From Bit to Block: Decoding on Erasure Channels
Abstract
We provide a general framework for bounding the block error threshold of a linear code C⊂eq F2N over the erasure channel in terms of its bit error threshold. Our approach relies on understanding the minimum support weight of any r-dimensional subcode of C, for all small values of r. As a proof of concept, we use our machinery to obtain a new proof of the celebrated result that Reed-Muller codes achieve capacity on the erasure channel with respect to block error probability.
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