parallelization - Changing a Part of a variable within ParallelDo

I want to evaluate nested do as a parallel computations. My formula looks like:

Do[
 Do[
  CC[[i, j]] += Kepf[[i, j]],{j, 1, Dimensions[Kepf][[2]]}
  ],{i, 1, Dimensions[Kepf][[1]]}
 ]

When previously I created 0 matrix CC and some matrix Kepf. I just want to insert matrix Kepf into matrix CC. When the matrices are very large it takes some time. So I want use parallel computations to shorten time.

Let`s consider a numerical example:

I create matrix A:

A = Table[0, {4}, {4}]

{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}

and matrix B:

B = Table[2 i + j, {i, 1, 2}, {j, 1, 2}]
{{3, 4}, {5, 6}}

then I evaluate the code

Do[A[[j]][[i]] += B[[i]][[j]], {i, 1, 2}, {j, 1, 2}]
{{3, 5, 0, 0}, {4, 6, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}

I`ve got what I wanted, but when I try to do parallel computing using the code

SetSharedVariable[A, B]
ParallelDo[A[[j]][[i]] += B[[i]][[j]], {i, 1, 2}, {j, 1, 2}]

It says that:

(kernel 2) Part::wrsym: Symbol A is Protected.
(kernel 1) Part::wrsym: Symbol A is Protected.
(kernel 2) Part::wrsym: Symbol A is Protected.
(kernel 1) Part::wrsym: Symbol A is Protected.

Any idea?

Answer

With

a = Table[0, {4}, {4}]
b = Table[2 i + j, {i, 1, 2}, {j, 1, 2}]

using

SetSharedVariable[a]
ParallelDo[a[[j, i]] += b[[i, j]], {i, 1, 2}, {j, 1, 2}]
a

{{3, 5, 0, 0}, {4, 6, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}

would work, but using

a += Transpose[b] ~PadRight~ Dimensions@a

{{3, 5, 0, 0}, {4, 6, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}

is much nicer and faster.