Related papers: A Lattice Based Joint Encryption, Encoding and Mod…
Recent advances in quantum computing pose a serious threat on the security of widely used public-key cryptosystems. Thus, new post-quantum cryptographic algorithms have been proposed as part of the associated US NIST process to enable…
We use random linear network coding (RLNC) based scheme for multipath communication in the presence of lossy links with different delay characteristics to obtain ultra-reliability and low latency. A sliding window version of RLNC is…
We demonstrate a decoding scheme for nested lattice codes which is able to decode a list of a particular size which contains the transmitted codeword with high probability. This list decoder is analogous to that used in random coding…
LDPC (Low Density Parity Check) codes are among the most powerful and widely adopted modern error correcting codes. The iterative decoding algorithms required for these codes involve high computational complexity and high processing…
We propose a new coding scheme using only one lattice that achieves the $\frac{1}{2}\log(1+\SNR)$ capacity of the additive white Gaussian noise (AWGN) channel with lattice decoding, when the signal-to-noise ratio $\SNR>e-1$. The scheme…
We introduce the use of Fourier analysis on lattices as an integral part of a lattice based construction. The tools we develop provide an elegant description of certain Gaussian distributions around lattice points. Our results include two…
This paper studies coding schemes for the $q$-ary symmetric channel based on binary low-density parity-check (LDPC) codes that work for any alphabet size $q=2^m$, $m\in\mathbb{N}$, thus complementing some recently proposed packet-based…
In this article, we study some parallel processing algorithms for multiplication and modulo operations. We demonstrate that the state transitions that are formed under these algorithms satisfy lattice-linearity, where these algorithms…
Physical-layer network coding (PNC) is a communications paradigm that exploits overlapped transmissions to boost the throughput of wireless relay networks. A high point of PNC research was a theoretical proof that PNC that makes use of…
We present a general framework for studying the multilevel structure of lattice network coding (LNC), which serves as the theoretical fundamental for solving the ring-based LNC problem in practice, with greatly reduced decoding complexity.…
NTRU public key cryptosystem is well studied lattice-based Cryptosystem along with Ajtai-Dwork and GGH systems. Underlying NTRU is a hard mathematical problem of finding short vectors in a certain lattice. (Shamir 1997) presented a…
In this paper, fast-decodable lattice code constructions are designed for the nonorthogonal amplify-and-forward (NAF) multiple-input multiple-output (MIMO) channel. The constructions are based on different types of algebraic structures,…
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…
The low-density parity-check (LDPC) lattices perform very well in high dimensions under generalized min-sum iterative decoding algorithm. In this work we focus on 1-level LDPC lattices. We show that these lattices are the same as lattices…
In recent years, establishing secure visual communications has turned into one of the essential problems for security engineers and researchers. However, only limited novel solutions are provided for image encryption, and limiting the…
A fundamental problem in coding theory is the design of an efficient coding scheme that achieves the capacity of the additive white Gaussian (AWGN) channel. The main objective of this short note is to point out that by concatenating a…
Lattice coding techniques may be used to derive achievable rate regions which outperform known independent, identically distributed (i.i.d.) random codes in multi-source relay networks and in particular the two-way relay channel. Gains stem…
A new coded modulation scheme is proposed. At the transmitter, the concatenation of a distribution matcher and a systematic binary encoder performs probabilistic signal shaping and channel coding. At the receiver, the output of a bitwise…
We propose a framework for constructing efficient code-based encryption schemes from codes that do not hide any structure in their public matrix. The framework is in the spirit of the schemes first proposed by Alekhnovich in 2003 and based…
The use of codes defined by sparse characteristic matrices, like QC-LDPC and QC-MDPC codes, has become an established solution to design secure and efficient code-based public-key encryption schemes, as also witnessed by the ongoing NIST…