This paper investigates some analytical aspects of the improved decoding algorithm for Low-density parity-check (LDPC) codes over the binary erasure channel (BEC) proposed by Hossein et al. in [1]. In this paper, we derive a necessary and sufficient condition for the improved decoding algorithm to successfully complete decoding when the decoder is set to guess a pre-determined number of guesses after the standard message-passing terminates at a stopping set. We then present improved bounds on the number of bits to be guessed for successful completion of the decoding process when a stopping set is encountered.
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