A (7,4) Hamming code is used to encode 4 information bits, (b₁, b₂, b₃, b₄) to generate 7 code word bits, (c₁, c₂, ..., c7), to form a codeword. An extra 2 bits are added (c8, c9) are added to the end, where c₇ = c₈ = c₉. These 9 bits are then transmitted over a BSC. The bits (r₁, r₂, ..., r₉) are received.

Parity check for Hamming Code decoding (H):

1	0	1	1	1	0	0
1	1	1	0	0	1	0
0	1	1	1	0	0	1

[Note: This is NOT the same as my assignment as I want to learn how to do it and not copy the answer, if this doesn't work please choose another suitable parity check]

1. Joint Probability Distribution of all variables in the system.

2. Draw the FFG (Forney-Style factor graph) of the Joint Probability Distributions.

3. For each node in the FFG develop the message computing rule using the sum-product rule.

4. Using Monto Carlo simulations, simulate the CER performance of the system. Use the belief propagation algorithm to decode the infomation bits.