arXiv subjects

Krishna Narayanan

Publications and source records attributed to Krishna Narayanan.

At least 19 recordsLinked to original sources

arXiv2026

A note on the exact partition polytope of Frieze and Teng

In 1994, Frieze and Teng proposed an integer linear programming formulation of the NP-Complete Exact Partition problem, whose LP-relaxation they claimed was non-degenerate. Contrary to their claim, we show how an instance of Exact Partition can produce a degenerate polytope, and study conditions for which this can happen. We then give details of one of the smallest such degenerate Frieze-Teng polytopes, along with a closely related non-degenerate Frieze-Teng polytope that encodes an equivalent problem. We note that for the purposes of the complexity results in the literature that use their formulation, these degenerate polytopes can be avoided via a simple preprocessing step.

math.CO↗

arXiv2026

Optimal Multi-bit Generative Watermarking Schemes Under Worst-Case False-Alarm Constraints

This paper considers the problem of multi-bit generative watermarking for large language models under a worst-case false-alarm constraint. Prior work established a lower bound on the achievable miss-detection probability in the finite-token regime and proposed a scheme claimed to achieve this bound. We show, however, that the proposed scheme is in fact suboptimal. We then develop two new encoding-decoding constructions that attain the previously established lower bound, thereby completely characterizing the optimal multi-bit watermarking performance. Our approach formulates the watermark design problem as a linear program and derives the structural conditions under which optimality can be achieved. In addition, we identify the failure mechanism of the previous construction and compare the tradeoffs between the two proposed schemes.

cs.IT↗

arXiv2026

Reinforcement Learning for Diffusion LLMs with Entropy-Guided Step Selection and Stepwise Advantages

Reinforcement learning (RL) has been effective for post-training autoregressive (AR) language models, but extending these methods to diffusion language models (DLMs) is challenging due to intractable sequence-level likelihoods. Existing approaches therefore rely on surrogate likelihoods or heuristic approximations, which can introduce bias and obscure the sequential structure of denoising. We formulate diffusion-based sequence generation as a finite-horizon Markov decision process over the denoising trajectory and derive an exact, unbiased policy gradient that decomposes over denoising steps and is expressed in terms of intermediate advantages, without requiring explicit evaluation of the sequence likelihood. To obtain a practical and compute-efficient estimator, we (i) select denoising steps for policy updates via an entropy-guided approximation bound, and (ii) estimate intermediate advantages using a one-step denoising reward naturally provided by the diffusion model, avoiding costly multi-step rollouts. Experiments on coding and logical reasoning benchmarks demonstrate state-of-the-art results, with strong competitive performance on mathematical reasoning, outperforming existing RL post-training approaches for DLMs. Code is available at https://github.com/vishnutez/egspo-dllm-rl.

cs.LG↗

arXiv2026

GRAM-DIFF: Gram Matrix Guided Diffusion for MIMO Channel Estimation

We propose GRAM-DIFF, a Gram-matrix-guided diffusion framework for semi-blind multiple input multiple output (MIMO) channel estimation. Recent diffusion-based estimators leverage learned generative priors to improve pilot-based channel estimation; but they do not exploit second-order structural information estimated from data symbols. In practical systems, the channel Gram matrix can be estimated from received symbols and it provides realization-level information about channel subspace structure. The proposed method integrates a pre-trained angular-domain diffusion prior with two complementary guidance mechanisms: a novel Gram-matrix guidance term that enforces second-order consistency during the reverse diffusion process, and likelihood guidance from pilot observations. Signal-to-noise ratio (SNR)-matched initialization and adaptive guidance scaling ensure stability and low inference latency. Simulations on 3GPP and QuaDRiGa channel models demonstrate consistent normalized mean-squared error (NMSE) improvements over deterministic diffusion baselines, achieving 4 to 6 dB SNR gains at an NMSE of 0.1 over the baseline in Fest et al. (2024). The framework exhibits graceful degradation under coherence-time constraints, smoothly reverting to likelihood-guided diffusion when data-based Gram estimates become unreliable.

cs.IT↗

arXiv2025

Inference-Time Search Using Side Information for Diffusion-Based Image Reconstruction

