Radio Losses for Concatenated Codes

The advent of higher powered spacecraft amplifiers and better ground receivers capable of tracking spacecraft carrier signals with narrower loop bandwidths requires better understanding of the carrier tracking loss (radio loss) mechanism of the concatenated codes used for deep-space missions. In this article, we present results of simulations performed for a (7,1/2), Reed–Solomon (255,223), interleaver depth-5 concatenated code in order to shed some light on this issue. Through these simulations, we obtained the performance of this code over an additive white Gaussian noise (AWGN) channel (the baseline performance) in terms of both its frame-error rate (FER) and its bit-error rate at the output of the Reed–Solomon decoder (RS-BER). After obtaining these results, we curve fitted the baseline performance curves for FER and RS-BER and calculated the high-rate radio losses for this code for an FER of 10−4 and its corresponding baseline RS-BER of 2.1× 10−6 for a carrier loop signal-to-noise ratio (SNR) of 14.8 dB. This calculation revealed that even though over the AWGN channel the FER value and the RS-BER value correspond to each other (i.e., these values are obtained by the same bit SNR value), the RS-BER value has higher high-rate losses than does the FER value. Furthermore, this calculation contradicted the previous assumption that at high data rates concatenated codes have the same radio losses as their constituent convolutional codes. Our results showed much higher losses for the FER and the RS-BER (by as much as 2 dB) than for the corresponding baseline BER of the convolutional code. Further simulations were performed to investigate the effects of changes in the data rate on the code’s radio losses. It was observed that as the data rate increased the radio losses for both the FER and the RS-BER approached their respective calculated high-rate values. Furthermore, these simulations showed that a simple two-parameter function could model the increase in the radio losses as the data rate increased for both the FER and the RS-BER. However, further simulations are required to obtain functions for the two parameters in terms of the loop SNR and the error rate for which the loss is calculated.