Multidimensional Cross Parity Check Codes as a Promising Solution to CubeSat Low Data Rate Downlinks

Abstract

Simple cross parity check codes have been well known for decades in the areas of magnetic recording and radiation-hardened memory in space applications. However, the computational power requirements of higher dimensional cross codes mean that priority has been given to different forward error correction methods, with the result that cross parity check codes have not become sufficiently generalized to include a higher number of dimensions. In the last two decades, the focus has mainly been on Reed-Solomon codes, Hamming codes, BCH codes, convolutional codes and turbo codes. In this paper, the issues behind generalized multidimensional parity check codes are explored again in relation to current main-stream interest by covering parity check codes in the form of low-density parity checks. I will put forward a new solution to the multidimensional parity check code decoding process for low data rate downlinks in CubeSat satellites. I propose that the high computational power of software-defined radio can be utilized for iterative decoding of CubeSat satellite transmissions in ground control segments, ensuring that onboard multidimensional parity encoders are as simple to use as possible.