Diffusion models have been used as priors for solving inverse problems. However, existing approaches typically overlook side information that could significantly improve reconstruction quality, especially in severely ill-posed settings. In this work, we propose a novel framework that incorporates side information into existing diffusion-based inverse problem solvers via inference-time search, in a plug-and-play, training-free manner. Through extensive experiments across a range of inverse problems, including inpainting, super-resolution, and several deblurring tasks, and across multiple diffusion-based inverse problem solvers (DPS, DAPS, and MPGD), we show that augmenting each solver with our framework consistently improves the quality of the reconstructions over the corresponding original method. To demonstrate the generality of our approach, we consider diverse forms of side information, including reference images, textual descriptions, and anatomical MRI scans. The code is available at this \href{https://github.com/mahdi-farahbakhsh/DISS}{repository}\footnote{https://github.com/mahdi-farahbakhsh/DISS}.

cs.CV↗

arXiv2025

Zak-OTFS Based Coded Random Access for Uplink mMTC

This paper proposes a grant-free coded random access (CRA) scheme for uplink massive machine-type communications (mMTC), based on Zak-orthogonal time frequency space (Zak-OTFS) modulation in the delay-Doppler domain. The scheme is tailored for doubly selective wireless channels, where conventional orthogonal frequency-division multiplexing (OFDM)-based CRA suffers from unreliable inter-slot channel prediction due to time-frequency variability. By exploiting the predictable nature of Zak-OTFS, the proposed approach enables accurate channel estimation across slots, facilitating reliable successive interference cancellation across user packet replicas. A fair comparison with an OFDM-based CRA baseline shows that the proposed scheme achieves significantly lower packet loss rates under high mobility and user density. Extensive simulations over the standardized Veh-A channel confirm the robustness and scalability of Zak-OTFS-based CRA, supporting its applicability to future mMTC deployments.

eess.SP↗

arXiv2025

Density Evolution Analysis of Sparse-Block IDMA

Sparse block interleaver division multiple access (SB-IDMA) is a recently introduced unsourced multiple access protocol that aims to improve the performance of the grant-free two-step random access transmission protocol of the 3GPP 5G New Radio standard. We introduced a density evolution analysis of the successive interference cancellation receiver of SB-IDMA, providing a theoretical characterization of its performance.

cs.IT↗

arXiv2025

In-Context Learning for Gradient-Free Receiver Adaptation: Principles, Applications, and Theory

In recent years, deep learning has facilitated the creation of wireless receivers capable of functioning effectively in conditions that challenge traditional model-based designs. Leveraging programmable hardware architectures, deep learning-based receivers offer the potential to dynamically adapt to varying channel environments. However, current adaptation strategies, including joint training, hypernetwork-based methods, and meta-learning, either demonstrate limited flexibility or necessitate explicit optimization through gradient descent. This paper presents gradient-free adaptation techniques rooted in the emerging paradigm of in-context learning (ICL). We review architectural frameworks for ICL based on Transformer models and structured state-space models (SSMs), alongside theoretical insights into how sequence models effectively learn adaptation from contextual information. Further, we explore the application of ICL to cell-free massive MIMO networks, providing both theoretical analyses and empirical evidence. Our findings indicate that ICL represents a principled and efficient approach to real-time receiver adaptation using pilot signals and auxiliary contextual information-without requiring online retraining.

cs.IT↗

arXiv2025

Relatively-Secure LLM-Based Steganography via Constrained Markov Decision Processes

Linguistic steganography aims to conceal information within natural language text without being detected. An effective steganography approach should encode the secret message into a minimal number of language tokens while preserving the natural appearance and fluidity of the stego-texts. We present a new framework to enhance the embedding efficiency of stego-texts generated by modifying the output of a large language model (LLM). The novelty of our approach is in abstracting the sequential steganographic embedding process as a Constrained Markov Decision Process (CMDP), which takes into consideration the long-term dependencies instead of merely the immediate effects. We constrain the solution space such that the discounted accumulative total variation divergence between the selected probability distribution and the original distribution given by the LLM is below a threshold. To find the optimal policy, we first show that the functional optimization problem can be simplified to a convex optimization problem with a finite number of variables. A closed-form solution for the optimal policy is then presented to this equivalent problem. It is remarkable that the optimal policy is deterministic and resembles water-filling in some cases. The solution suggests that usually adjusting the probability distribution for the state that has the least random transition probability should be prioritized, but the choice should be made by taking into account the transition probabilities at all states instead of only the current state.

cs.IT↗

arXiv2025

Source-Channel Separation Theorems for Distortion Perception Coding

It is well known that separation between lossy source coding and channel coding is asymptotically optimal under classical additive distortion measures. Recently, coding under a new class of quality considerations, often referred to as perception or realism, has attracted significant attention due to its close connection to neural generative models and semantic communications. In this work, we revisit source-channel separation under the consideration of distortion-perception. We show that when the perception quality is measured on the block level, i.e., in the strong-sense, the optimality of separation still holds when common randomness is shared between the encoder and the decoder; however, separation is no longer optimal when such common randomness is not available. In contrast, when the perception quality is the average per-symbol measure, i.e., in the weak-sense, the optimality of separation holds regardless of the availability of common randomness.

