The rank of sparse random matrices
SODA '20: ACM-SIAM Symposium on Discrete Algorithms Salt Lake City Utah January, 2020, pp. 579-591, 2020.
We determine the rank of a random matrix A over an arbitrary field with prescribed numbers of non-zero entries in each row and column. As an application we obtain a formula for the rate of low-density parity check codes. This formula vindicates a conjecture of Lelarge [Proc. IEEE Information Theory Workshop 2013]. The proofs are based on ...More
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