66 problems

Let terminated spatially-coupled low-density parity-check (SC-LDPC) codes be constructed from an underlying LDPC code ensemble, and let their BP threshold and the MAP threshold of…

Consider a smooth family of binary-input memoryless symmetric channels ordered by degradation, with channel parameter $\epsilon$ equal to the channel entropy. Let…

Consider the binary Type-II LDPC construction with $l=4$, where $d$ denotes the minimum distance of the code and $d_L$ denotes its minimum pseudo-weight under the relevant decoding…

Generalized-polygon pseudocodeword-weight conjecture. We conjecture that incidence graphs of generalized $N$-gons yield LDPC codes with $w_{\min}$ very close to $d_{\min}$ and, par…

Type II girth-eight tree-bound conjecture. We conjecture that, in general,

Consider the two schemes described in the source: linear LDPC encoding and decoding directly over a non-symmetric channel, and the corresponding LDPC coset-code ensemble obtained t…

Consider a code ensemble with edge-perspective variable-node degree distribution satisfying $\lambda_2>0$, and let $l$ denote the number of density-evolution iterations. Although t…

Consider density evolution for a terminated LDPC convolutional code with arbitrary termination length $L$, using the window updating schedule described in the paper. Starting from…

Conjecture on the structure underlying their performance. The observed performance results are a consequence of the column-weight-four array codes having minimum distance significa…

Let the three schemes in Figure (a), Figure (b), and Figure (c) be the coding schemes discussed in the paper, and interpret codeword-averaged performance as the performance average…

Refined scaling conjecture. As $n$ tends to infinity,

Let $h_n$ denote the normalized conditional entropy in the code ensemble, and let $\tau$ and $\rho$ be the degree sequences appearing in Theorem 1. For each admissible random varia…

Let $w$ and $n$ be positive integers with $w\mid n$. Let $C\leq\mathbb{F}_2^n$ be a linear code spanned by vectors of Hamming weight at most $w$, and suppose that … For…

The tail sequence is used for synchronization in space data systems employing short low-density parity-check codes, and $E_b/N_0$ denotes the energy-per-bit-to-noise-power-spectral…

Let good quantum low-density parity-check (LDPC) codes be defined on expander graphs, with the associated Hamiltonians given by sums of products of a bounded number of Pauli matric…

Let the LDPC code and CPM-modulated system described above be punctured using a puncturing pattern selected by an optimization procedure, rather than the random puncturing consider…

Proximal decoding is an optimization-based decoding method in which the estimate may move toward the final codeword without convergence being achieved. Proximal-decoding convergenc…

DIA-metric incompatibility conjecture. The forged metric of DIA has disrupted the proper assumptions underlying PB-OSD's operation.

Uninformative-failure-trajectories conjecture. Because of the poor performance of NMS, the trajectories of its decoding failures hold no informative clues for DIA to improve the bi…

Decoding-trajectory conjecture. Harnessing the entire decoding trajectory of the a posteriori log-likelihood ratios through neural networks could yield a more reliable metric, more…

Rotor-code conjecture. Under these assumptions, $\phi_\infty(\mathcal{S})$ represents a good quantum LDPC rotor code.

Large-degree variable-node mismatch conjecture. The decoder is in general able to overcome this mismatch for VNs with a large number of incoming messages.

Let $\mathcal{A}$ and $\mathcal{B}$ be the classical codes used in the lifted product construction over a group $G$, and let $\mathcal{A}\otimes_G\mathcal{B}$ denote their lifted p…

A QC-LDPC code is a quasi-cyclic low-density parity-check code. Performance-limitation conjecture. The class of QC-LDPC codes has limited achievable performance. This conjecture as…

Conjecture on Beemer et al.'s search. The limited search in Beemer et al. suffers from the same problems as the methods proposed by Mitchell et al. and Esfahanizadeh et al.