Related papers: Analysis of cubic permutation polynomials for turb…
An interleaver is a critical component for the channel coding performance of turbo codes. Algebraic constructions are of particular interest because they admit analytical designs and simple, practical hardware implementation. Also, the…
This paper proposes and proves a theorem which stipulates sufficient conditions the coefficients of two quadratic permutation polynomials (QPP) must satisfy, so that the permutations generated by them are identical. The result is used to…
An interleaver is a critical component for the channel coding performance of turbo codes. Algebraic constructions are of particular interest because they admit analytical designs and simple, practical hardware implementation.…
An interleaver is a critical component for the channel coding performance of turbo codes. Algebraic constructions are of particular interest because they admit analytical designs and simple, practical hardware implementation. Sun and…
Quadratic permutation polynomial interleavers over integer rings have recently received attention in practical turbo coding systems from deep space applications to mobile communications. In this correspondence, a necessary and sufficient…
An interleaver is a critical component for the channel coding performance of turbo codes. Algebraic constructions are important because they admit analytical designs and simple, practical hardware implementation. The spread factor of an…
In this work, we consider the minimum distance properties and convergence thresholds of 3-dimensional turbo codes (3D-TCs), recently introduced by Berrou et al.. Here, we consider binary 3D-TCs while the original work of Berrou et al.…
Constant amplitude zero autocorrelation (CAZAC) sequences have modulus one and ideal periodic autocorrelation function. Such sequences are used in cellular radio communications systems, e.g., for reference signals, synchronization signals…
A new construction is proposed for low density parity check (LDPC) codes using quadratic permutation polynomials over finite integer rings. The associated graphs for the new codes have both algebraic and pseudo-random nature, and the new…
The structure and size of the interleaver used in a turbo code critically affect the distance spectrum and the covariance property of a component decoder's information input and soft output. This paper introduces a new class of…
Cryptanalysis increases the level of confidence in cryptographic algorithms. We analyze the security of a symmetric cryptographic algorithm - quantum permutation pad (QPP) [8]. We found the instances of ciphertext the same as plaintext even…
This paper presents an efficient quadratic programming (QP) decoder via the alternating direction method of multipliers (ADMM) technique, called QP-ADMM, for binary low-density parity-check (LDPC) codes. Its main contents are as follows:…
We present a theory of quantum serial turbo-codes, describe their iterative decoding algorithm, and study their performances numerically on a depolarization channel. Our construction offers several advantages over quantum LDPC codes. First,…
Every Latin square of prime power order $q$ is uniquely described by a local permutation polynomial (LPP) in the polynomial ring $\mathbb{F}_q[x,y]$. Despite this equivalence, one may find in the literature only some preliminary results on…
This paper addresses biquadratic polynomial programming (BPP), an NP-hard optimization problem closely related to biquadratic tensors. We first establish several necessary and sufficient conditions for the positive semi-definiteness and…
This work aims to introduce the framework of polynomial optimization theory to solve fractional polynomial problems (FPPs). Unlike other widely used optimization frameworks, the proposed one applies to a larger class of FPPs, not…
Quantum linear system solvers typically realize the inverse map as a polynomial transformation of the spectrum, so their practical cost hinges on implementing this transformation at a low polynomial degree. We introduce constrained optimal…
We present an interleaving scheme that yields quasi-cyclic turbo codes. We prove that randomly chosen members of this family yield with probability almost 1 turbo codes with asymptotically optimum minimum distance, i.e. growing as a…
It has been widely observed that there exists a fundamental trade-off between the minimum (Hamming) distance properties and the iterative decoding convergence behavior of turbo-like codes. While capacity achieving code ensembles typically…
Let $q$ be a prime power, $2\le r\le q$, and $f=a{\tt X}+{\tt X}^{r(q-1)+1}\in\Bbb F_{q^2}[{\tt X}]$, where $a\ne 0$. The conditions on $r,q,a$ that are necessary and sufficient for $f$ to be a permutation polynomial (PP) of ${\Bbb…