cs.IT↗

arXiv2024

Delay-Doppler Signal Processing with Zadoff-Chu Sequences

Much of the engineering behind current wireless systems has focused on designing an efficient and high-throughput downlink to support human-centric communication such as video streaming and internet browsing. This paper looks ahead to design of the uplink, anticipating the emergence of machine-type communication (MTC) and the confluence of sensing, communication, and distributed learning. We demonstrate that grant-free multiple access is possible even in the presence of highly time-varying channels. Our approach provides a pathway to standards adoption, since it is built on enhancing the 2-step random access procedure which is already part of the 5GNR standard. This 2-step procedure uses Zadoff-Chu (ZC) sequences as preambles that point to radio resources which are then used to upload data. We also use ZC sequences as preambles / pilots, but we process signals in the Delay-Doppler (DD) domain rather than the time-domain. We demonstrate that it is possible to detect multiple preambles in the presence of mobility and delay spread using a receiver with no knowledge of the channel other than the worst case delay and Doppler spreads. Our approach depends on the mathematical properties of ZC sequences in the DD domain. We derive a closed form expression for ZC pilots in the DD domain, we characterize the possible self-ambiguity functions, and we determine the magnitude of the possible cross-ambiguity functions. These mathematical properties enable detection of multiple pilots through solution of a compressed sensing problem. The columns of the compressed sensing matrix are the translates of individual ZC pilots in delay and Doppler. We show that columns in the design matrix satisfy a coherence property that makes it possible to detect multiple preambles in a single Zak-OTFS subframe using One-Step Thresholding (OST), which is an algorithm with low complexity.

eess.SP↗

arXiv2024

OD-Stega: LLM-Based Relatively Secure Steganography via Optimized Distributions

We consider coverless steganography where a Large Language Model (LLM) is used to generate stego-texts in combination with arithmetic coding. An efficient method should embed secret bits in as few language tokens as possible while keeping the stego-text as natural as possible. We show that this problem is equivalent to maximizing the entropy of a replacement probability distribution of the next token generation, subject to a constraint on the divergence between the new distribution and the original one produced by the LLM. A closed-form solution is provided under either the KL divergence or the total variation constraint. Several important practical issues are also tackled: 1) An often-overlooked tokenization mismatch issue is resolved with a simple prompt selection approach, 2) The combination of the optimized distribution and the vocabulary truncation technique is considered, and 3) The incorporation of the proposed approach with existing (potentially non arithmetic coding based) techniques, e.g., the Discop technique.

cs.IT↗

arXiv2024

Evolution of the 5G New Radio Two-Step Random Access towards 6G Unsourced MAC

This report summarizes some considerations on possible evolutions of grant-free random access in the next generation of the 3GPP wireless cellular standard. The analysis is carried out by mapping the problem to the recently-introduced unsourced multiple access channel (UMAC) setup. By doing so, the performance of existing solutions can be benchmarked with information-theoretic bounds, assessing the potential gains that can be achieved over legacy 3GPP schemes. The study focuses on the two-step random access (2SRA) protocol introduced by Release 16 of the 5G New Radio standard, investigating its applicability to support large MTC / IoT terminal populations in a grant-free fashion. The analysis shows that the existing 2SRA scheme may not succeed in providing energy-efficient support to large user populations. Modifications to the protocol are proposed that enable remarkable gains in both energy and spectral efficiency while retaining a strong resemblance to the legacy protocol.

cs.IT↗

arXiv2024

LightCode: Light Analytical and Neural Codes for Channels with Feedback

The design of reliable and efficient codes for channels with feedback remains a longstanding challenge in communication theory. While significant improvements have been achieved by leveraging deep learning techniques, neural codes often suffer from high computational costs, a lack of interpretability, and limited practicality in resource-constrained settings. We focus on designing low-complexity coding schemes that are interpretable and more suitable for communication systems. We advance both analytical and neural codes. First, we demonstrate that PowerBlast, an analytical coding scheme inspired by Schalkwijk-Kailath (SK) and Gallager-Nakibo\u{g}lu (GN) schemes, achieves notable reliability improvements over both SK and GN schemes, outperforming neural codes in high signal-to-noise ratio (SNR) regions. Next, to enhance reliability in low-SNR regions, we propose LightCode, a lightweight neural code that achieves state-of-the-art reliability while using a fraction of memory and compute compared to existing deeplearning-based codes. Finally, we systematically analyze the learned codes, establishing connections between LightCode and PowerBlast, identifying components crucial for performance, and providing interpretation aided by linear regression analysis.

