arXiv subjects

Muriel Médard

Publications and source records attributed to Muriel Médard.

At least 19 recordsLinked to original sources

arXiv2026

Leveraging Code Structure to Improve Soft Output for GRAND, GCD, OSD, and SCL

In addition to a codeword, error correction decoders that provide blockwise soft output (SO) return an estimate of the likelihood that the decoding is correct. Following Forney, such estimates have traditionally only been possible for list decoders with the approximate soft output being the likelihood that a decoding is correct given it is assumed to be in the list. Recently, it has been established that Guessing Random Additive Noise Decoding (GRAND), Guessing Codeword Decoding (GCD), Ordered Statistics Decoding (OSD), and Successive Cancellation List (SCL) decoding can provide accurate soft output without the need for list decoding. Central to the improvement is the evaluation of an estimate of the likelihood that the correct decoding has not been found. We explore how binary linear codebook constraints can be leveraged to further enhance SO precision. We evaluate performance by adapting a forecasting statistic called the Brier Score. Results indicate that the SO generated by the approach is essentially as accurate as the maximum a posteriori estimate.

cs.IT↗

arXiv2026

Improving the decoding performance of CA-polar codes

We investigate the use of modern code-agnostic decoders to convert CA-SCL from an incomplete decoder to a complete one. When CA-SCL fails to identify a codeword that passes the CRC check, we apply a code-agnostic decoder that identifies a codeword that satisfies the CRC. We establish that this approach gives gains of up to 0.2 dB in block error rate for CA-polar codes from the 5G New Radio standard. If, instead, the message had been encoded in a systematic CA-polar code, the gain improves to more than 1.5 dB. Leveraging recent developments in blockwise soft output, we additionally establish that it is possible to control the undetected error rate even when using the CRC for error correction.

cs.IT↗

arXiv2026

Efficient Soft-Output Guessing for Enhanced Quantum Tanner Code Decoding

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 rather than individual parity checks, we mitigate the effects of trapping sets and cycles, resulting in improved convergence. Because our decoder preserves the message passing structure of standard belief propagation (BP), it is compatible with many BP enhancements. We demonstrate this with OSD postprocessing, quaternary BP, and RelayBP, each yielding further gains. Standalone SOGRAND outperforms the standard BP+OSD baseline by over two orders of magnitude in logical error rate. In combination with the Relay principle, SOGRAND outperforms RelayBP by over one order of magnitude, providing a way forward for scalable decoding of the emerging class of Tanner-code-based quantum codes.

quant-ph↗

arXiv2026

Sensing-Aided Ordered Reliability Bits Guessing Random Additive Noise Decoding

Integrated sensing and communication (ISAC) is a key enabler for future wireless systems, providing environmental information that can support tasks beyond conventional data transmission. However, its impact on channel decoding remains less explored. This paper studies sensing-aided ordered reliability bits guessing random additive noise decoding (ORBGRAND) over single-input single-output narrowband fading channels. Environmental information is used to construct a geometry-based prior for the channel coefficient, which is fused with pilot observations via linear minimum mean square error (LMMSE) estimation. The resulting posterior channel estimate and uncertainty are used to compute the log-likelihood ratios (LLRs) supplied to ORBGRAND, improving the reliability ordering that drives its noise-guessing process. Simulation results demonstrate improved block error rate and reduced average query complexity, with the largest gains in pilot-limited regimes.

eess.SP↗

arXiv2026

NOVA: Fundamental Limits of Knowledge Discovery Through AI

Can AI systems discover new knowledge through iterative self-improvement, and at what cost? We introduce NOVA, which models the ``generate, verify, accumulate, retrain'' loop as an adaptive sampling process over a knowledge space. We give sufficient conditions for accumulated genuine knowledge to cover a finite domain and show how violations produce contamination, forgetting, exploration failure, and acceptance failure. We then analyze how adaptive generation arises from recursive retraining. In an explicit distribution-level model where accepted artifacts influence the next generator, we identify a recursive-feedback phase transition. Unanchored feedback can lock generation onto early accepted artifacts and leave initially reachable valid artifacts undiscovered with positive probability. Anchoring updates to a persistent base distribution prevents unbounded distortion and guarantees continued exposure. Under imperfect verification, we identify a contamination trap: as easy knowledge is exhausted, even small false-positive rates can admit invalid artifacts faster than genuine discoveries. We show that Good--Turing estimation is a local batch-diversity diagnostic, not an estimator of the historically undiscovered valid mass governing long-term progress. Under a Zipf tail with exponent $α>1$, the cumulative generation cost of obtaining $D$ distinct genuine discoveries satisfies $R_{\rm cum}(D)=Θ(c_{\rm gen}D^α)$. When the valid base distribution has such a tail, anchored retraining preserves the exposure needed for this scaling law. Finally, we show how human guidance, generation, and verification can redirect or expand discovery when autonomous sampling stalls because of repetition, vanishing exposure, or unreliable verification.

