Packet error rates of terminated and tailbiting convolutional codes

When a convolutional code is used to provide forward error correction for packet data transmission, the standard performance measures of convolutional codes, i.e., bit error rate and first-event error rate, become less useful. Instead we are interested in the average probability of block (or packet) error. In this paper a modified transfer function approach is used to obtain a union bound on the block error rate of terminated and tailbiting convolutional codes. The performance of these block codes obtained from termination and tailbiting is compared to the performance of some standard block codes for various information block lengths and also compared to the sphere packing lower bound for optimal block codes. The conclusion is that block codes derived from convolutional codes form a competitive class of short block length block codes. Keywords— convolutional code, block code, block error probability, packet error probability, union bound, terminated convolutional code, tailbiting convolutional code, sphere packing bound