7 problems

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…

Negativity conjecture. If $\mathsf{h}^*<\mathsf{h}^{\mathrm{stab}}$, then for every $\mathsf{h}>\mathsf{h}^*$ there exists an $\mathsf{x}\in\mathcal{X}$ such that

Consider a protograph ensemble defined by an $m\times n$ protograph parity-check matrix $H$. Let $d$ be the number of non-zero entries in $H$, and let $r:[d]\to[m]$, $c:[d]\to[n]$,…

A check node is a node representing a measurement equation, and its degree is the number of neighboring variable nodes. Let $N$ check nodes have the same nonzero value. Modified Eq…

Consider an iterative decoding algorithm whose density-evolution behavior is analyzed over several stages, and suppose the current sufficient conditions are those of Theorem … can…

In MSE quantization, consider the two properties of the code and $I_{{\mathsf{c}}}$ in density evolution: starting from any $I_{{\mathsf{b}}} \in [0,1]$, density evolution converge…