Exact probability of erasure and a decoding algorithm for convolutional codes on the binary erasure channel

Analytic expressions for the exact probability of erasure for systematic, rate- 1/2 convolutional codes used to communicate over the binary erasure channel and decoded using the soft-input, soft-output (SISO) and a posteriori probability (APP) algorithms are given. An alternative forward-backward algorithm which produces the same result as the SISO algorithm is also given. This low-complexity implementation, based upon lookup tables, is of interest for systems which use convolutional codes, such as turbo codes.