Syndrome entropy of a binary linear code is the entropy corresponding to a product of a binary m×n matrix and a vector of length n generated from a binary i.i.d. source. In this paper, we investigate the syndrome entropy of a matrix contained in an ensemble of m×n binary matrices, such as random matrix ensembles, and constant row weight ensembles. In the analysis, the first and the second moment of the coset weight distribution of an ensemble play a crucial role. The result presented in the paper can be used to derive a lower bound of block error probability of some classes of LDPC codes.
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