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.