cs.AI↗

arXiv2026

Enhanced GCD through ORBGRAND-AI: Exploiting Partial and Total Correlation in Noise

There have been significant advances in recent years in the development of forward error correction decoders that can decode codes of any structure, including practical realizations in synthesized circuits and taped out chips. While essentially all soft-decision decoders assume that bits have been impacted independently on the channel, for one of these new approaches it has been established that channel dependencies can be exploited to achieve superior decoding accuracy, resulting in Ordered Reliability Bits Guessing Random Additive Noise Decoding Approximate Independence (ORBGRAND-AI). Building on that capability, here we consider the integration of ORBGRAND-AI as a pattern generator for Guessing Codeword Decoding (GCD). We first establish that a direct approach delivers mildly degraded block error rate (BLER) but with reduced number of queried patterns when compared to ORBGRAND-AI. We then show that with a more nuanced approach it is possible to leverage total correlation to deliver an additional BLER improvement of ~0.75$ dB while retaining reduced query numbers.

eess.SP↗

arXiv2026

Generalized Segmented GRAND for Guesswork Reduction in Turbo Product Decoding

Guessing random additive noise decoding (GRAND) can efficiently decode any moderately redundant code with near maximum likelihood (ML) performance via noise effect guessing. For binary linear codes, Rowshan and Yuan's Segmented GRAND was the first to show that constrained guessing can reduce guesswork. Although powerful, their approach requires a specific parity-check matrix structure that limits the number of constraints that can be exploited as well as the class of applicable codes. Here we introduce GSegGRAND, a generalization of Segmented GRAND that circumvents its limitations. Built on a novel parity check structure and a transformation that maps codes into this structure, GSegGRAND efficiently incorporates up to log2(n) constraints for a wide range of codes, reducing guesswork by an additional 75% over Segmented GRAND. To leverage that advantage for soft-output decoding, we derive an accurate soft-output (SO) equation for GSegGRAND by extending soft-output GRAND (SOGRAND) to incorporate constrained guessing. Applying this SO to turbo product decoding, GSegGRAND achieves up to 88% guesswork reduction, making it a promising candidate for low-latency decoding in future communication systems.

cs.IT↗

arXiv2026

SOGRAND decoding of LDPC codes

Long forward error correction codes are typically constructed by concatenating shorter component codes that are then decoded through iterative Soft-Input Soft-Output (SISO) of their components. The recently introduced Soft Output Guessing Random Additive Noise Decoding (SOGRAND) has been shown to enable accurate SISO component decoding for a broad range of component codes. Here we establish that by specializing its SISO computation to Single Parity Check codes, SOGRAND offers an alternative existing Check Node (CN) update for decoding Low Density Parity Check codes. Simulation results demonstrate similar or better decoding performance than Gallager's sum-product algorithm and norm-min-sum, while offering two distinct low complexity, hardware friendly CN update algorithms.

cs.IT↗

arXiv2026

Optimum Peer-Turbo: A Scalable and Efficient Solution for P2P Broadcasting

Blockchain systems such as Solana or Monad employ tree- or star-shaped broadcast topologies in which a single source node disseminates message shards to a set of target peers within a strictly bounded time window. In these architectures, shard propagation must complete before the next consensus step, making timely delivery to a large fraction of the validator set essential. A fundamental limitation of such designs is that the outbound bandwidth of the source node constitutes the primary system bottleneck. In this paper, we introduce peer Turbo, a technique that allows target nodes to exchange shards using Random Linear Network Coding (RLNC), thereby assisting each other in completing decoding without requiring explicit shard state coordination. We use a tractable fluid approximation of the degree of freedom distribution of peer-Turbo-enabled systems show that this approach reduces source bandwidth required for a set service quality by up to one order of magnitude, or equivalently reduces propagation latency by one order of magnitude under fixed bandwidth constraints.

