ERROR-CORRECTING CODES FOR LIST DECODING

In the list-of-L decoding of a block code the receiver of a noisy sequence lists L possible transmitted messages, and is in error only if the correct message is not on the list. This paper considers (n, e, L) codes, which correct all sets of e or fewer errors in a block of n bits under list-of-L decoding. New geometric relations between the number of errors corrected under list-of-1 decoding and the (larger) number corrected under list-of-L decoding of the same code lead to new lower bounds on the maximum rate of (n, e, L) codes. They show that a jammer who can change a fixed fraction p < 1 /2 of the bits in an -bit linear block code cannot prevent reliable communication at a positive rate using list-of-L decoding for sufficiently large n and an L <n. The new bounds are stronger for small n but weaker for fixed e/n in the limit of large n and L than known random coding bounds. © 1991 IEEE