Convolutional

The CCSDS convolutional code uses rate 1/2 (one output bit for every input bit, doubling the data rate) and constraint length 7 (each output bit depends on the current input bit and the previous 6). Decoding uses the Viterbi algorithm, which finds the most probable transmitted sequence. It works by maintaining $2^6 = 64$ possible encoder states (a trellis — a graph of states over time) and pruning unlikely paths as each new bit arrives, keeping only the best path into each state.

Convolutional coding provides the highest coding gain (the reduction in required SNR for a given error rate) of the three options, at the cost of halving the effective data rate. It is specified for deep-space missions where the signal arrives extremely weak and every fraction of a dB matters. It is often concatenated with RS: the convolutional code handles random bit errors while RS handles the residual burst errors that the Viterbi decoder occasionally produces.