Implement an optimal digital fountain decoder that uses the method of Richardson and Urbanke (2001b) derived for fast encoding of sparse-graph codes (section 47.7) to handle the matrix inversion required for optimal decoding. Now that you have changed the decoder, you can reoptimize the degree distribution, using higher-weight packets. By how much can you reduce the overhead? Confirm the assertion that this approach makes digital fountain codes viable as erasure-correcting codes for all block lengths, not just the large block lengths for which LT codes are excellent.