2 research outputs found
Error exponents of typical random codes
We define the error exponent of the typical random code as the long-block
limit of the negative normalized expectation of the logarithm of the error
probability of the random code, as opposed to the traditional random coding
error exponent, which is the limit of the negative normalized logarithm of the
expectation of the error probability. For the ensemble of uniformly randomly
drawn fixed composition codes, we provide exact error exponents of typical
random codes for a general discrete memoryless channel (DMC) and a wide class
of (stochastic) decoders, collectively referred to as the generalized
likelihood decoder (GLD). This ensemble of fixed composition codes is shown to
be no worse than any other ensemble of independent codewords that are drawn
under a permutation--invariant distribution (e.g., i.i.d. codewords). We also
present relationships between the error exponent of the typical random code and
the ordinary random coding error exponent, as well as the expurgated exponent
for the GLD. Finally, we demonstrate that our analysis technique is applicable
also to more general communication scenarios, such as list decoding (for
fixed-size lists) as well as decoding with an erasure/list option in Forney's
sense.Comment: 26 pages, submitted for publicatio