On Some Properties of the Bit Decoding Algorithms
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چکیده
|In this paper, we study certain properties of the bit decoding algorithms for the case of linear binary codes . We focus on the probability distribution function (pdf) of the bit LLR using an AWGN channel model with BPSK modulation. We prove that the pdf of the bit LLR of a speci c bit position is independent of the transmitted code-word. It is also shown that the pdf of a given bit LLR when the corresponding bit takes the values of zero and one are symmetric with respect to each other (re ection of one another with respect to the origin). Among other things, this result shows that the resulting binary channel will be symmetrical in the sense that the probability of error for zero and one will be the same. Another important result nds a suÆcient condition on the code structure such that the pdf of the bit LLR for two given bit positions are the same. We nd such a condition using the code automorphism group and show that for the important class of cyclic codes this suÆcient condition is always satis ed. This means that any given two bit positions in a cyclic code have the same pdf for their bit LLR.
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تاریخ انتشار 2001