On the Error Performance Bound of Ordered Statistics Decoding of Linear Block Codes

In this paper, a novel simplified statistical approach
to evaluate the error performance bound of Ordered Statistics
Decoding (OSD) of Linear Block Codes (LBC) is investigated.
First, we propose a novel statistic which depicts the number
of errors contained in the ordered received noisy codeword.
Then, simplified expressions for the probability mass function
and cumulative distribution function are derived exploiting the
implicit statistical independence property of the samples of
the received noisy codeword before reordering. Second, we
incorporate the properties of this new statistic to derive the
simplified error performance bound of the OSD algorithm for
all order−I reprocessing. Finally, with the proposed approach,
we obtain computationally simpler error performance bounds of
the OSD than those proposed in literature for all length LBCs.