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A generalized low-density parity-check (GLDPC) code is a class of codes, where single parity check nodes in a conventional low-density parity-check (LDPC) code are replaced by linear codes with higher parity check constraints. In this…

The decoding throughput in the postprocessing is one of the bottlenecks for a continuous-variable quantum key distribution (CV-QKD) system. In this paper, we propose a layered decoder to decode quasi-cyclic multi-edge type LDPC (QC-METLDPC)…

Low Density Parity Check (LDPC) codes are linear error correcting codes used in communication systems for Forward Error Correction (FEC). But, intensive computation is required for encoding and decoding of LDPC codes, making it difficult…

Ordered statistics decoding has been instrumental in addressing decoding failures that persist after normalized min-sum decoding in short low-density parity-check codes. Despite its benefits, the high computational complexity of effective…

Low-density parity-check (LDPC) codes are an important feature of several communication and storage applications, offering a flexible and effective method for error correction. These codes are computationally complex and require the…

Recently, we introduced a new class of finite alphabet iterative decoders (FAIDs) for low-density parity-check (LDPC) codes. These decoders are capable of surpassing belief propagation in the error floor region on the Binary Symmetric…

This paper proposes a highly efficient global coded-multiplexing scheme, conceptualized as Orthogonal Frequency Division Multiplexing over a finite field (FF-OFDM), for reliable multiuser communications. By utilizing a prime length cyclic…

This paper describes an efficient implementation of binning for the relay channel using low-density parity-check (LDPC) codes. We devise bilayer LDPC codes to approach the theoretically promised rate of the decode-and-forward relaying…

Fast decoding algorithms are decisive for real-time quantum error correction and for analyzing properties of error correction codes. Here, we develop variants of the union-find decoder that simplify its implementation and provide potential…

Recently, a novel lookup table based decoding method for binary low-density parity-check codes has attracted considerable attention. In this approach, mutual-information maximizing lookup tables replace the conventional operations of the…

Low-density parity-check (LDPC) codes together with belief propagation (BP) decoding yield exceptional error correction capabilities in the large block length regime. Yet, there remains a gap between BP decoding and maximum likelihood…

We propose four finite-length scaling laws to predict the frame error rate (FER) performance of spatially-coupled low-density parity-check codes under full belief propagation (BP) decoding with a limit on the number of decoding iterations…

The equivalent binary parity check matrices for the binary images of the cycle-free non-binary LDPC codes have numerous bit-level cycles. In this paper, we show how to transform these binary parity check matrices into their cycle-free…

In this paper we investigate the behavior of iteratively decoded low-density parity-check codes over the binary erasure channel in the so-called ``waterfall region." We show that the performance curves in this region follow a very basic…

Decoding quantum error-correcting codes is a key challenge in enabling fault-tolerant quantum computation. In the classical setting, linear programming (LP) decoders offer provable performance guarantees and can leverage fast practical…

We derive a new fast convergent Density Evolution algorithm for finding optimal rate Low-Density Parity-Check (LDPC) codes used over the binary erasure channel (BEC). The fast convergence property comes from the modified Density Evolution…

The performance of maximum-likelihood (ML) decoding on the binary erasure channel for finite-length low-density parity-check (LDPC) codes from two random ensembles is studied. The theoretical average spectrum of the Gallager ensemble is…

This paper outlines a three-step procedure for determining the low bit error rate performance curve of a wide class of LDPC codes of moderate length. The traditional method to estimate code performance in the higher SNR region is to use a…

We propose a quantized decoding algorithm for low- density parity-check codes where the variable node update rule of the standard min-sum algorithm is replaced with a look-up table (LUT) that is designed using an information-theoretic…

In goal-oriented communications, the objective of the receiver is often to apply a Deep-Learning model, rather than reconstructing the original data. In this context, direct learning over compressed data, without any prior decoding, holds…