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Hassan Khodaiemehr

Publications and source records attributed to Hassan Khodaiemehr.

13 recordsLinked to original sources
arXiv2026

Rateless Nested Lattice Codes for Secure Cooperative V2X Broadcast over Fading and Erasure Channels

Vehicle-to-everything (V2X) sidelink and uplink broadcast must deliver safety-critical and application-layer data reliably under fast time-varying fading, intermittent packet erasures, and exposure to passive eavesdroppers. Fixed-rate physical-layer codes are poorly matched to these conditions because link quality and the number of successfully received symbols vary across vehicles and over time. This paper proposes a unified vehicular communication framework that combines rateless Construction-D' Raptor lattices, nested-lattice physical-layer security (PLS) with direct-sequence spread spectrum (DSSS), and blockchain-assisted trust management for decode-and-forward (DF) cooperative relaying. At the physical layer, Raptor codes provide incremental redundancy over unreliable V2X links; multilevel lattice decoding enables power-efficient joint coding and modulation; nested shaping and spread spectrum limit fine-lattice recovery by eavesdroppers; and a distributed ledger records decoding success at relays to support reputation-aware relay selection. We model the vehicular air interface as a block-Rayleigh fading channel with additive Gaussian noise and random symbol erasures, representative of urban V2X sidelink behavior. The proposed code concatenates Luby-transform (LT) codes with quasi-cyclic low-density parity-check (QC-LDPC) precodes within Construction-D', with girth-4 cycle removal on the Tanner graph. AWGN benchmarks show competitive symbol error rate (SER) and improved frame error rate (FER) versus matched-length LDPC and LDLC lattices. Under block-Rayleigh fading with erasures, for n=995 at average VNR of 1.5 dB and erasure probability 0.15, rateless Raptor reception achieves 0.3% outage with about 2.3 packets on average, outperforming LDLC and LDPC under identical channels, while an eavesdropper with 8 dB combined SNR and spreading loss fails in 62% of sessions.

cs.IT↗
arXiv2026

Orbit Reduction and Learned Run Distributions for Finite-Blocklength Binary Deletion Channels

In DNA data storage, racetrack memories, and packet networks, data are written as many short strands of fixed length. The receiver knows where each strand begins and ends, and deletions occur only inside a strand. The relevant limit for such systems is the block capacity $C_N(d)$, the largest mutual information between a length-$N$ input and the output of a binary deletion channel with deletion probability $d$. Because the boundaries are known, $C_N(d)/N$ is never smaller than the classical capacity $C(d)$. Computing $C_N(d)$ is hard because the input takes $2^N$ values. For $0\le d<1$, we show that the optimal input is unique, gives positive probability to every string, and is unchanged by complementing or reversing the strings. We then introduce the optimized run distribution (ORD), which assigns one probability to each number of runs; it is optimal for $N\le3$ and is solved with a numerical optimality certificate up to $N=16$. For longer strands, an exact recursion for the output distribution gives unbiased rate estimates, and an empirical Bernstein inequality turns them into confidence intervals. Within the statistical precision, a one-parameter Markov input performs as well as the best inputs found. For strands of 100-200 bits, known boundaries increase the rate by up to 0.026 bits per symbol beyond the best certified upper bound on the capacity of the unsegmented channel. Via Fano's inequality, the block capacity also bounds the rate of any code that uses a single strand; in the tabulated case, this bound is tighter than the best known finite-length bound for strands longer than about 90 bits. Conversely, block rates yield lower bounds on $C(d)$; at $d=0.1$, the bound is within $1.1\times10^{-4}$ bits/use of the best certified lower bound. Finally, InfoNCE estimates, even with the optimal critic, empirically lose most of their ability to rank inputs as the strand length grows.

cs.IT↗
arXiv2026

Improved Lower Bounds on the Capacity of the Binary Deletion Channel via a Learning Approach to Run-Length Inputs

