Bit commitment with 1-out-of-2 oblivious transfer
It turned out that the protocol I designed was good.

Bob can't cheat because its impossible for him to discover $b$ because at every $\binom{1}{2}-OT$ iterations, Bob can only discover $b_i$ or $b_{i+1}$ for $i\geq1$ and $i=2k-1$ such that $1\leq k\leq\frac{n}{2}$ ($i$ is uneven). 

Alice has an exponentially small chance to cheat without getting caught because if she would like to do so, Alice would have to lie on the reveal phase for every row for one of the $b_i$ or $b_{i+1}$, hoping that Bob discovered the other one. (She doesn't know which one Bob discovered). If Bob finds out that one of the bit isn't the one he discovered during the oblivious transfer or that one row doesn't equal the others, Bob rejects.