arXiv subjects

Hessam Mahdavifar

Publications and source records attributed to Hessam Mahdavifar.

At least 19 recordsLinked to original sources

arXiv2026

Quantum LDPC and High-Rate CSS Codes from Fair-Density Parity-Check Codes

We construct quantum LDPC (qLDPC) and high-rate CSS codes from our recently introduced classical fair-density parity-check (FDPC) codes. To this end, we introduce a structured sparsification of FDPC parity-check matrices, which reduces their check weights while preserving the underlying combinatorial structure and distance guarantees. Combined with the hypergraph-product construction, this yields finite-length qLDPC codes with analytically controlled blocklength, dimension, certified distance, and stabilizer weight. For quantum blocklengths $N<10^5$, the constructions introduced here span guaranteed rates from approximately $0.35\%$ to $25.8\%$ and certified quantum distances from $12$ to $69$, with stabilizer weights between $8$ and $16$. In the large-blocklength regime, allowing the FDPC order and sparsified check weight to scale moderately with blocklength yields a family of high-rate CSS codes, which we refer to as quantum FDPC (qFDPC) codes, with rate $R_Q$ and minimum distance $D$ satisfying \[ R_Q = 1-O\left(\frac{1}{\log\log N}\right), \ \ D=Ω(N^{1/4}), \] and stabilizer weight $O(\log N\log\log N)$. Finally, the analytically available FDPC weight distribution provides explicit information about the logical operators of the resulting hypergraph-product codes. Over the quantum erasure channel, this structure yields rigorous first-order maximum likelihood (ML) expressions and a higher-order weight-distribution approximation to the ML logical block error probability. This enables estimation of finite-length operating points and the onset of the error-floor regime. To the best of our knowledge, beyond surface-code-type constructions, this is the first finite-rate qLDPC framework to provide both finite-length certified minimum-distance information and an analytical characterization of low-weight logical multiplicities.

cs.IT↗

arXiv2026

Precoding Design for Limited-Feedback MIMO Systems via Character-Polynomial Codes

This paper presents a precoding codebook design for limited-feedback multiple-input multiple-output (MIMO) systems under the equal-gain transmission (EGT) constraint. In particular, we demonstrate that character--polynomial (CP) codes provide a structured solution that achieves constant-envelope transmission, low storage complexity, and Grassmannian packing without dependence on array geometry or channel statistics. In contrast to geometry-dependent discrete Fourier transform (DFT) codebooks used in current 5G systems and unstructured Grassmannian codebooks with high storage complexity, CP codebooks combine practical implementation advantages with near-optimal packing performance. For multiple-input single-output (MISO) systems, we derive an upper bound on the mean squared quantization error and show that the distortion relative to the EGT baseline vanishes asymptotically as the number of transmit antennas increases and the code rate approaches one. For MIMO systems with two receive antennas, we develop an iterative method to establish the EGT baseline. Simulation results under Rayleigh, correlated, and clustered delay line (CDL) channel models show that CP codebooks approach the EGT baseline across all channel conditions while outperforming phase shift keying (PSK) and 5G DFT codebooks in several operating regimes, and, in the Rayleigh fading case, incur negligible packing loss relative to numerically optimized Grassmannian codebooks obtained via the alternating projection (AP) method.

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arXiv2026

Multi-Tag Collision Recovery in UHF-RFID Using Self-Attention Decoding

Passive ultra high frequency (UHF) radio frequency identification (RFID) enables battery-free tags to communicate with a reader through backscatter. When multiple tags respond in the same time slot, their waveforms overlap at the reader, and a conventional reader that follows framed slotted ALOHA (FSA) discards the resulting collided slot. This limits the throughput of the overall protocol even though the received signal still contains recoverable information about the responding tags. To address this limitation, we propose Self-Attention Tag Recovery (SATR), a transformer-based decoding algorithm that operates directly on the baseband in-phase and quadrature (I/Q) samples received during a standard tag response. SATR uses self-attention to model the temporal structure of the modulated waveform and learns candidate tag representations. It jointly estimates the number of responding tags and, more importantly, decodes the bit sequence of each detected tag. We numerically evaluate the decoding and throughput performance of SATR over a range of collision sizes and recovery configurations, and validate it with measurements of commercial UHF-RFID tags. The results show that, with proper design and training, SATR can reliably decode collisions of up to four tags. It achieves a throughput of approximately $0.815$ tags per slot under single acknowledgment and $1.87$ tags per slot under full recovery, corresponding to $2.2$ and $5.1$ times the conventional FSA limit of $1/e \approx 0.368$ tags per slot, while approaching optimal decoding performance and outperforming existing collision recovery methods.

