Application of List Viterbi Algorithms to Improve the Performance in Space Missions using Convolutional Codes

Currently, several space missions are still using convolutional codes, which are among the available coding options of the CCSDS telemetry recommendation. When convolutional codes are employed, the CCSDS specification mandates the use of an outer CRC code to perform error detection over the transfer frame. Alternatively, the CRC code may be used, together with list Viterbi decoding of the inner convolutional code, to significantly improve the performance of the coding scheme. In this paper, we first compute the distance spectrum of the concatenation of the outer CRC code and the inner convolutional codes recommended by the CCSDS. By means of a union bound on the block error probability under maximum-likelihood decoding, we estimate the extra coding gain achievable by the concatenation with respect to the use of the Viterbi algorithm applied to the decoding of the inner convolutional code only. The extra coding gain is close to 3 dB. Then, we consider the application of the list Viterbi algorithm and we discuss some techniques useful to reduce its complexity in practical implementations. Results show that it is possible to approach the 3 dB extra coding gain with negligible increase in the decoding complexity with respect to Viterbi decoding of the inner convolutional code.