On the joint design of compressed sensing and network coding for wireless communications

Abstract

Compressed sensing and network coding techniques have seen a widespread interest in many disciplines during the last decade. Recently, a novel idea emerged for the combination of these areas in wireless communications to leverage the benefits from network coding while taking advantage of the correlations in the (sensory) data. The potential gains, such as lower latency for large‐scale sensing scenarios, reduced energy consumption, and a decrease in the amount of data during transmissions, are alluring to many use‐cases. However, a common issue one faces when joining both techniques is encountered in the fact that network coding is designed to operate over finite fields, whereas compressed sensing is mainly concerned with real numbers. This paper studies the impact of compressed sensing on network coding to enable one step decoding for the reconstruction of compressed data. We emphasize and discuss the design of the sensing and coding matrices, as well as the algorithms that enable accurate reconstructions. We employ the KL1p compressed sensing library and the NS3 simulator to evaluate this joint design. Our simulations show that using normalized coefficient matrices drawn from Gaussian distributions has higher efficiency and scalability including, but not limited to, multi‐hop networks, where the recoding feature of network coding can be exploited. Furthermore, the Subspace Pursuit algorithm outperforms the state‐of‐the‐art reconstruction algorithms, with respect to the reconstruction signal‐to‐noise ratio, by more than two folds compared to the other benchmark algorithms in cluster‐based Wireless Sensor Networks, where recoding using real network codes are involved.

An Enhanced Subsampling Technique in Compressive Sensing using Linear Interpolation and Random Measurement Matrix

“…The underdetermined CS problem as stated in [4][5][6][7] and also explained earlier, was formulated in MATLAB as follows:…”

“…While sparsity refers to when a signal (matrix) has fewer non-zero entries than zero entries [3], incoherence has to do with the requirement that measurements of the original signal taken need to evenly represent random sections of the given signal. More precisely, as mathematically presented in the CS problem stated in [4][5][6][7], and subsequently in this paper, the measurement matrix, Φ, should not be parallel with the columns of the transform basis matrix, Ψ, such that it only subsamples signals from those columns at the expense of the other columns [3]. What incoherence aims at is to have randomness with measurements taken from a signal to increase the efficiency of its reconstruction.…”

The security of vulnerable senior citizens through dynamically sensed signal acquisition

“…Among them, Maroua et al studied dynamic sensing methods. 11 The authors thoroughly studied joint design of compressed sensing and network coding in wireless communication as well as the impact of compressed sensing on network coding. The authors realized one-step decoding and reconstruction of compressed data.…”

“…It is assumed that m sensor data variables s 1 ,s 2 , … ,s m and their corresponding sensor data s m+1 are selected in the multiple linear regression analysis to form observation data. And select h group to build the training data set, so that the observed data equations are (11) Multiple linear regression coefficients 𝛽 j (1 ≤ j ≤ k) are obtained by the least square's estimation method.…”

“…Presently, the intellgient systems to detect senior's abnormal behavior is still in the initial stages globally, but there is some research on dynamic sensing technology as well as abnormal signal recognition. Among them, Maroua et al studied dynamic sensing methods 11 . The authors thoroughly studied joint design of compressed sensing and network coding in wireless communication as well as the impact of compressed sensing on network coding.…”