The best constructive lower bounds on the capacity of the binary deletion channel come from random codes with independent run lengths, yet the two strongest such bounds, due to Drinea and Mitzenmacher and to Venkataramanan, Tatikonda, and Ramchandran, have been evaluated mainly for geometric or low-parameter run-length laws. We let a learning algorithm choose the run-length law freely, which raises three challenges. First, the Drinea-Mitzenmacher functional is an infinite sum over the ways deletions merge runs; we show that it depends on the law only through its mean, its full-deletion probability, and bilinear forms in the law and its renewal weights, so that gradients of truncations are exact and every truncation can only lower the bound. Second, for non-Markov inputs the output is no longer Markov and the Venkataramanan-Tatikonda-Ramchandran analysis breaks down; we show that the residual length of the current input run turns the output into a hidden Markov chain, which extends the bound to every finite-support law. Third, its correction term counts only output runs formed from three input runs; we prove a larger correction that accounts for every output run formed by several input runs, which improves the published bound even for truncated geometric laws. Certified by interval arithmetic, the new bounds exceed all previously published deterministic lower bounds at every tabulated deletion probability, by up to $6.86\times10^{-3}$ bits per channel use and 6.8%. At large deletion probability the learned laws concentrate on run-length clusters with survivor counts about two standard deviations apart, like a pulse-amplitude constellation.

cs.IT↗
arXiv2026

SILMARILS: Information-Theoretic and Quantum-Secure Designated-Verifier Signatures

SILMARILS is built from a minimal algebraic core over $\mathbb{F}_p$ using true randomness and perfect $2$-out-of-$2$ Shamir secret sharing. The framework supports both two-party and three-party modes. In the two-party setting, SILMARILS realizes a transferable designated-verifier (TDV) signature scheme. The designated verifier can simulate accepting transcripts indistinguishable from real ones, achieving Jakobsson-Sako-Impagliazzo DV security. The verifier may publish a receipt $r$ enabling public verification, yet even with $r$, no external party can tell whether a transcript was signed or simulated. As DV signatures permit simulation, standard EUF-CMA cannot hold for the designated verifier; instead, we prove $\mathsf{EUF\text{-}CMA}^{\neg\mathsf{DV}}$ security for all non-designated verifiers in both the random oracle model (ROM) and quantum random oracle model (QROM). In the three-party mode, adopting the broadcast model of Fitzi et al., we obtain a statistically secure signature protocol with simulation-based security and error $1/p$. We analyze security in the Pure IT model, the IT+ROM, and the QROM, extending the Fitzi et al. framework to quantum adversaries with classical I/O. Correctness, secrecy, transferability, and unforgeability for non-designated parties remain equivalent to simulation-based security. Thanks to its simple algebraic structure, SILMARILS offers very compact keys and signatures for the blockchain settings we target, where standardized PQC schemes are already more than sufficient. Our goal is not to compare SILMARILS with PQC, but to highlight its suitability for lightweight TDV authentication. A fair comparison with other DV schemes is omitted due to space and the complexity of aligning models.

cs.CR↗
arXiv2025

Blockchain Security Risk Assessment in Quantum Era, Migration Strategies and Proactive Defense

The emergence of quantum computing presents a formidable challenge to the security of blockchain systems. Traditional cryptographic algorithms, foundational to digital signatures, message encryption, and hashing functions, become vulnerable to the immense computational power of quantum computers. This paper conducts a thorough risk assessment of transitioning to quantum-resistant blockchains, comprehensively analyzing potential threats targeting vital blockchain components: the network, mining pools, transaction verification mechanisms, smart contracts, and user wallets. By elucidating the intricate challenges and strategic considerations inherent in transitioning to quantum-resistant algorithms, the paper evaluates risks and highlights obstacles in securing blockchain components with quantum-resistant cryptography. It offers a hybrid migration strategy to facilitate a smooth transition from classical to quantum-resistant cryptography. The analysis extends to prominent blockchains such as Bitcoin, Ethereum, Ripple, Litecoin, and Zcash, assessing vulnerable components, potential impacts, and associated STRIDE threats, thereby identifying areas susceptible to quantum attacks. Beyond analysis, the paper provides actionable guidance for designing secure and resilient blockchain ecosystems in the quantum computing era. Recognizing the looming threat of quantum computers, this research advocates for a proactive transition to quantum-resistant blockchain networks. It proposes a tailored security blueprint that strategically fortifies each component against the evolving landscape of quantum-induced cyber threats. Emphasizing the critical need for blockchain stakeholders to adopt proactive measures and implement quantum-resistant solutions, the paper underscores the importance of embracing these insights to navigate the complexities of the quantum era with resilience and confidence.

