Problems of Information Transmission, Vol. 40, No. 4, 2004, pp. 297–317. Translated from Problemy Peredachi Informatsii, No. 4, 2004, pp. 3–25.
Original Russian Text Copyright
2004 by Burnashev, Schlegel, Krzymien, Shi.
Analysis of the Dynamics of Iterative Interference
Cancellation in Iterative Decoding
M. V. Burnashev
, and Z. Shi
Institute for Information Transmission Problems, RAS, Moscow
Department of Electrical and Computer Engineering, University of Alberta, Canada
Department of Electrical Engineering, University of Utah, USA
Received May 18, 2004
Abstract—Characteristics of a successive cancellation scheme, widely used in iterative de-
coding, is investigated. Comparison with another popular method, the minimum mean-square
error (MMSE) method, is also provided.
Iterative decoding in digital data transmission systems has become very popular with invention
of turbo coding . Methods of iterative processing have quickly been realized to be applicable not
only to turbo coded signals but also to joint decoding of code-division multiple access (CDMA) sys-
tems, intersymbol interference limited channels, multiple-input multiple-output (MIMO) systems,
and others. In particular, iterative decoding of CDMA systems is proved to be a very powerful
decoding method, which has the potential of realizing a signiﬁcant portion of the capacity of such
a channel [2–8].
Key issues for iterative decoders are convergence conditions. Usually, it is not possible to
investigate their convergence by purely analytical methods. For that reason, such methods are
typically combined with computer simulations. An example is density evolution analysis, ﬁrst
applied to low-density parity-check (LDPC) codes . It should be noted that in many cases
densities involved are either exactly Gaussian, or they are well approximated by Gaussian densities.
In these cases, much simpler analysis can be used instead [7, 10–12]. In particular, it has been
shown in  that simple iterative cancellation receivers (see Section 3) can achieve the capacity of a
multiple access channel if powers (or rates) of participating users are chosen in a certain optimal way.
In this paper, which is a mathematical supplement to , dynamics of the behavior of iterative
decoders with iterative cancellation is studied by analytical methods. Some of the results derived
are used in  to describe the behavior of large-scale CDMA systems under various transmission
conditions (without mathematical proofs). Comparison to decoders using linear minimum mean-
square error (MMSE) ﬁlters is also presented.
We consider the model in which the input, d =(d
, and the output, y =(y
channel vectors are related by the formula
+ σn, (1)
Supported in part by the INTAS, Grant 00-738, and Russian Foundation for Basic Research, project
2004 MAIK “Nauka/Interperiodica”