Heuristic Search Based Soft-Input Soft-Output Decoding of Arithmetic Codes
Yali Liu
1
and Jiangtao Wen
2
1
Dept. of Electronics Engineering
Tsinghua University, Beijing, China
E-mail: liuyl02@mails.tsinghua.edu
2
Morphbius Technology Inc.
Ottawa, Canada K2J 3S7
E-mail: gwen@morphbius.com
Recent research (e.g. [1]) has shown that by introducing a “forbidden symbol” (FS),
one can significantly improve the error resilience of the decoding of arithmetic codes
(ACs) when the bitstream is transmitted over error prone channels. The FS was used to
facilitate continuous pruning of possible source paths and deemed necessary because the
number of such paths can grow exponentially. However, the FS is an extra overhead
whose introduction in many applications is prohibited or highly undesirable.
In this paper we took a different approach to error resilient AC decoding. Instead of
an FS, we utilized heuristic search algorithms (HSAs) in artificial intelligence ([2]) for
finding the minimal-weight path through directed and non-negatively-weighted graphs.
HSAs were designed to efficiently deal with exponential growth of paths without the
assistance of an embedded “error” flag such as the FS. Instead, an HSA maintains a list
(Open) of nodes that might need to be examined, and, starting from only the root node ( r)
in Open, removes the most “promising” (based on a pre-determined metric) node n from
Open, and checks if n is a solution. If yes, the algorithm exits; otherwise, it adds all
children of n that are not currently in Open to Open, and records the concatenation of the
optimal path p (r, n) from r to n and the edge e(n, c ) between n and the child c as the
current optimal path p(r, c ) from r to c, along with the value of optimality metric for this
path. For any child c that is already in Open, the algorithm checks if the recorded
“optimal” path to c should be updated to p (r, n)+e (n, c). This process is repeated until a
solution to the target problem is found. It can be proven that ([2]) if the optimality metric
depends only on the weights of the edges between nodes that are already examined, the
optimality of the solution found by such an HSA (“optimal search”) is guaranteed.
Otherwise, if the optimality metric also depends on estimates of the weights of
unexamined edges (i.e. “heuristic information”), the algorithm (“heuristic search”) may
not always find the truly optimal solution, depending on the “quality” of the heuristic
information. By using “good” heuristic information, the complexity of the search can be
significantly reduced while maintaining the “quality” of the solutions found.
The paper described an optimal search based and a heuristic search based decoding
algorithm for ACs and compared their performance and complexity with the traditional
“hard” bit based AC decoder. Simulation results showed that both algorithms easily out-
performed traditional “hard” bits based arithmetic decoder, while the heuristic search
based algorithm achieved a very good tradeoff between performance and complexity.
Acknowledgement : The authors wish to thank Prof. Kun Tang of Tsinghua University
for his help to this research.
References:
[1] M. Grangetto, P. Cosman, “MAP decoding of arithmetic codes with a forbidden
symbol”, Proc. ACIVS 2002, Ghent, Belgium, Sept. 2002.
[2] N.J. Nilsson, Problem-Solving Methods in Artificial Intelligence, McGraw-Hill, 1971.
Proceedings of the Data Compression Conference (DCC’04)
1068-0314/04 $ 20.00 © 2004 IEEE