cs.IT↗

arXiv2023

Transformers are Provably Optimal In-context Estimators for Wireless Communications

Pre-trained transformers exhibit the capability of adapting to new tasks through in-context learning (ICL), where they efficiently utilize a limited set of prompts without explicit model optimization. The canonical communication problem of estimating transmitted symbols from received observations can be modeled as an in-context learning problem: received observations are a noisy function of transmitted symbols, and this function can be represented by an unknown parameter whose statistics depend on an unknown latent context. This problem, which we term in-context estimation (ICE), has significantly greater complexity than the extensively studied linear regression problem. The optimal solution to the ICE problem is a non-linear function of the underlying context. In this paper, we prove that, for a subclass of such problems, a single-layer softmax attention transformer (SAT) computes the optimal solution of the above estimation problem in the limit of large prompt length. We also prove that the optimal configuration of such a transformer is indeed the minimizer of the corresponding training loss. Further, we empirically demonstrate the proficiency of multi-layer transformers in efficiently solving broader in-context estimation problems. Through extensive simulations, we show that solving ICE problems using transformers significantly outperforms standard approaches. Moreover, just with a few context examples, it achieves the same performance as an estimator with perfect knowledge of the latent context. The code is available \href{https://github.com/vishnutez/in-context-estimation}{here}.

eess.SP↗

arXiv2023

LLMZip: Lossless Text Compression using Large Language Models

We provide new estimates of an asymptotic upper bound on the entropy of English using the large language model LLaMA-7B as a predictor for the next token given a window of past tokens. This estimate is significantly smaller than currently available estimates in \cite{cover1978convergent}, \cite{lutati2023focus}. A natural byproduct is an algorithm for lossless compression of English text which combines the prediction from the large language model with a lossless compression scheme. Preliminary results from limited experiments suggest that our scheme outperforms state-of-the-art text compression schemes such as BSC, ZPAQ, and paq8h.

cs.IT↗

arXiv2023

On the Advantages of Asynchrony in the Unsourced MAC

In this work we demonstrate how a lack of synchronization can in fact be advantageous in the problem of random access. Specifically, we consider a multiple-access problem over a frame-asynchronous 2-user binary-input adder channel in the unsourced setup (2-UBAC). Previous work has shown that under perfect synchronization the per-user rates achievable with linear codes over the 2-UBAC are limited by 0.5 bit per channel use (compared to the capacity of 0.75). In this paper, we first demonstrate that arbitrary small (even single-bit) shift between the user's frames enables (random) linear codes to attain full capacity of 0.75 bit/user. Furthermore, we derive density evolution equations for irregular LDPC codes, and prove (via concentration arguments) that they correctly track the asymptotic bit-error rate of a BP decoder. Optimizing the degree distributions we construct LDPC codes achieving per-user rates of 0.73 bit per channel use.

cs.IT↗

arXiv2022

Monitoring edge-geodetic sets in graphs

We introduce a new graph-theoretic concept in the area of network monitoring. In this area, one wishes to monitor the vertices and/or the edges of a network (viewed as a graph) in order to detect and prevent failures. Inspired by two notions studied in the literature (edge-geodetic sets and distance-edge-monitoring sets), we define the notion of a monitoring edge-geodetic set (MEG-set for short) of a graph $G$ as an edge-geodetic set $S\subseteq V(G)$ of $G$ (that is, every edge of $G$ lies on some shortest path between two vertices of $S$) with the additional property that for every edge $e$ of $G$, there is a vertex pair $x, y$ of $S$ such that $e$ lies on all shortest paths between $x$ and $y$. The motivation is that, if some edge $e$ is removed from the network (for example if it ceases to function), the monitoring probes $x$ and $y$ will detect the failure since the distance between them will increase. We explore the notion of MEG-sets by deriving the minimum size of a MEG-set for some basic graph classes (trees, cycles, unicyclic graphs, complete graphs, grids, hypercubes, corona products...) and we prove an upper bound using the feedback edge set of the graph. We also show that determining the smallest size of an MEG-set of a graph is NP-hard, even for graphs of maximum degree at most~9.

math.CO↗