LDPC Codes with Different Frame Sizes over Multipath Fading Channels

This paper provides theoretical and simulation performance of space communications systems over block fading channels. Data frames are usually used in both coded and uncoded communications systems. If the duration of a frame is less than coherence time of the fading channel (which is inversely proportional to the Doppler spread), then the block fading model can be assumed. In other words, it is assumed that the fade amplitude is approximately constant over the frame duration. The analytical frame error rate over block fading channel can be derived if the frame error rate performance over AWGN channel is available, and the probability density function of fade amplitudes is known.This paper investigates the trade-offs in system performance versus coding frame size in block fading channels and provides guidance on how to select appropriate frame sizes as a function of the fading channel severity. We first show the performance of random codes over such channels by extending the known theoretical results to block fading. Then, we validate these new theoretical results with high-fidelity simulations using examples for both coded and uncoded systems. For coded systems, we consider the standard rate 1/2 CCSDS LDPC codes with frame sizes of 1024 and 16384 information bits, which are likely to be used by upcoming lunar missions such as the Human Landing System. We show that although the longer block codes provide clear gains compared to shorter codes in AWGN channels, this advantage is dramatically reduced depending on the severity of the fading channel, which we vary from a Rician parameter of 0 dB to 20 dB. Finally in this paper we proposed analytical results for frame error rates in partial fading where each received codeword can observe two or more independent fades. Some simulations are also provided for partial fading.