Related papers: Trapping Set Enumerators for Repeat Multiple Accum…
Trellises are crucial graphical representations of codes. While conventional trellises are well understood, the general theory of (tail-biting) trellises is still under development. Iterative decoding concretely motivates such theory. In…
Subcode-ensemble decoders improve iterative decoding by running multiple decoders in parallel over carefully chosen subcodes, increasing the likelihood that at least one decoder avoids the dominant trapping structures. Achieving strong…
Low density parity-check (LDPC) codes are a class of linear block codes that are decoded by running belief propagation (BP) algorithm or log-likelihood ratio belief propagation (LLR-BP) over the factor graph of the code. One of the…
The chain length of a set family $\mathcal{S} \subseteq 2^{[m]}$ is the largest ascending sequence of sets in containment order in the union-closure of $\mathcal S$. In this work, we provide a significantly simpler and more optimal…
This paper presents several new construction techniques for low-density parity-check (LDPC) and systematic repeat-accumulate (RA) codes. Based on specific classes of combinatorial designs, the improved code design focuses on high-rate…
In the last decade there has been a great interest in extending results for codes equipped with the Hamming metric to analogous results for codes endowed with the rank metric. This work follows this thread of research and studies the…
This paper proposes a novel maximum-likelihood (ML) soft-decision decoding framework for linear block codes, termed error-building decoding (EBD). The complete decoding process can be performed using only the parity-check matrix, without…
The performance and the decoding complexity of a novel coding scheme based on the concatenation of maximum distance separable (MDS) codes and linear random fountain codes are investigated. Differently from Raptor codes (which are based on a…
This paper introduces a new methodology for using LLM-based systems for accurate and efficient semantic tagging of UN Security Council resolutions. The main goal is to leverage LLM performance variability to build ensemble systems for data…
We investigate random spatially coupled low-density parity-check (SC-LDPC) code ensembles over finite fields. Under different variable-node edge-spreading rules, the random Tanner graphs of several coupled ensembles are defined by multiple…
The design of low-density parity-check (LDPC) code ensembles optimized for a finite number of decoder iterations is investigated. Our approach employs EXIT chart analysis and differential evolution to design such ensembles for the binary…
Some new results are derived concerning random coding error exponents and expurgated exponents for list decoding with a deterministic list size $L$. Two asymptotic regimes are considered, the fixed list-size regime, where $L$ is fixed…
Decoding sequences that stem from multiple transmissions of a codeword over an insertion, deletion, and substitution channel is a critical component of efficient deoxyribonucleic acid (DNA) data storage systems. In this paper, we consider a…
In this paper, we propose a characterization of elementary trapping sets (ETSs) for irregular low-density parity-check (LDPC) codes. These sets are known to be the main culprits in the error floor region of such codes. The characterization…
A lower bound on the maximum likelihood (ML) decoding error exponent of linear block code ensembles, on the erasure channel, is developed. The lower bound turns to be positive, over an ensemble specific interval of erasure probabilities,…
Block codes are considered for improving the reliability of messages stored in a computer memory with both stuck-at defects and random errors. It is assumed that the side information about the state of the defects is available to the…
This paper provides simple lower bounds on the number of iterations which is required for successful message-passing decoding of some important families of graph-based code ensembles (including low-density parity-check codes and variations…
The capability of accurately determining code similarity is crucial in many tasks related to software development. For example, it might be essential to identify code duplicates for performing software maintenance. This research introduces…
Cumulative weight enumerators of random linear codes are introduced, their asymptotic properties are studied, and very sharp thresholds are exhibited; as a consequence, it is shown that the asymptotic Gilbert-Varshamov bound is a very sharp…
Recent Large Language Models (LLMs) have demonstrated remarkable capabilities in generating text that closely resembles human writing across wide range of styles and genres. However, such capabilities are prone to potential abuse, such as…