Related papers: Error Floor Approximation for LDPC Codes in the AW…
A new method for analyzing low density parity check (LDPC) codes and low density generator matrix (LDGM) codes under bit maximum a posteriori probability (MAP) decoding is introduced. The method is based on a rigorous approach to spin…
In this article we present a construction of error correcting codes, that have representation as very sparse matrices and belong to the class of Low Density Parity Check Codes. LDPC codes are in the classical Hamming metric. They are very…
Error exponents characterize the exponential decay, when increasing message length, of the probability of error of many error-correcting codes. To tackle the long standing problem of computing them exactly, we introduce a general,…
This paper proposes a method for designing error correction codes by combining a known coding scheme with an autoencoder. Specifically, we integrate an LDPC code with a trained autoencoder to develop an error correction code for intractable…
Sparse superposition codes are a recent class of codes introduced by Barron and Joseph for efficient communication over the AWGN channel. With an appropriate power allocation, these codes have been shown to be asymptotically…
In this work, we show that polar belief propagation (BP) decoding exhibits an error floor behavior which is caused by clipping of the log-likelihood ratios (LLR). The error floor becomes more pronounced for clipping to smaller LLR-values.…
For an arbitrary degree distribution pair (DDP), we construct a sequence of low-density parity-check (LDPC) code ensembles with girth growing logarithmically in block-length using Ramanujan graphs. When the DDP has minimum left degree at…
We propose a new coding scheme using only one lattice that achieves the $\frac{1}{2}\log(1+\SNR)$ capacity of the additive white Gaussian noise (AWGN) channel with lattice decoding, when the signal-to-noise ratio $\SNR>e-1$. The scheme…
For LDPC codes operating over additive white Gaussian noise channels and decoded using message-passing decoders with limited precision, absorbing sets have been shown to be a key factor in error floor behavior. Focusing on this scenario,…
We propose a systematic design of protograph-based quasi-cyclic (QC) low-density parity-check (LDPC) codes with low error floor. We first characterize the trapping sets of such codes and demonstrate that the QC structure of the code…
In this work, we investigate the decoding of Low-Density Parity-Check (LDPC) codes using informed dynamic scheduling algorithms that require a reduced number of iterations. In particular, we devise the weighted residual layered belief…
We obtain exact expressions for the asymptotic behaviour of the average probability of the block decoding error for ensembles of regular low density parity check error correcting codes, by employing diagrammatic techniques. Furthermore, we…
This paper is concerned with bounds on the maximum-likelihood (ML) decoding error probability of Reed-Solomon (RS) codes over additive white Gaussian noise (AWGN) channels. To resolve the difficulty caused by the dependence of the Euclidean…
Elementary trapping sets (ETSs) are the main culprits for the performance of LDPC codes in the error floor region. Due to the large quantity, complex structures, and computational difficulties of ETSs, how to eliminate dominant ETSs in…
We study the performance of nonbinary low-density parity-check (LDPC) codes over finite integer rings over two channels that arise from the Lee metric. The first channel is a discrete memory-less channel (DMC) matched to the Lee metric. The…
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…
We consider the effect of LLR saturation on belief propagation decoding of low-density parity-check codes. Saturation occurs universally in practice and is known to have a significant effect on error floor performance. Our focus is on…
When binary linear error-correcting codes are used over symmetric channels, a relaxed version of the maximum likelihood decoding problem can be stated as a linear program (LP). This LP decoder can be used to decode error-correcting codes at…
We study the decoding transition for quantum error correcting codes with the help of a mapping to random-bond Wegner spin models. Families of quantum low density parity-check (LDPC) codes with a finite decoding threshold lead to both known…
Consider communication over a binary-input memoryless output-symmetric channel with low density parity check (LDPC) codes and maximum a posteriori (MAP) decoding. The replica method of spin glass theory allows to conjecture an analytic…