374 citations · 818 across the 73 of their papers we have counts for
63 papers · 1 filter
The Most Informative Bit and Beyond: A Proof of the Courtade--Kumar Conjecture and Multibit Extensions
Hessam Mahdavifar, Ahmad Beirami
Let \(X=(X_1,\ldots,X_n)\) be uniform on the Boolean cube, and let \(Y\) be obtained by passing its coordinates independently through a binary symmetric channel with crossover prob…
Quantum LDPC and High-Rate CSS Codes from Fair-Density Parity-Check Codes
Hessam Mahdavifar
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 spar…
Univariate Bicycle Quantum LDPC Codes: Explicit Logical Structure and Distance Bounds
Sheida Rabeti, Hessam Mahdavifar
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…
Multiple-Bases Belief Propagation List Decoding for Quantum LDPC Codes
Sheida Rabeti, Hessam Mahdavifar
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)…
Covering in Hamming and Grassmann Spaces: New Bounds and Reed--Solomon-Based Constructions
Samin Riasat, Hessam Mahdavifar
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 gen…
List Decoding and New Bicycle Code Constructions for Quantum LDPC Codes
Sheida Rabeti, Hessam Mahdavifar
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 Mul…
Layered Normalized Min-Sum Decoding with Bit Flipping for FDPC Codes
Niloufar Hosseinzadeh, Mohsen Moradi, Hessam Mahdavifar
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…
Efficient Low-Memory Fast Stack Decoding with Variance Polarization for PAC Codes
Mohsen Moradi, Hessam Mahdavifar
Polarization-adjusted convolutional (PAC) codes have recently emerged as a promising class of error-correcting codes, achieving near-capacity performance particularly in the short…
On the High-Rate FDPC Codes: Construction, Encoding, and a Generalization
Mohsen Moradi, Sheida Rabeti, Hessam Mahdavifar
Recently introduced Fair-Density Parity-Check (FDPC) codes, targeting high-rate applications, offer superior error-correction performance (ECP) compared to 5G Low-Density Parity-Ch…
Bounds and New Constructions for Girth-Constrained Regular Bipartite Graphs
Sheida Rabeti, Mohsen Moradi, Hessam Mahdavifar
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…
Efficient Covering Using Reed--Solomon Codes
Samin Riasat, Hessam Mahdavifar
We propose an efficient algorithm to find a Reed-Solomon (RS) codeword at a distance within the covering radius of the code from any point in its ambient Hamming space. To the best…
PAC codes with Bounded-Complexity Sequential Decoding: Pareto Distribution and Code Design
Mohsen Moradi, Hessam Mahdavifar
Recently, a novel variation of polar codes known as polarization-adjusted convolutional (PAC) codes has been introduced by Arıkan. These codes significantly outperform conventional…
A New Metric Function for SC-based Polar Decoders: Polarization, Pruning, and Fast Decoders
Mohsen Moradi, Hessam Mahdavifar
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…
Decoding Analog Subspace Codes: Algorithms for Character-Polynomial Codes
Samin Riasat, Hessam Mahdavifar
We propose efficient minimum-distance decoding and list-decoding algorithms for a certain class of analog subspace codes, referred to as character-polynomial (CP) codes, recently i…
Finite-Length Analysis of Polar Secrecy Codes for Wiretap Channels
Hessam Mahdavifar, Fariba Abbasi
In a classical wiretap channel setting, Alice communicates with Bob through a main communication channel, while her transmission also reaches an eavesdropper Eve through a wiretap…
Abelian Group Codes for Classical and Classical-Quantum Channels: One-shot and Asymptotic Rate Bounds
James Chin-Jen Pang, Sandeep Pradhan, Hessam Mahdavifar
We study the problem of transmission of information over classical and classical-quantum channels in the one-shot regime where the underlying codes are constrained to be group code…
Bounds on the Statistical Leakage-Resilience of Shamir's Secret Sharing
Utkarsh Gupta, Hessam Mahdavifar
Secret sharing is an instrumental tool for sharing secret keys in distributed systems. In a classical threshold setting, this involves a dealer who has a secret/key, a set of parti…
High-Rate Fair-Density Parity-Check Codes
Hessam Mahdavifar
We introduce fair-density parity-check (FDPC) codes targeting high-rate applications. In particular, we start with a base parity-check matrix of dimension $2 \sqrt{n} \times…
Matrix Completion over Finite Fields: Bounds and Belief Propagation Algorithms
Mahdi Soleymani, Qiang Liu, Hessam Mahdavifar +1
We consider the low rank matrix completion problem over finite fields. This problem has been extensively studied in the domain of real/complex numbers, however, to the best of auth…
Iterative Sketching for Secure Coded Regression
Neophytos Charalambides, Hessam Mahdavifar, Mert Pilanci +1
Linear regression is a fundamental and primitive problem in supervised machine learning, with applications ranging from epidemiology to finance. In this work, we propose methods fo…
Machine Learning-Aided Efficient Decoding of Reed-Muller Subcodes
Mohammad Vahid Jamali, Xiyang Liu, Ashok Vardhan Makkuva +3
Reed-Muller (RM) codes achieve the capacity of general binary-input memoryless symmetric channels and are conjectured to have a comparable performance to that of random codes in te…
Orthonormal Sketches for Secure Coded Regression
Neophytos Charalambides, Hessam Mahdavifar, Mert Pilanci +1
In this work, we propose a method for speeding up linear regression distributively, while ensuring security. We leverage randomized sketching techniques, and improve straggler resi…
Low-Complexity Decoding of a Class of Reed-Muller Subcodes for Low-Capacity Channels
Mohammad Vahid Jamali, Mohammad Fereydounian, Hessam Mahdavifar +1
We present a low-complexity and low-latency decoding algorithm for a class of Reed-Muller (RM) subcodes that are defined based on the product of smaller RM codes. More specifically…
New Bounds on the Size of Binary Codes with Large Minimum Distance
James Chin-Jen Pang, Hessam Mahdavifar, S. Sandeep Pradhan
Let denote the maximum size of a binary code of length and minimum Hamming distance . Studying , including efforts to determine it as well to derive bound…