cs.CR↗
arXiv2025

Full-Diversity Construction-D Lattices: Design and Decoding Perspective on Block-Fading Channels

This paper introduces a novel framework for constructing algebraic lattices based on Construction-D, leveraging nested linear codes and prime ideals from algebraic number fields. We focus on the application of these lattices in block-fading (BF) channels, which are characterized by piecewise-constant fading across blocks of transmitted symbols. This approach results in a semi-systematic generator matrix, providing a structured foundation for high-dimensional lattice design for BF channels. The proposed Construction-D lattices exhibit the full diversity property, making them highly effective for error performance improvement. To address this, we develop an efficient decoding algorithm designed specifically for full-diversity Construction-D lattices. Simulations indicate that the proposed lattices notably enhance error performance compared to full-diversity Construction-A lattices in diversity-2 cases. Interestingly, unlike AWGN channels, the expected performance enhancement of Construction-D over Construction-A, resulting from an increased number of nested code levels, was observed only in the two-level and diversity-2 cases. This phenomenon is likely attributed to the intensified effects of error propagation that occur during successive cancellation at higher levels, as well as the higher diversity orders. These findings highlight the promise of Construction-D lattices as an effective coding strategy for enhancing communication reliability in BF channels.

cs.IT↗
arXiv2024

Improving Privacy-Preserving Techniques for Smart Grid using Lattice-based Cryptography

Advancements in communication and information tech birthed the Smart Grid, optimizing energy and data transmission. Yet, user privacy is at risk due to frequent data collection. Existing privacy schemes face vulnerability with quantum machines. To tackle this, the LPM2DA scheme is introduced, utilizing lattice-based encryption and signatures for secure data aggregation. It ensures privacy, integrity, and authentication, enabling statistical analysis while preserving user privacy. Traditional aggregation schemes suffer from weak network models and centralization issues. Enter SPDBlock, a blockchain-based solution ensuring privacy, integrity, and resistance to attacks. It detects and prosecutes malicious entities while efficiently handling multi-dimensional data transmission. Through distributed decryption and secret sharing, only valid data can be decrypted with minimal involvement from smart meters. Performance tests reveal SPDBlock's superiority in communication and computational efficiency over traditional schemes.

cs.CR↗
arXiv2020

Design and Practical Decoding of Full-Diversity Construction A Lattices for Block-Fading Channels

Block-fading channel (BF) is a useful model for various wireless communication channels in both indoor and outdoor environments. The design of lattices for BF channels offers a challenging problem, which differs greatly from its counterparts like AWGN channels. Recently, the original binary Construction A for lattices, due to Forney, has been generalized to a lattice construction from totally real and complex multiplication (CM) fields. This generalized algebraic Construction A of lattices provides signal space diversity, intrinsically, which is the main requirement for the signal sets designed for fading channels. In this paper, we construct full-diversity algebraic lattices for BF channels using Construction A over totally real number fields. We propose two new decoding methods for these lattices which have complexity that grows linearly in the dimension of the lattice. The first decoder is proposed for generalized Construction A lattices with a binary LDPC code as underlying code. This decoding method contains iterative and non-iterative phases. In order to implement the iterative phase, we propose the definition of a parity-check matrix and Tanner graph for Construction A lattices. We also prove that using an underlying LDPC code that achieves the outage probability limit over one-BF channel, the constructed algebraic LDPC lattices together with the proposed decoding method admit diversity order n. Then, we modify the proposed algorithm by removing its iterative phase which enables full-diversity practical decoding of all generalized Construction A lattices without any assumption about their underlying code. We provide some instances showing that algebraic Construction A lattices obtained from binary codes outperform the ones based on non-binary codes in BF channels. We generalize algebraic Construction A lattices over a wider family of number fields namely monogenic number fields.

