Greedy Algorithm for Compressed Sensing over Finite Fields: Balancing Recovery and Efficiency

Compressed sensing promises a drastic reduction in data traffic, especially in wireless sensor network (WSN) applications, by exploiting data correlation. Although its original deployments used the field of real numbers, recent research has shown that finite field compressed sensing has unique advantages for practical applications. In particular, it allows us to exploit the discrete nature of the signals employed to reduce quantization errors and enables seamless integration with digital error-correcting codes and novel techniques like network coding. We study the performance of the most recent finite field compress sensing algorithm (F2OMP-loop) regarding two essential metrics for practical applications: the recovery probability as a function of the sensing matrices’ size and the average number of iterations needed to recover a sparse vector. These metrics have repercussions for the memory footprint and execution time of the algorithm. Our results show that the studied algorithm increases the decoding probability up to 75% compared to the state-ofthe- art version for some matrices’ sizes. We also report the sparsity parameter range for which the F2OMP-loop algorithm is practically implementable. For example, for a sparsity ratio of 50%, the iterative algorithm requires only 27 iterations, i.e., a number low enough for practical WSN applications.