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arXiv2026

Multiple-Bases Belief Propagation List Decoding for Quantum LDPC Codes

In this paper, we propose a belief-propagation (BP)-based decoder, termed the Multiple-Bases Belief-Propagation List Decoder (MBBP-LD), for quantum low-density parity-check (QLDPC) codes. The key idea is to generate \emph{structured decoding diversity} by constructing multiple redundant parity-check representations via cycle-free subtree decompositions of the Tanner graph, and running BP decoding in parallel across these representations. This extends the classical Multiple-Bases Belief-Propagation (MBBP) framework to the quantum setting while preserving the linear-time complexity and efficiency of standard BP decoding, and avoids the need for super-linear post-processing. Simulation results demonstrate that MBBP-LD improves upon existing BP-based decoders, including BP with ordered statistics decoding (BP-OSD) and belief propagation with guided decimation (BPGD) across several QLDPC codes, while requiring substantially fewer total BP iterations. For bivariate bicycle codes $[[144,12,12]]$ and $[[288,12,18]]$, MBBP-LD achieves up to $20\%$ reduction in error rate compared to BPGD and up to $30\%$ compared to BP-OSD in the low- and moderate-error regimes. For the larger B1 code $[[882, 24, 18 \leq d \leq 24]]$, MBBP-LD attains comparable or improved performance relative to BPGD while maintaining BP-like decoding latency under parallel implementation.

cs.IT↗

arXiv2026

Univariate Bicycle Quantum LDPC Codes: Explicit Logical Structure and Distance Bounds

We introduce univariate bicycle (UB) codes, a structured subclass of generalized bicycle (GB) quantum low-density parity-check (LDPC) codes obtained via a Frobenius relation. This construction reduces the code design space from a two-polynomial search in GB codes to a single-polynomial search, while preserving sparsity. We provide an explicit algebraic characterization of the logical coset spaces by constructing a basis for the logical quotient space, yielding a complete parametrization of logical operators. Leveraging this structure, we derive upper bounds on the minimum distance by relating structured logical representatives to cycle-density properties of associated circulant matrices. Finally, simulation results for short- to medium-length UB codes (block lengths ranging from a few hundred to approximately $10^3$) demonstrate competitive performance relative to existing GB and bivariate bicycle (BB) codes despite the additional algebraic restriction.

cs.IT↗

arXiv2026

Efficient Low-Memory Fast Stack Decoding with Variance Polarization for PAC Codes

Polarization-adjusted convolutional (PAC) codes have recently emerged as a promising class of error-correcting codes, achieving near-capacity performance particularly in the short block-length regime. In this paper, we propose an enhanced stack decoding algorithm for PAC codes that significantly improves parallelization by exploiting specialized bit nodes, such as rate-0 and rate-1 nodes. For a rate-1 node with $N_0$ leaf nodes in its corresponding subtree, conventional stack decoding must either explore all $2^{N_0}$ paths, or, same as in fast list decoding, restrict attention to a constant number of candidate paths. In contrast, our approach introduces a pruning technique that removes candidate paths with small path metrics while ensuring that the probability of pruning the correct path decays exponentially with the threshold. Furthermore, we propose a novel approximation method for estimating variance polarization under the binary-input additive white Gaussian noise (BI-AWGN) channel. Leveraging these approximations, we develop an efficient stack-pruning strategy that selectively preserves decoding paths whose bit-metric values align with their expected means. This targeted pruning substantially reduces the number of active paths in the stack, thereby decreasing both decoding latency and computational complexity. Numerical results demonstrate that for a PAC$(128,64)$ code, our method achieves up to a 70\% reduction in the average number of paths without degrading error-correction performance.

cs.IT↗

arXiv2026

Multibeam Phased Arrays with Spherical Gold Spatio-temporal Coding for Fading-Resilient and Delay Robust Beam Isolations

Future integrated sensing and communication (ISAC) systems require simultaneous multibeam operation with low-latency hardware and robust isolation under synchronization error and fading. Conventional code-division multiplexing using Walsh-Hadamard codes is extremely time-sensitive. This paper demonstrates that conventional temporal-only coded multibeam arrays suffer from inter-beam sidelobe level (SLL) collapse to within a few dB of the main lobe, with variations exceeding 10-20 dB over delay. By embedding moderate-length Gold sequences into a spherical spatial codebook, the proposed Spherical-Gold scheme leverages both temporal and spatial correlation bounds, achieving effective inter-beam isolation without increasing RF complexity. Measurement results and verifications are performed using an Analog Devices ADAR3002 Ka-band 256-element receiver with four simultaneous beams. The proposed scheme demonstrates at least 15 dB rejection with less than 2.5 dB variation in SLL under time error and fading, whereas temporal-only CDMA degrades to approximately -5 to -7 dB SLL with nearly 8 dB variation under time delay.

