The recent progress in optical communications and signal processing outlines the fact that the parallel computing falls well behind the optical transmission systems' capabilities. Even though that photonic networks-on-chips (NOCs) can be employed to enable future computing and signal processing functions, there is a number of limitations (such as frequent O-E-O conversions, temperature sensitivity, and reliability issues) to be overcome before such schemes become widely adopted. All this strengthens the need for novel optical computing paradigms to be introduced. In this paper, we discuss novel optical processing schemes to overcome the computing limitations of photonic NOCs. We describe both continuous-time (CT) and discrete-time (DT) implementations of photonic integrated circuits (PIC)-based basic building blocks for all-optical computing. In addition, we need to use all-optical error correction schemes to deal with the accumulated errors due to the impact of noise. To perform all-optical linear block encoding and decoding we discuss and propose the use of SOA based XOR gates, while for CT implementation, the employment of Mach-Zehnder interferometer-based multiplier to perform probabilities multiplication, is considered. Also, the use of Y-junctions and phase modulators for all-optical FFT is discussed. Finally, we will describe and propose our approach of how to perform all-optical multiplication and addition in Galois field (GF), which represent the basic operations required in nonbinary LDPC coding and byte-based computing functions.