29 problems

A quantum low-density parity-check code is a quantum error-correcting code with sparse parity checks, and an adversarial error is an error chosen without a probabilistic restrictio…

Let BB codes denote the Bivariate Bicycle codes considered with parameters $[[72,12,6]]$ under a circuit-level depolarizing noise model. Let $W$ be the decoding-window size, with t…

The trellis-based decoder and the neural polar decoder are compared through their frame error rates at various block lengths, with both decoders theoretically expected to perform s…

IRUF distance-guarantee conjecture. Given the geometric similarity between toric codes and the other three code families, IRUF does not provide a distance guarantee for rotated tor…

Let an interleaved Reed–Solomon code have rate $R$, interleaving order $s$, and suppose the errors are random. Multivariate interpolation decoding interpolates an $s+1$-variate pol…

Let $p$ be prime, and let $SL(2,\mathbb{Z}_p)$ denote the group of $2\times 2$ matrices over $\mathbb{Z}_p$ with determinant one. Consider quantum Margulis codes constructed from t…

A quantum low-density parity-check (QLDPC) code is a quantum error-correcting code represented by a sparse stabilizer parity-check matrix, and weak symmetry informally means that t…

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…

Let LSD denote the localized statistics decoding algorithm for quantum low-density parity-check codes, with clusters initialized and grown using input reliabilities. LSD's erasure-…

A $d_v$-$3$, $d_c$-$6$ QLDPC code is a quantum low-density parity-check code with variable-node degree $3$ and check-node degree $6$. An interconnected 6-cycle structure is a struc…

The $B3$ code is a quantum LDPC code whose one circulant matrix is composed of juxtaposed $6$-cycles and whose other circulant matrix has girth $10$. Girth-10 performance conjectur…

In an alternative decoding strategy, a read is assigned to a specific index only when its decoded soft information exceeds a reliability threshold, and otherwise the read is discar…

SCAN absorption-set conjecture. The absorption set under SCAN decoding is limited to the trivial permutation.

Consider a polar code with automorphisms used in automorphism-en ensemble (AE) decoding, and denote by $[\mathbbm{1}]$ the equivalence class of the identity automorphism. AE-decode…

Let $s$ be the current error $0$-chain in the bundle complex, and let its bundle projection be a $0$-chain in the base complex. A $1$-chain $w$ in the base complex is required to s…

Let $d_Z$ denote the $Z$-distance of the quantum LDPC code, and consider the proposed homology-decoding algorithm described in the paper, which uses local updates by fiber strings…

Rate-0 and Rate-1 pruning conjecture. Asymptotically, most of the savings in latency comes from pruning Rate-0 and Rate-1 nodes.

DFR overlap-dependence conjecture. The DFR corresponding to error vectors in $\mathcal E(n,t,i_0,i_1)$ depends on the number of overlapping ones between the columns $i_0$ and $i_1$…

Power-IRS success probability conjecture. Based on observed failure rates and formal bounds for Power decoding of Reed–Solomon codes, the probability that Power-IRS succeeds on…

Throughput conjecture. The coded throughput will remain approximately the same for any polar code, as the PCIe link is saturated and data transfer is the bottleneck.

Let $\mathbf Q$, $\mathbf S$, and $\mathbf R_R$ be the matrices arising in the interpolation-based decoding analysis, with $s$ the interleaving order, $k$ the relevant dimension pa…

Let $s$ be the interleaving order and let $\tau$ denote the decoding radius appearing in the decoding results. The results are stated under the restriction $\tau\geq s$. Conjecture…

Consider the joint informed and uninformed fingerprinting games and the corresponding log-likelihood score functions for joint decoding. A suitable accusation algorithm must assign…

Universal joint-decoder conjecture. The joint log-likelihood decoder against the interleaving attack, using this score function, works against arbitrary attacks and asymptotically…

Let the joint decoder be tailored against the interleaving attack, and let the joint uninformed capacity denote the optimal asymptotic rate in the uninformed fingerprinting game. I…