28 problems

Capacity-achieving conjecture. GSC-PCC ensembles with any convolutional component codes should be capable of achieving the binary erasure channel capacity.

Let $gap$ denote the gap to channel capacity, let $\langle P_e\rangle$ denote the average probability of error, and consider sparse-graph codes with iterative decoding. Khandekar–M…

Consider a sequence of capacity-achieving degree distributions, and let $\delta$ denote the gap to channel capacity. Let the number of decoding iterations required to approach capa…

Consider transmission over a general memoryless channel, with maximum a posteriori (MAP) decoding and belief propagation (BP) decoding; in the binary erasure channel (BEC), these d…

Consider an LDPC-code ensemble and its MAP EXIT function. The Maxwell construction is the balance-of-areas prescription relating the MAP EXIT curve to the area under the belief-pro…

Let $({\lambda},{\rho})$ be a dd pair, let $P({\tt{x}})$ be the polynomial defined in the paper, and let $\epsilon({\tt{x}})$ denote the associated channel-parameter function. The…

Let an APP decoder be used for a forward-error-correction (FEC) code, such as a Turbo code or Polar code. Uniform Lipschitz continuity means that the decoder's input-output mapping…

Let a stabilizer-induced subgraph be a subgraph induced by a subset of stabilizer generators in the decoding graph, and let a trapping set (TS) be the relevant decoding-dynamical s…

QTS isomorphism conjecture. The isomorphic nature of the two disjoint subsets results in a set of qubits at level $2$ of $T(v_r)$ for every $v_r\in V_i$, which limits the qubit sep…

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…

Let D-IRA ring codes denote doubly-irregular repeat-accumulate codes over integer rings, and let $d_c$ denote check-node degree. D-IRA performance conjecture. The performance advan…

Let D-IRA ring codes be doubly-irregular repeat-accumulate codes over integer rings, with check-node degree denoted by $d_c$. D-IRA ring-code conjecture. The performance improvemen…

DRSD error-floor conjecture. With a proper choice of the parameters, the proposed DRSD should not have a worse error floor than a plain iterative EaE decoder for product codes with…

For spatially-coupled SC-TC with Gray mapping, let the BP threshold be the channel threshold obtained under belief-propagation decoding, and let the MAP threshold be the threshold…

Let $\alpha=C/R$, and let $q^{\mathrm{BEC}}_t$ and $q^{\mathrm{BSC}}_t$ be the dynamical systems initialized at $x_0$ by … and … Here $\iota^{\mathrm{BP}}_\ell$ is the soft informa…

Let $q^{\mathrm{BEC}}_\ell(x)$ denote the state after $\ell$ iterations of the BEC dynamical system for a code ensemble generated by a monotone function, initialized at $x$. Unique…

Let an LDPC decoding algorithm use the min-sum (MS) algorithm with noise perturbations, and let a spurious fixed-point attractor be an attractor of the decoding dynamics that does…

BEC speed upper-bound conjecture. The upper bound of the speed on the BEC is also an upper bound of the speed on the other channels with the same channel entropy.

Consider certain families of iteratively decoded code ensembles and general channel models. Let $\bar{\mathbb{P}}^{(n)}_{e,\operatorname{it}}(p)$ denote the optimal error probabili…

Let $\mathcal{C}$ be an LDPC code, let $\mathcal{D}$ be a decoder diversity set, and let $\mathcal{E}^{[t]}(\Lambda^{(A,B)})$ be the union of the error sets associated with all tra…

Let TPPC and single-level LDPC denote the two coding schemes being compared, and let the sector length of each code tend to infinity. Asymptotic TPPC SNR-gain conjecture. As the se…

Let $Y_t=\{N(t),\bar{R}(t)\}$ be the decoder state at time $t$, let $H_t$ be the process history, and let $f(Y_t)$ denote the expected one-step drift computed under the uniform edg…

Let $t$ denote the discrete decoding time, let $R_{i,j,k}(t)$ be the number of edges connected to IVNs of type $r_{i,j,k}$, and let $\bar{R}_{i,j,k}(t)=E[R_{i,j,k}(t)\mid H_t]$, wh…

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…

Fossorier's conjecture. Owing to the inaccurate reliability information delivered at the last iteration of BP decoding, order-$p$ OSD in cascade connection with BP should result in…