A crucial phase in performing the quantum cryptographic protocol is the error-correction phase which commences after the raw bit transmission and consists of publicly disclosing the parity of blocks of bits and discarding bits until almost all errors are removed. We develop a formal mathematical model for analyzing the procedure based on specific assumption about the length of the blocks. We further derive a simple analytical bound which can server as an estimate for the cot of performing the error-correction. At the end, we present a simulation model developed to test the analytical derivations and conclude that there is a very good agreement between the simulations and the bound for moderate error rates.