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arXiv2026

Cost-Aware Neural Early Stopping for Local Constraint OSD Decoders

Local constraint ordered statistics decoding (LC-OSD) provides strong soft decision performance for short block length linear codes, but its practical cost is dominated by the number of tested error patterns (TEPs). This paper proposes a neural early stopping (NES) protocol for LC-OSD with explicit cost control through one trade-off parameter balancing frame error risk and search effort. The proposed approach is trained with frame error rate (FER)-aligned supervision at predefined checkpoints, and learns if additional search is still likely to improve the current best candidate. Later, stopping is decided by comparing predicted continuation need with a cost measured in TEPs. Experimental results across multiple code families show that the proposed protocol significantly reduces average TEP count with only marginal FER degradation, using a single global model for the range of all operating signal-to-noise ratios (SNRs).

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arXiv2026

Covering in Hamming and Grassmann Spaces: New Bounds and Reed--Solomon-Based Constructions

We study covering problems in Hamming and Grassmann spaces through a unified coding-theoretic and information-theoretic framework. Viewing covering as a form of quantization in general metric spaces, we introduce the notion of the average covering radius as a natural measure of average distortion, complementing the classical worst-case covering radius. By leveraging tools from one-shot rate-distortion theory, we derive explicit non-asymptotic random-coding bounds on the average covering radius in both spaces, which serve as fundamental performance benchmarks. On the construction side, we develop efficient puncturing-based covering algorithms for generalized Reed--Solomon (GRS) codes in the Hamming space and extend them to a new family of subspace codes, termed character-Reed--Solomon (CRS) codes, for Grassmannian quantization under the chordal distance. Our results reveal that, despite poor worst-case covering guarantees, these structured codes exhibit strong average covering performance. In particular, numerical results in the Hamming space demonstrate that RS-based constructions often outperform random codebooks in terms of average covering radius. In the one-dimensional Grassmann space, we numerically show that CRS codes over prime fields asymptotically achieve average covering radii within a constant factor of the random-coding bound in the high-rate regime. Together, these results provide new insights into the role of algebraic structure in covering problems and high-dimensional quantization.

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arXiv2025

Deep Reinforcement Learning-Aided Strategies for Big Data Offloading in Vehicular Networks

We consider vehicular networking scenarios where existing vehicle-to-vehicle (V2V) links can be leveraged for an effective uploading of large-size data to the network. In particular, we consider a group of vehicles where one vehicle can be designated as the \textit{leader} and other \textit{follower} vehicles can offload their data to the leader vehicle or directly upload it to the base station (or a combination of the two). In our proposed framework, the leader vehicle is responsible for receiving the data from other vehicles and processing it in order to remove the redundancy (deduplication) before uploading it to the base station. We present a mathematical framework of the considered network and formulate two separate optimization problems for minimizing (i) total time and (ii) total energy consumption by vehicles for uploading their data to the base station. We employ deep reinforcement learning (DRL) tools to obtain solutions in a dynamic vehicular network where network parameters (e.g., vehicle locations and channel coefficients) vary over time. Our results demonstrate that the application of DRL is highly beneficial, and data offloading with deduplication can significantly reduce the time and energy consumption. Furthermore, we present comprehensive numerical results to validate our findings and compare them with alternative approaches to show the benefits of the proposed DRL methods.

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arXiv2025

Deep Learning-Enabled Multi-Tag Detection in Ambient Backscatter Communications

Ambient backscatter communication (AmBC) enables battery-free connectivity by letting passive tags modulate existing RF signals, but reliable detection of multiple tags is challenging due to strong direct link interference, very weak backscatter signals, and an exponentially large joint state space. Classical multi-hypothesis likelihood ratio tests (LRTs) are optimal for this task when perfect channel state information (CSI) is available, yet in AmBC such CSI is difficult to obtain and track because the RF source is uncooperative and the tags are low-power passive devices. We first derive analytical performance bounds for an LRT receiver with perfect CSI to serve as a benchmark. We then propose two complementary deep learning frameworks that relax the CSI requirement while remaining modulation-agnostic. EmbedNet is an end-to-end prototypical network that maps covariance features of the received signal directly to multi-tag states. ChanEstNet is a hybrid scheme in which a convolutional neural network estimates effective channel coefficients from pilot symbols and passes them to a conventional LRT for interpretable multi-hypothesis detection. Simulations over diverse ambient sources and system configurations show that the proposed methods substantially reduce bit error rate, closely track the LRT benchmark, and significantly outperform energy detection baselines, especially as the number of tags increases.