cs.IT↗

arXiv2026

The Benefit of Decoder-Provided Pilots in Highly Dynamic Channels

Communications in highly dynamic channels relying on training-based channel estimation experience a trade-off between increasing channel measurement accuracy by sending more frequent training sequences and increasing data rate by sending fewer training sequences. Simultaneously, most communication systems use forward error correction to enable error detection and correction at the receiver. This paper presents decoder-provided pilots for time-varying channels by using decoded codewords as training sequences to update the channel estimate at the receiver. In contrast to approaches such as data-aided channel estimation, decision-feedback equalization, joint channel estimation and error correction, and turbo equalization, the decoder-provided pilots approach is non-iterative, which is ideal for low-latency requirements in highly dynamic scenarios. Furthermore, it is modulation-, code-, and decoder-agnostic, meaning it can be implemented on top of virtually any communication system that uses forward error correction. From an information-theoretic perspective, we derive the fundamental limits of decoder-provided pilots' ability to simultaneously sense the channel and transmit data. Simulation results demonstrate that decoder-provided pilots significantly improve performance, that when coding across frequency, soft-output can further enhance performance, and that when coding across time, short codes can outperform long codes of the same rate in fast-fading channels.

cs.IT↗

arXiv2026

Pricing Innovation Under Latency Constraints: A Mean-Field Analysis of Coded Payload Delivery

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.

cs.IT↗

arXiv2026

OPTIMUM-DERAM: Highly Consistent, Scalable, and Secure Multi-Object Memory using RLNC

This paper introduces OPTIMUM-DERAM, a highly consistent, scalable, secure, and decentralized shared memory solution. Traditional distributed shared memory implementations offer multi-object support by multi-threading a single object memory instance over the same set of data hosts. While theoretically sound, the amount of resources required made such solutions prohibitively expensive in practical systems. OPTIMUM-DERAM proposes a decentralized, reconfigurable, atomic read/write shared memory (DeRAM) that: (i) achieves improved performance and storage scalability by leveraging Random Linear Network Codes (RLNC); (ii) scales in the number of supported atomic objects by introducing a new object placement and discovery approach based on a consistent hashing ring; (iii) scales in the number of participants by allowing dynamic joins and departures leveraging a blockchain oracle to serve as a registry service; and (iv) is secure against malicious behavior by tolerating Byzantine failures. Experimental results over a globally distributed set of nodes, help us realize the performance and scalability gains of OPTIMUM-DERAM over previous distributed shared memory solutions (i.e., the ABD algorithm [3])

cs.DC↗

arXiv2026

Revisiting the Interface between Error and Erasure Correction in Wireless Standards

Modern 5G communication systems implement a combination of error correction and feedback-based erasure correction (HARQ/ARQ) as reliability mechanisms, which can introduce substantial delay and resource inefficiency. We propose forward erasure correction using network coding as a more delay-efficient alternative. We present a mathematical characterization of network delay for existing reliability mechanisms and network coding. Through simulations in a network slicing environment, we demonstrate that network coding not only improves the in-order delivery delay and goodput for the applications utilizing the slice, but also benefits other applications sharing the network by reducing resource utilization for the coded slice. Our analysis and characterization point towards ideas that require attention in the 6G standardization process. These findings highlight the need for greater modularity in protocol stack design that enables the integration of novel technologies in future wireless networks.

cs.NI↗

arXiv2025

Guessing Decoding of Short Blocklength Codes

Future beyond-5G and 6G systems demand ultra-reliable, low-latency communication with short blocklengths, motivating the development of universal decoding algorithms. Guessing decoding, which infers the noise or codeword candidate in order of decreasing (exact or approximate) likelihood, offers a universal framework applicable to short codes. In this paper, we present a unified treatment of two prominent recent families of guessing decoding: guessing random additive noise decoding (GRAND) and guessing codeword decoding (GCD). For each, we (i) present algorithmic implementations and ordering strategies; (ii) prove maximum-likelihood (ML) optimality under appropriate stopping criteria; (iii) derive saddle-point approximations for the average number of queries; and (iv) validate theoretical predictions with simulations. We further analyze the performance degradation due to limited search budgets relative to ML performance, compare key metrics (worst-case and average complexity, hardware considerations), and highlight how advances in one approach transfer naturally to the other. Our results clarify the operating regimes where GRAND and GCD demonstrate superior performance. This work provides both theoretical insights and practical guidelines for deploying universal guessing decoders in next-generation short-blocklength communications.

