Theoretical and experimental upper and lower bounds on the efficiency of convolutional codes in a binary symmetric channel

Problems of Information Transmission. 2022. Vol. 58. No. 2. P. 122–136.

Kurmukova A., Ivanov F., Zyablov V. V.

We propose a new approach to the analytical estimation of the error burst probability, the probability of erroneous decoding, and the probability of error per bit for convolutional codes with Viterbi decoding in a binary symmetric channel (BSC). Upper and lower estimates of the probability of error per bit and of the erroneous decoding probability are based on active distances and the distance spectrum of active distances for a convolutional code. The estimates are derived for rate 1/2 convolutional codes, but they can also be generalized to any convolutional code with rate 1/n. Calculation of the estimates described here has linear time complexity in the error burst minimal length if code distance properties are known. The computational complexity does not depend on the crossover probability of a BSC. Simulation results show that the considered estimates are rather tight, especially for small crossover probabilities.

Keywords: декодирование, decoding, convolutional code, Viterbi Algorithm, сверточный код, алгоритм Витерби

Publication based on the results of: New data protection methods in cyber-physical systems (2022)