On the Probability of Partial Decoding in Sparse Network Coding

Hadi Sehat; Peyman Pahlevani

Home/Archive/arXiv

arXiv · 1907.12051

On the Probability of Partial Decoding in Sparse Network Coding

Hadi Sehat·Peyman Pahlevani

View original source ↗Read source document ↗Export metadata ↓

Abstract

Sparse Network Coding (SNC) has been a promising network coding scheme as an improvement for Random Linear Network Coding (RLNC) in terms of the computational complexity. However, in this literature, there has been no analytical expressions for the probability of decoding a fraction of source messages after transmission of some coded packets. In this work, we looked into the problem of the probability of decoding a fraction of source messages, i.e., partial decoding, in the decoder for a system which uses SNC. We exploited the Principle of Inclusion and Exclusion to derive expressions of partial decoding probability. The presented model predicts the probability of partial decoding with an average deviation of 6%. Our results show that SNC has a great potential for recovering a fraction of the source message, especially in higher sparsity and lower Galois Field size. Moreover, to achieve a better probability of partial decoding throughout transmissions, we define a sparsity tuning scheme that significantly increases the probability of partial decoding. Our results show that this tuning scheme achieves a 16% improvement in terms of probability of decoding a fraction of source packets with respect to traditional SNC.

Explore related subjects

cs.IT math.IT

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Hadi Sehat, Peyman Pahlevani. 2019-07-28. On the Probability of Partial Decoding in Sparse Network Coding. https://arxiv.org/abs/1907.12051

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Fundamental Scaling Laws of Covert Communication in the Presence of Block Fading

Covert communication is the undetected transmission of sensitive information over a communication channel. In wireless communication systems, channel impairments such as signal fading present challenges in the effective implementation and analysis of covert communication systems. This paper generalizes early work in the covert communication field by considering asymptotic results for the number of bits that can be covertly transmitted in $n$ channel uses on a block fading channel. Critical to the investigation is characterizing the performance of optimal detectors at the adversary. Matching achievable and converse results are presented.

cs.IT↗

arXiv2026

Sequence Reconstruction over the Deletion Channel

In this paper, we consider the Levenshtein's sequence reconstruction problem in the case where the transmitted codeword is chosen from $\{0,1\}^n$ and the channel can delete up to $t$ symbols from the transmitted codeword. We determine the minimum number of channel outputs (assuming that they are distinct) required to reconstruct a list of size $\ell-1$ of candidate sequences, one of which corresponds to the original transmitted sequence. More specifically, we determine the maximum possible size of the intersection of $\ell \geq 3$ deletion balls of radius $t$ centered at $x_1, x_2, \dots, x_{\ell}$, where $x_i \in \{0,1\}^n$ for all $i \in \{1,2,\dots,\ell\}$ and $x_i \neq x_j$ for $i \neq j$, with $ n \geq t+\ell-1$ and $t \geq 1$.

cs.IT↗

arXiv2026

A generalization of the map $χ$

The mapping $ χ_n:\mathbb{F}_2^n \to \mathbb{F}_2^n$ defined by $y=χ_n(x)$ with $y_i = x_i + x_{i+1}x_{i+2} + x_{i+2}$, where the indices are computed modulo $n$, has been widely studied for its application in lightweight cryptography. In this paper, we generalize this mapping and completely characterize all these shift-invariant permutations of the form $y_i=x_{i+u}+x_{i+v}(x_{i+w}+a_i)$, where $0\le u, v, w<n$ and $a_i\in \mathbb{F}_2$, $1\le i\le n$.

cs.IT↗