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Existing approaches typically rely on fixed length penalties, but such penalties are hard to tune and fail to adapt to the evolving reasoning abilities of LLMs, leading to suboptimal trade-offs between accuracy and conciseness. To address…
The capacity achieving probability mass function (PMF) of a finite signal constellation with an average power constraint is in most cases non-uniform. A common approach to generate non-uniform input PMFs is Huffman shaping, which consists…
Constrained codes are used to prevent errors from occurring in various data storage and data transmission systems. They can help in increasing the storage density of magnetic storage devices, in managing the lifetime of electronic storage…
We introduce a new quantum optimization algorithm for dense Linear Programming problems, which can be seen as the quantization of the Interior Point Predictor-Corrector algorithm \cite{Predictor-Corrector} using a Quantum Linear System…
A new class of folded subspace codes for noncoherent network coding is presented. The codes can correct insertions and deletions beyond the unique decoding radius for any code rate $R\in[0,1]$. An efficient interpolation-based decoding…
Recent years have witnessed the emergence of textual commonsense knowledge bases, aimed at providing more nuanced and context-rich knowledge. The integration of external commonsense into language models has been shown to be a key enabler in…
We propose a method to improve traditional character-based PPM text compression algorithms. Consider a text file as a sequence of alternating words and non-words, the basic idea of our algorithm is to encode non-words and prefixes of words…
The Run Length Encoding (RLE) compression method is a long standing simple lossless compression scheme which is easy to implement and achieves a good compression on input data which contains repeating consecutive symbols. In its pure form…
Just as the Hamming weight spectrum of a linear block code sheds light on the performance of a maximum likelihood decoder, the pseudo-weight spectrum provides insight into the performance of a linear programming decoder. Using properties of…
Fully homomorphic encryption (FHE) allows an untrusted party to evaluate arithmetic cir- cuits, i.e., perform additions and multiplications on encrypted data, without having the decryp- tion key. One of the most efficient class of FHE…
Training and serving Large Language Models (LLMs) require partitioning data across multiple accelerators, where collective operations are frequently bottlenecked by network bandwidth. Lossless compression using Huffman codes is an effective…
Ensuring safety is a foundational requirement for large language models (LLMs). Achieving an appropriate balance between enhancing the utility of model outputs and mitigating their potential for harm is a complex and persistent challenge.…
The rank decoding problem has been the subject of much attention in this last decade. This problem, which is at the base of the security of public-key cryptosystems based on rank metric codes, is traditionally studied over finite fields.…
An efficient decoding algorithm for horizontally u-interleaved LRPC codes is proposed and analyzed. Upper bounds on the decoding failure rate and the computational complexity of the algorithm are derived. It is shown that interleaving…
The linearly constrained matrix rank minimization problem is widely applicable in many fields such as control, signal processing and system identification. The tightest convex relaxation of this problem is the linearly constrained nuclear…
A new protograph-based framework for message passing (MP) decoding of low density parity-check (LDPC) codes with Hamming weight amplifiers (HWAs), which are used e.g. in the NIST post-quantum crypto candidate LEDAcrypt, is proposed. The…
The complexity-performance trade-off is a fundamental aspect of the design of low-density parity-check (LDPC) codes. In this paper, we consider LDPC codes for the binary erasure channel (BEC), use code rate for performance metric, and…
Typically, forward error correction (FEC) codes are designed based on the minimization of the error rate for a given code rate. However, for applications that incorporate hybrid automatic repeat request (HARQ) protocol and adaptive…
It is well known that time dependent Hamilton-Jacobi-Isaacs partial differential equations (HJ PDE), play an important role in analyzing continuous dynamic games and control theory problems. An important tool for such problems when they…
In order to understand the performance of a code under maximum-likelihood (ML) decoding, one studies the codewords, in particular the minimal codewords, and their Hamming weights. In the context of linear programming (LP) decoding, one's…