Difference between MFB bound and ML bound for ISI channels?

I am considering a straight forward simulation setup in matlab.

I am transmitting a random sequence $\mathbf{x}$ of $\{+1,-1\}$ over a two-tap ISI channel $\mathbf{h}=[h_0 \hspace{2mm} h_1]$. The channel output is the noisy filtered vector $\mathbf{y}=\mathbf{H}\mathbf{x} + \mathbf{n}$. At receiver, I am implementing ML detector via Viterbi Algorithm to compute $\mathbf{\hat{x}}$.

I want to compare BER vs SNR for my simulation with the Matched Filtered Bound and Maximum Likelihood Bound. So what is the difference between these two and how can I compute these? ML bound uses notion of $d_{min}$ but I don't understand how to compute it for any $\mathbf{h}$.

Can someone guide me here.

• Do you have any references for the maximum likelihood bound? – MBaz Mar 7 '17 at 0:01
• Take a look at G. Forney, "Maximum-likelihood sequence estimation of digital sequences in the presence of intersymbol interference," in IEEE Transactions on Information Theory, vol. 18, no. 3, pp. 363-378, May 1972. – NAASI Mar 16 '17 at 0:16