Chase-3-like algorithms achieving bounded-distance decoding

For the decoding of a binary block code of Hamming distance of d over AWGN channels, a soft-decision decoder is said to achieve bounded-distance (BD) decoding if its squared error-correction radius is equal to d. A Chase-3-like algorithm outputs the best (most likely) codeword in a list of candidates generated by a conventional algebraic binary decoder whose input sequences have nonzero entries confined in the most unreliable positions. Let ¿(d) denote the smallest size of input sequence sets of Chase-3-like algorithms which achieve BD decoding. In this paper, we show that there are positive numbers C
₁
and C
₂
such that C
₁
¿ ¿(d)d
^-1/2
¿ C
₂
for sufficiently large d.