7 research outputs found
On the Minimal Pseudo-Codewords of Codes from Finite Geometries
In order to understand the performance of a code under maximum-likelihood
(ML) decoding, it is crucial to know the minimal codewords. In the context of
linear programming (LP) decoding, it turns out to be necessary to know the
minimal pseudo-codewords. This paper studies the minimal codewords and minimal
pseudo-codewords of some families of codes derived from projective and
Euclidean planes. Although our numerical results are only for codes of very
modest length, they suggest that these code families exhibit an interesting
property. Namely, all minimal pseudo-codewords that are not multiples of a
minimal codeword have an AWGNC pseudo-weight that is strictly larger than the
minimum Hamming weight of the code. This observation has positive consequences
not only for LP decoding but also for iterative decoding.Comment: To appear in Proc. 2005 IEEE International Symposium on Information
Theory, Adelaide, Australia, September 4-9, 200
CONVERGENCE IMPROVEMENT OF ITERATIVE DECODERS
Iterative decoding techniques shaked the waters of the error correction and communications
field in general. Their amazing compromise between complexity and performance
offered much more freedom in code design and made highly complex codes, that were
being considered undecodable until recently, part of almost any communication system.
Nevertheless, iterative decoding is a sub-optimum decoding method and as such, it has
attracted huge research interest. But the iterative decoder still hides many of its secrets,
as it has not been possible yet to fully describe its behaviour and its cost function.
This work presents the convergence problem of iterative decoding from various angles
and explores methods for reducing any sub-optimalities on its operation. The decoding
algorithms for both LDPC and turbo codes were investigated and aspects that contribute
to convergence problems were identified. A new algorithm was proposed, capable of providing
considerable coding gain in any iterative scheme. Moreover, it was shown that
for some codes the proposed algorithm is sufficient to eliminate any sub-optimality and
perform maximum likelihood decoding. Its performance and efficiency was compared to
that of other convergence improvement schemes.
Various conditions that can be considered critical to the outcome of the iterative decoder
were also investigated and the decoding algorithm of LDPC codes was followed
analytically to verify the experimental results