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arXiv2025

Efficient Decoders for Sensing Subspace Code

Sparse antenna array sensing of source/target via direction of arrival (DoA) estimation motivates design of the sensing framework in joint communication and sensing (JCAS) systems for sixth generation (6G) communication systems. Recently, it is established by Mahdavifar, Rajamäki, and Pal that array geometry of sparse arrays has fundamental connections with the design of subspace codes in coding theory. This was then utilized to design efficient \textit{sensing subspace codes} that estimate the DoA with good resolution. Specifically, the Bose-Chowla sensing subspace code provides near optimal code design for unique DoA estimation with tight theoretical upper bound on the error performance. However, the currently known decoder for these codes, to estimate the DoA, is a traditional \textit{Maximum-a-Posterior (MAP) decoder} with complexity that is cubic with the number of antennas. In this work, we propose novel efficient decoding algorithms for sensing subspace codes, that reduce the complexity down to quadratic while providing new knobs to tune in order to tradeoff complexity with error performance. The decoders are further evaluated for their performance via Monte Carlo simulations for a range of SNRs demonstrating promising performance that smoothly approaches the MAP performance as the complexity grows from quadratic to cubic in the number of antennas.

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arXiv2025

List Decoding and New Bicycle Code Constructions for Quantum LDPC Codes

In this paper, we propose a new decoder, called the Multiple-Bases Belief-Propagation List Decoder (MBBP-LD), for Quantum Low-Density Parity-Check (QLDPC) codes. It extends the Multiple-Bases Belief-Propagation (MBBP) framework, originally developed for classical cyclic LDPC codes. The proposed method preserves the linear-time complexity of standard BP decoder while improving the logical error rate. To further reduce the logical error rate, a new decision rule is introduced for the post-processing list decoder, outperforming the conventional least-metric selector (LMS) criterion. For the recently developed and implemented bivariate bicycle (BB) code with parameters $[[144,12,12]]$, our proposed MBBP-LD decoder achieves up to 40\% lower logical error rate compared to the state-of-the-art decoder for short QLDPC codes, i.e., BP with ordered-statistics decoding (BP-OSD), while retaining the linear-time complexity of the plain BP decoder. In addition, we explore a new subclass of BB codes, that we refer to as the univariate bicycle (UB) codes, specifically with lower-weight parity checks ($w=6,8$). This reduces the polynomial search space for the code compared to general BB codes, i.e., by reducing the search space over two polynomial components in BB codes to just a single polynomial component in UB codes. Simulations demonstrate the promising performance of these codes under various types of BP decoders.

cs.IT↗

arXiv2025

Layered Normalized Min-Sum Decoding with Bit Flipping for FDPC Codes

Fair-density parity-check (FDPC) codes have been recently introduced demonstrating improved performance compared to low-density parity-check (LDPC) codes standardized in 5G systems particularly in high-rate regimes. In this paper, we introduce a layered normalized min-sum (LNMS) message-passing decoding algorithm for the FDPC codes. We also introduce a syndrome-guided bit flipping (SGBF) method to enhance the error-correction performance of our proposed decoder. The LNMS decoder leverages conflict graph coloring for efficient layered scheduling, enabling faster convergence by grouping non-conflicting check nodes and updating variable nodes immediately after each layer. In the event of decoding failure, the SGBF method is activated, utilizing a novel reliability metric that combines log-likelihood ratio (LLR) magnitudes and syndrome-derived error counts to identify the least reliable bits. A set of candidate sequences is then generated by performing single-bit flips at these positions, with each candidate re-decoded via LNMS. The optimal candidate is selected based on the minimum syndrome weight. Extensive simulation results demonstrate the superiority of the proposed decoder. Numerical simulations on FDPC$(256,192)$ code with a bit-flipping set size of $T = 128$ and a maximum of $5$ iterations demonstrate that the proposed decoder achieves approximately a $0.5\,\mathrm{dB}$ coding gain over standalone LNMS decoding at a frame error rate (FER) of $10^{-3}$, while providing coding gains of $0.75-1.5\,\mathrm{dB}$ over other state-of-the-art codes including polar codes and 5G-LDPC codes at the same length and rate and also under belief propagation decoding.

cs.IT↗

arXiv2025

A New Metric Function for SC-based Polar Decoders: Polarization, Pruning, and Fast Decoders

