible…
Hybrid variational quantum algorithms are promising for solving practical problems, such as combinatorial optimization, quantum chemistry simulation, quantum machine learning, and quantum error correction on noisy quantum computers.…
Motivated by the sequence reconstruction problem initiated by Levenshtein, reconstruction codes were introduced by Cai \emph{et al}. to combat errors when a fixed number of noisy channels are available. The central problem on this topic is…
Reconstruction codes are generalizations of error-correcting codes that can correct errors by a given number of noisy reads. The study of such codes was initiated by Levenshtein in 2001 and developed recently due to applications in modern…
We consider the problem of encoding range minimum queries (RMQs): given an array A[1..n] of distinct totally ordered values, to pre-process A and create a data structure that can answer the query RMQ(i,j), which returns the index containing…
This paper investigates the construction of linear network codes for broadcasting a set of data packets to a number of users. The links from the source to the users are modeled as independent erasure channels. Users are allowed to inform…
System-generated logs are typically converted into categorical log templates through parsing. These templates are crucial for generating actionable insights in various downstream tasks. However, existing parsers often fail to capture…
We introduce and analyse an efficient decoder for the quantum Tanner codes of that can correct adversarial errors of linear weight. Previous decoders for quantum low-density parity-check codes could only handle adversarial errors of weight…
In this paper, a new problem of transmitting information over the adversarial insertion-deletion channel with feedback is introduced. Suppose that the encoder transmits $n$ binary symbols one-by-one over a channel, in which some symbols can…
Recent years have seen rapid development in the subject of quantum coding theory, with breakthroughs on many exciting classes of codes, including quantum LDPC codes, quantum locally testable codes, and quantum codes with interesting…
Residual Vector Quantization (RVQ) has become a dominant approach in neural speech and audio coding, providing high-fidelity compression. However, speech coding presents additional challenges due to real-world noise, which degrades…