Random Ensemble Bounds for Decoding Error Probability

This chapter derives various random ensemble bounds for decoding error probability. The decoding error probability of the Viterbi decoding algorithm is analyzed for convolutional codes but only for the ensemble of time-varying convolutional codes. The errors in the output from the Viterbi decoder are first grouped in error bursts, and then distribution of the lengths of these error events is upperbounded for the ensemble of periodically time-varying convolutional codes. These upper bounds are then used to obtain upper bounds on the burst error probability. The chapter derives upper bounds for the burst and bit error probabilities that are exponentially decreasing with the memory of the convolutional code. A general lower bound for the decoding error probability of convolutional coding is proved, and it is shown how the R0-criterion can be used to quantize the channel outputs.