Code concatenation is used to construct code
families with good
theoretical and
practical properties. The underlying idea has been
first proposed by
Forney in 1966 where simple and powerful code
constructions have
been derived. In this talk we address concatenated
code constructions
based on simple subcodes, where we are interested
in asymptotic
properties of the underlying random coding
ensembles. For
example, a linear growth of the minimum distance of the
overall code with
block length guarantees that for good communication
channels the residual
error probability after decoding gets
arbitrarily close to
zero if the block length tends to infinity. On
the other hand, since
concatenated codes are generally decoded
iteratively,
iterative decoder convergence is another issue
which needs to be
addressed besides distance growth.
In particular, we consider the ensemble of
codes formed by a serial
concatenation of an
outer code (for example a repetition code) with
multiple accumulators
through uniform random interleavers. Based on
finite length weight
enumerators for these codes, asymptotic
expressions for the
minimum distance and an arbitrary number of
accumulators larger
than one are derived. In accordance with earlier
results in the
literature, we first show that the minimum distance of
repeat-accumulate
codes can grow, at best, sublinearly with the block
length. Then, for
repeat-accumulate-accumulate codes and code
rates of 1/3 or
smaller, it is proved that these codes exhibit
linear distance
growth with block length, where the gap to the random
coding bound can be
made arbitrarily small by increasing the number of
accumulators beyond
two.
Finally, we briefly present hybrid
concatenated coding schemes which
represent a mixture
between serial and parallel concatenation.
We
show that such
structures also exhibit linear distance growth with
block length (albeit
with a smaller growth rate coefficient), but as
an advantage have
better convergence properties than multiple serially
concatenated codes.