Related papers: Fountain Codes under Maximum Likelihood Decoding
As one of their many applications, large language models (LLMs) have recently shown promise in automating register transfer level (RTL) code generation. However, conventional LLM decoding strategies, originally designed for natural…
Recursive decoding techniques are considered for Reed-Muller (RM) codes of growing length $n$ and fixed order $r.$ An algorithm is designed that has complexity of order $n\log n$ and corrects most error patterns of weight up to…
In this paper, we study the performance of finite-length LDPC codes in the waterfall region. We propose an algorithm to predict the error performance of finite-length LDPC codes over various binary memoryless channels. Through numerical…
Large Language Models (LLMs) have demonstrated great promise in generating code, especially when used inside an evolutionary computation framework to iteratively optimize the generated algorithms. However, in some cases they fail to…
We consider the problem of universal decoding for arbitrary unknown channels in the random coding regime. For a given random coding distribution and a given class of metric decoders, we propose a generic universal decoder whose average…
In this paper, we propose a methodology to compute the optimal finite-length coding rate for random linear network coding schemes over a line network. To do so, we first model the encoding, reencoding, and decoding process of different…
Constrained sequence codes have been widely used in modern communication and data storage systems. Sequences encoded with constrained sequence codes satisfy constraints imposed by the physical channel, hence enabling efficient and reliable…
Large language model (LLM) watermarks enable authentication of text provenance, curb misuse of machine-generated text, and promote trust in AI systems. Current watermarks operate by changing the next-token predictions output by an LLM. The…
In this letter, we develop an efficient linear programming (LP) decoding algorithm for low-density parity-check (LDPC) codes. We first relax the maximum likelihood (ML) decoding problem to a LP problem by using check-node decomposition.…
The 3D MIMO code is a robust and efficient space-time coding scheme for the distributed MIMO broadcasting. However, it suffers from the high computational complexity if the optimal maximum-likelihood (ML) decoding is used. In this paper we…
Large Language Models (LLMs) like GPT are state-of-the-art text generation models that provide significant assistance in daily routines. However, LLM execution is inherently sequential, since they only produce one token at a time, thus…
Large Language Models (LLMs) have demonstrated exceptional code generation capabilities, yet their token-level mechanisms remain underexplored, particularly in compressed models. Through systematic analysis of programming language token…
We present a new model for LT codes which simplifies the analysis of the error probability of decoding by belief propagation. For any given degree distribution, we provide the first rigorous expression for the limiting error probability as…
Fault-tolerant quantum computation (FTQC) is expected to address a wide range of computational problems. To realize large-scale FTQC, it is essential to encode logical qubits using quantum error-correcting codes. High-rate concatenated…
This paper is focused on the performance analysis of binary linear block codes (or ensembles) whose transmission takes place over independent and memoryless parallel channels. New upper bounds on the maximum-likelihood (ML) decoding error…
We consider the decoding of LDPC codes over GF(q) with the low-complexity majority algorithm from [1]. A modification of this algorithm with multiple thresholds is suggested. A lower estimate on the decoding radius realized by the new…
Multilingual Large Language Models (LLMs) have gained large popularity among Natural Language Processing (NLP) researchers and practitioners. These models, trained on huge datasets, show proficiency across various languages and demonstrate…
A class of linear block codes which simultaneously generalizes Gabidulin codes and a class of skew cyclic codes is defined. For these codes, both a Hartmann-Tzeng-like bound and a Roos-like bound, with respect to their rank distance, are…
This paper considers the achievable rates and decoding complexity of low-density parity-check (LDPC) codes over statistically independent parallel channels. The paper starts with the derivation of bounds on the conditional entropy of the…
In this paper, we represent Raptor codes as multi-edge type low-density parity-check (MET-LDPC) codes, which gives a general framework to design them for higher-order modulation using MET density evolution. We then propose an efficient…