Performance upper bounds for terminated convolutional codes

In this paper, we present performance upper bounds for convolutional codes terminated with finite input sequence. To obtain the upper bounds, we define a generalized weight enumerator representing the relation between the Hamming distance of the coded output and the Hamming distance of selected input bits of the code. The upper bounds on frame error rate (FER) and average bit error rate (BER) of selected bits are obtained from the generalized weight enumerators. We present a low complexity method to compute the weight enumerator of terminated convolutional codes based on a modified trellis. We also present a generalized weight enumerator of single error event to provide tighter performance upper bounds by removing codewords composed of multiple error events from the weight enumerator.