Abstract
The turbo decoding algorithm of a decade ago constituted
a milestone in error-correction coding for digital communications,
and has inspired extensions to generalized receiver topologies,
including turbo equalization, turbo synchronization, and turbo
CDMA, among others. Despite an accrued understanding of iterative
decoding over the years, the “turbo principle” remains elusive
to master analytically, thereby inciting interest from researchers
outside the communications domain. In this spirit, we develop a
tutorial presentation of iterative decoding for parallel and
serial concatenated codes, in terms hopefully accessible to a
broader audience. We motivate iterative decoding as a
computationally tractable attempt to approach maximum-likelihood
decoding, and characterize fixed points in terms of a
“consensus” property between constituent decoders. We review how
the decoding algorithm for both parallel and serial concatenated
codes coincides with an alternating projection algorithm, which
allows one to identify conditions under which the algorithm indeed
converges to a maximum-likelihood solution, in terms of particular
likelihood functions factoring into the product of their
marginals. The presentation emphasizes a common framework
applicable to both parallel and serial concatenated codes.