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Speculative Decoding (SD) accelerates inference in large language models by using a smaller draft model to propose tokens, which are then verified by a larger target model. However, the throughput gains of SD are fundamentally limited by a…
Quantum low-density parity-check codes are a promising candidate for fault-tolerant quantum computing with considerably reduced overhead compared to the surface code. However, the lack of a practical decoding algorithm remains a barrier to…
Much progress has been made on decoding algorithms for error-correcting codes in the last decade. In this article, we give an introduction to some fundamental results on iterative, message-passing algorithms for low-density parity check…
We propose a new fast word embedding technique using hash functions. The method is a derandomization of a new type of random projections: By disregarding the classic constraint used in designing random projections (i.e., preserving pairwise…
Diffusion Large Language Models (dLLMs) have achieved rapid progress, viewed as a promising alternative to the autoregressive paradigm. However, most dLLM decoders still adopt a global confidence threshold, and do not explicitly model local…
We consider a point-to-point communication scenario where the receiver maintains a specific linear function of a message vector over a finite field. When the value of the message vector undergoes a sparse update, the transmitter broadcasts…
Quantum error correction (QEC) is required for large-scale computation, but incurs a significant resource overhead. Recent advances have shown that by jointly decoding logical qubits in algorithms composed of transversal gates, the number…
The order statistics based list decoding techniques for linear binary block codes of small to medium block length are investigated. The construction of the list of the test error patterns is considered. The original order statistics…
Several recently proposed code-based cryptosystems base their security on a slightly generalized version of the classical (syndrome) decoding problem. Namely, in the so-called restricted (syndrome) decoding problem, the error values stem…
In this paper, we introduce DICOD, a convolutional sparse coding algorithm which builds shift invariant representations for long signals. This algorithm is designed to run in a distributed setting, with local message passing, making it…
The practice of speculative decoding, whereby inference is probabilistically supported by a smaller, cheaper, ``drafter'' model, has become a standard technique for systematically reducing the decoding time of large language models. This…
Practically good error-correcting codes should have good parameters and efficient decoding algorithms. Some algebraically defined good codes such as cyclic codes, Reed-Solomon codes, and Reed-Muller codes have nice decoding algorithms.…
The generalized Hamming weight of linear codes is a natural generalization of the minimum Hamming distance. They convey the structural information of a linear code and determine its performance in various applications, and have become one…
Coded distributed computation has become common practice for performing gradient descent on large datasets to mitigate stragglers and other faults. This paper proposes a novel algorithm that encodes the partial derivatives themselves and…
A new class of space time codes with high performance is presented. The code design utilizes tailor-made permutation codes, which are known to have large minimal distances as spherical codes. A geometric connection between spherical and…
Effective iterative decoding of short BCH codes faces two primary challenges: identifying an appropriate parity-check matrix and accelerating decoder convergence. To address these issues, we propose a systematic scheme to derive an…
In this paper, we propose an efficient reliability based segmentation-discarding decoding (SDD) algorithm for short block-length codes. A novel segmentation-discarding technique is proposed along with the stopping rule to significantly…
Chase-like decoding algorithms are a popular choice for soft-input decoding of algebraic codes. In this paper, we evaluate the performance of different test pattern sets using three methods. For test pattern sets with a certain structure…
The weighted-Hamming metric generalizes the Hamming metric by assigning different weights to blocks of coordinates. It is well-suited for applications such as coding over independent parallel channels, each of which has a different level of…
This study investigates the problem of learning linear block codes optimized for Belief-Propagation decoders significantly improving performance compared to the state-of-the-art. Our previous research is extended with an enhanced system…