I am working on the implementation and investigation of DVB-S2 LDPC codes.

Normally the output of the Matched filter after the channel and before the LDPC decoder is scaled by a factor of 4* Eb/No. (In the case of Soft Inputs)

I am using BPSK modulation and the noise being added is AWGN.

In the case of Hard Inputs the scaling factor 4* Eb/No varies, in the case of code rate of 9/10 the optimum scaling factor we found was 1.6 * Eb/No. For code rate of 1/2 it was 2.6 * Eb/No.

Can some one explain to me why is there a difference in this scaling factor? Is there a theoretical method to calculate this? Is it a code defined parameter? 

Any help would be greatly appreciated.