cs.IT↗

arXiv2025

Group Probability Decoding of Turbo Product Codes over Higher-Order Fields

Binary turbo product codes (TPCs) are powerful error-correcting codes constructed from short component codes. Traditionally, turbo product decoding passes log likelihood ratios (LLRs) between the component decoders, inherently losing information when bit correlation exists. Such correlation can arise exogenously from sources like intersymbol interference and endogenously during component code decoding. To preserve these correlations and improve performance, we propose turbo product decoding based on group probabilities. We theoretically predict mutual information and signal-to-noise ratio (SNR) gains of group over bit-probability decoding. To translate these theoretical insights to practice, we revisit non-binary TPCs that naturally support group-probability decoding. We show that any component list decoder that takes group probabilities as input and outputs block-wise soft-output can partially preserve bit correlation, which we demonstrate with symbol-level ORBGRAND combined with soft-output GRAND (SOGRAND). Our results demonstrate that group-probability-based turbo product decoding achieves SNR gains of up to 0.3 dB for endogenous correlation and 0.7 dB for exogenous correlation, compared to bit-probability decoding.

cs.IT↗

arXiv2025

LINC: An In-Network Coding Approach to Tame Packet Loss in Hybrid Wireless-Fiber Backbones

The emergence of ultra-low latency applications, such as financial transactions, has driven the development of hybrid backbone networks that rely on fiber, satellite, and microwave links. Despite providing low latencies, these hybrid networks suffer from occasional environmental packet loss caused by poor weather, construction, and line of sight blockage. Paradoxically, today's hybrid backbones rely on conventional transport protocols that take packet loss to signal network congestion, as opposed to transient environmental obstacles. A common approach to address this challenge is to use network coding (NC) between the end hosts to recover from these occasional packet loss events. However, current NC proposals assume full access to the end-hosts' stack to perform end-to-end encoding/decoding operations. In this paper, we introduce LINC, a novel system that provides in-network NC capabilities to mitigate environmental packet loss events without requiring cooperation from the end hosts. LINC uses a systematic block coding approach on a link-by-link basis, encoding and decoding packets inside the network. We model the tradeoff in goodput between end-to-end retransmissions and redundant packets introduced by LINC, and propose an optimization formulation to determine the optimal choice of coding parameters. Our simulations on real-world backbone topologies demonstrate that LINC reduces the end-to-end latency by up to 18% by eliminating unnecessary retransmissions.

cs.NI↗

arXiv2025

The Linear Reliability Channel

We introduce and analyze a discrete soft-decision channel called the linear reliability channel (LRC) in which the soft information is the rank ordering of the received symbol reliabilities. We prove that the LRC is an appropriate approximation to a general class of discrete modulation, continuous noise channels when the noise variance is high. The central feature of the LRC is that its combinatorial nature allows for an extensive mathematical analysis of the channel and its corresponding hard- and soft-decision maximum likelihood (ML) decoders. In particular, we establish explicit error exponents for ML decoding in the LRC when using random codes under both hard- and soft-decision decoding. This analysis allows for a direct, quantitative evaluation of the relative advantage of soft-decision decoding. The discrete geometry of the LRC is distinct from that of the BSC, which is characterized by the Hamming weight, offering a new perspective on code construction for soft-decision settings.

cs.IT↗

arXiv2025

Rethinking Reliability Using Network Coding: a Practical 5G Evaluation

This work presents the design and implementation of a real-time network coding system integrated into the IP layer of a 5G testbed, offering an alternative to conventional retransmission-based reliability mechanisms such as ARQ and HARQ. Using a netfilter-based packet interception framework, we inject forward erasure correction using Random Linear Network Coding (RLNC) into live traffic between a gNB and UE over a 3GPP RF link. We evaluate a block coding scheme, analyzing its impact on throughput, jitter, and resource usage. Results show that with appropriate code rate selection, RLNC can fully recover from packet losses using fewer transmissions than ARQ/HARQ and maintain a high throughput, particularly under moderate-to-high packet loss rates. These findings demonstrate that network coding can effectively replace retransmission-based reliability in future wireless systems, with the potential for more efficient resource utilization.

cs.NI↗