cs.IT↗
arXiv2017

Construction and Encoding of QC-LDPC Codes Using Group Rings

Quasi-cyclic (QC) low-density parity-check (LDPC) codes which are known as QC-LDPC codes, have many applications due to their simple encoding implementation by means of cyclic shift registers. In this paper, we construct QC-LDPC codes from group rings. A group ring is a free module (at the same time a ring) constructed in a natural way from any given ring and any given group. We present a structure based on the elements of a group ring for constructing QC-LDPC codes. Some of the previously addressed methods for constructing QC-LDPC codes based on finite fields are special cases of the proposed construction method. The constructed QC-LDPC codes perform very well over the additive white Gaussian noise (AWGN) channel with iterative decoding in terms of bit-error probability and block-error probability. Simulation results demonstrate that the proposed codes have competitive performance in comparison with the similar existing LDPC codes. Finally, we propose a new encoding method for the proposed group ring based QC-LDPC codes that can be implemented faster than the current encoding methods. The encoding complexity of the proposed method is analyzed mathematically, and indicates a significate reduction in the required number of operations, even when compared to the available efficient encoding methods that have linear time and space complexities.

cs.IT↗
arXiv2016

Construction of Full-Diversity LDPC Lattices for Block-Fading Channels

LDPC lattices were the first family of lattices which have an efficient decoding algorithm in high dimensions over an AWGN channel. Considering Construction D' of lattices with one binary LDPC code as underlying code gives the well known Construction A LDPC lattices or 1-level LDPC lattices. Block-fading channel (BF) is a useful model for various wireless communication channels in both indoor and outdoor environments. Frequency-hopping schemes and orthogonal frequency division multiplexing (OFDM) can conveniently be modelled as block-fading channels. Applying lattices in this type of channel entails dividing a lattice point into multiple blocks such that fading is constant within a block but changes, independently, across blocks. The design of lattices for BF channels offers a challenging problem, which differs greatly from its counterparts like AWGN channels. Recently, the original binary Construction A for lattices, due to Forney, have been generalized to a lattice construction from totally real and complex multiplication fields. This generalized Construction A of lattices provides signal space diversity intrinsically, which is the main requirement for the signal sets designed for fading channels. In this paper we construct full diversity LDPC lattices for block-fading channels using Construction A over totally real number fields. We propose a new iterative decoding method for these family of lattices which has complexity that grows linearly in the dimension of the lattice. In order to implement our decoding algorithm, we propose the definition of a parity check matrix and Tanner graph for full diversity Construction A lattices. We also prove that the constructed LDPC lattices together with the proposed decoding method admit diversity order n-1 over an n-block-fading channel.

cs.IT↗
arXiv2016

LDPC Lattice Codes for Full-Duplex Relay Channels

Low density parity check (LDPC) lattices are obtained from Construction D' and a family of nested binary LDPC codes. We consider an special case of these lattices with one binary LDPC code as underlying code. This special case of LDPC lattices can be obtained by lifting binary LDPC codes using Construction A lattices. The LDPC lattices were the first family of lattices which have efficient decoding in high dimensions. We employ the encoding and decoding of the LDPC lattices in a cooperative transmission framework. We establish two efficient shaping methods based on hypercube shaping and Voronoi shaping, to obtain LDPC lattice codes. Then, we propose the implementation of block Markov encoding for one-way and two-way relay networks using LDPC lattice codes. This entails owning an efficient method for decomposing full-rate codebook into lower rate codebooks. We apply different decomposition schemes for one-way and two-way relay channels which are the altered versions of the decomposition methods of low density lattice codes (LDLCs). Due to the lower complexity of the decoding for LDPC lattices comparing to LDLCs, the complexity of our schemes are significantly lower than the ones proposed for LDLCs. The efficiency of the proposed schemes are presented using simulation results.

cs.IT↗
arXiv2016

Practical Encoder and Decoder for Power Constrained QC-LDPC lattices

LDPC lattices were the first family of lattices that equipped with iterative decoding algorithms under which they perform very well in high dimensions. In this paper, we introduce quasi cyclic low density parity check (QC-LDPC) lattices as a special case of LDPC lattices with one binary QC-LDPC code as their underlying code. These lattices are obtained from Construction A of lattices providing us to encode them efficiently using shift registers. To benefit from an encoder with linear complexity in dimension of the lattice, we obtain the generator matrix of these lattices in "quasi cyclic" form. We provide a low-complexity decoding algorithm of QC-LDPC lattices based on sum product algorithm. To design lattice codes, QC-LDPC lattices are combined with nested lattice shaping that uses the Voronoi region of a sublattice for code shaping. The shaping gain and shaping loss of our lattice codes with dimensions $40$, $50$ and $60$ using an optimal quantizer, are presented. Consequently, we establish a family of lattice codes that perform practically close to the sphere bound.

cs.IT↗