In this paper, we propose a method to obtain the optimal metric function at each depth of the polarization tree through a process we call polarization of the metric function. This polarization process generates an optimal metric at intermediate levels of the polarization tree, which can be applied in fast successive-cancellation-based (FSC) and SC list-based (FSCL) decoders -- decoders that partially explore the binary tree representation. We prove that at each step of the polarization tree, the expected value of the metric function random variable is the mutual information of the corresponding channel, while its variance equals the varentropy of the channel -- two parameters that are particularly relevant in finite block-length regimes. Additionally, we show that after polarization, the variances of the bit metrics approach zero for binary-input discrete memoryless channels (BI-DMCs). Moreover, we provide an estimate for calculating the variance of the binary-input additive white Gaussian noise (BI-AWGN) channel. We introduce a list-pruning strategy for FSCL decoding that retains only the paths whose metric values are close to the average. As a result, our method significantly reduces the number of required sorting operations in FSCL-based decoding algorithms. We also derive an upper bound, as a function of the polarized channel varentropy, on the probability that the distance between a bit-metric random variable and the bit-channel mutual information exceeds a given threshold. Leveraging this result, we further propose a varentropy-based list-pruning strategy for the SCL (VPSCL) decoding algorithm that adapts to the varentropy of the corresponding bit-channel. Our proposed pruning strategy also benefits stack decoding (VPStack) by discarding partial paths and avoiding unnecessary extensions.

cs.IT↗

arXiv2025

PAC codes with Bounded-Complexity Sequential Decoding: Pareto Distribution and Code Design

Recently, a novel variation of polar codes known as polarization-adjusted convolutional (PAC) codes has been introduced by Arıkan. These codes significantly outperform conventional polar and convolutional codes, particularly for short codeword lengths, and are shown to operate very close to the optimal bounds. It has also been shown that if the rate profile of PAC codes does not adhere to certain polarized cutoff rate constraints, the computation complexity for their sequential decoding grows exponentially. In this paper, we address the converse problem, demonstrating that if the rate profile of a PAC code follows the polarized cutoff rate constraints, the required computations for its sequential decoding can be bounded with a distribution that follows a Pareto distribution. This serves as a guideline for the rate-profile design of PAC codes. For a high-rate PAC\,$(1024,899)$ code, simulation results show that the PAC code with Fano decoder, when constructed based on the polarized cutoff rate constraints, achieves a coding gain of more than $0.75$ dB at a frame error rate (FER) of $10^{-5}$ compared to the state-of-the-art 5G polar and LDPC codes.

cs.IT↗

arXiv2025

A Locally Differential Private Coding-Assisted Succinct Histogram Protocol

A succinct histogram captures frequent items and their frequencies across clients and has become increasingly important for large-scale, privacy-sensitive machine learning applications. To develop a rigorous framework to guarantee privacy for the succinct histogram problem, local differential privacy (LDP) has been utilized and shown promising results. To preserve data utility under LDP, which essentially works by intentionally adding noise to data, error-correcting codes naturally emerge as a promising tool for reliable information collection. This work presents the first practical $(ε,δ)$-LDP protocol for constructing succinct histograms using error-correcting codes. To this end, polar codes and their successive-cancellation list (SCL) decoding algorithms are leveraged as the underlying coding scheme. More specifically, our protocol introduces Gaussian-based perturbations to enable efficient soft decoding. Experiments demonstrate that our approach outperforms prior methods, particularly for items with low true frequencies, while maintaining similar frequency estimation accuracy.

cs.CR↗

arXiv2025

Bounds and New Constructions for Girth-Constrained Regular Bipartite Graphs

In this paper, we explore the design and analysis of regular bipartite graphs motivated by their application in low-density parity-check (LDPC) codes specifically with constrained girth and in the high-rate regime. We focus on the relation between the girth of the graph, and the size of the sets of variable and check nodes. We derive bounds on the size of the vertices in regular bipartite graphs, showing how the required number of check nodes grows with respect to the number of variable nodes as girth grows large. Furthermore, we present two constructions for bipartite graphs with girth $\mathcal{G} = 8$; one based on a greedy construction of $(w_c, w_r)$-regular graphs, and another based on semi-regular graphs which have uniform column weight distribution with a sublinear number of check nodes. The second construction leverages sequences of integers without any length-$3$ arithmetic progression and is asymptotically optimal while maintaining a girth of $8$. Also, both constructions can offer sparse parity-check matrices for high-rate codes with medium-to-large block lengths. Our results solely focus on the graph-theoretic problem but can potentially contribute to the ongoing effort to design LDPC codes with high girth and minimum distance, specifically in high code rates.

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