This is an implementation of the maximum likelihood decoding of Reed Muller codes based on their trellis structure resulting from the sqaring construction. For details about the decoding algorithm see:

• Forney Jr, G. David. "Coset codes. I. Introduction and geometrical classification." Information Theory, IEEE Transactions on 34.5 (1988): 1123-1151.
• Forney Jr, G. David. "Coset codes. II. Binary lattices and related codes." Information Theory, IEEE Transactions on 34.5 (1988): 1152-1187.

RM(1,3) is the (8,4,4) linear block code.

• Instantiatiate the objecct obj = RM(1,3)
• Construct a vector v = [0 1 0 0]
• Encode the vector v to get the codeword x = encode(obj,v)
• Construct an error vector e = [0 0 0 1 0 0 0.25]
• Add the error vector e with codeword to get the received vector r=x e
• Decode the received vector r to the codeword y = decode(obj,r)

As compared to bounded distance decoding, maximum likelihood soft-decoding decoding algorithm is much more efficient in terms of (i) error correcting capability and (ii) complexity. The decoding algorithm, using the trellis structure, takes the dynamic programming approach to reduce the computational complexity significantly.

The test cases can be founded in accomapaning file mainTest.m

The decoding algorithm relies on the trellis structure of the code. The trellis structures of Reed Muller codes of dimenstion upto 32 is simpler and thus can be solved using the dynamic programming approach. However, for dimention greater than 32, the corresponding trellises contain enormous number of nodes which makes the decoding infeasible.

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Copyright (c) 2016 Mortuza Ali

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