Muriel Médard

Lukas Rapp, Muriel Médard, Eugene Tang et al.

We introduce a generalized low-density parity-check decoding framework for quantum Tanner codes utilizing soft-output guessing random additive noise decoding (SOGRAND). By soft-output decoding entire component codes, we mitigate trapping sets and cycles, resulting in improved convergence. SOGRAND, combined with ordered statistic decoding (OSD) post-processing, outperforms the standard belief propagation plus OSD baseline by up to three orders of magnitude in logical error rate, providing a way forward for scalable decoding of the emerging class of Tanner-code-based quantum codes.

Muriel Médard, Tarun Chitra, Moritz Grundei et al.

We study pricing mechanisms for low-latency payload delivery in settings where participant rewards depend on the time required to reconstruct a payload. In such environments, the decoding time distribution determines deadline-meeting probabilities and therefore bounds a participant's willingness to pay for additional delivery rate. Using a mean-field formulation, we derive price-rate bounds from simple stochastic arrival models and instantiate them for (i) unsharded transmission and (ii) sharded delivery under three regimes: uncoded sharding, fixed-rate erasure coding, and rateless coding. These bounds yield a comparative characterization of how symbol usefulness translates into economic value under deadline-driven utilities. We further analyze a two-lane service consisting of a base lane and a Random Linear Network Coding (RLNC) fast lane. In this turbo decoding setting, a receiver combines shards arriving via both lanes to minimize time to decode. Under a fixed base-lane price-rate pair and an aggregate rate constraint, we derive a fast-lane pricing bound and show how even modest additional RLNC rate can generate measurable utility gains, depending on the base-lane propagation regime. The framework extends naturally to stepwise reward schedules with multiple deadlines, and we illustrate its applicability on representative scenarios motivated by blockchain message dissemination and latency-sensitive competition.