12 research outputs found
Multi-Trial GuruswamiâSudan Decoding for Generalised ReedâSolomon Codes
An iterated refinement procedure for the Guruswami--Sudan list decoding
algorithm for Generalised Reed--Solomon codes based on Alekhnovich's module
minimisation is proposed. The method is parametrisable and allows variants of
the usual list decoding approach. In particular, finding the list of
\emph{closest} codewords within an intermediate radius can be performed with
improved average-case complexity while retaining the worst-case complexity.Comment: WCC 2013 International Workshop on Coding and Cryptography (2013
A STUDY OF ERASURE CORRECTING CODES
This work focus on erasure codes, particularly those that of high performance,
and the related decoding algorithms, especially with low
computational complexity. The work is composed of different pieces,
but the main components are developed within the following two main
themes.
Ideas of message passing are applied to solve the erasures after the
transmission. Efficient matrix-representation of the belief propagation
(BP) decoding algorithm on the BEG is introduced as the recovery
algorithm. Gallager's bit-flipping algorithm are further developed
into the guess and multi-guess algorithms especially for the
application to recover the unsolved erasures after the recovery algorithm.
A novel maximum-likelihood decoding algorithm, the In-place
algorithm, is proposed with a reduced computational complexity. A
further study on the marginal number of correctable erasures by the
In-place algoritinn determines a lower bound of the average number
of correctable erasures. Following the spirit in search of the most likable
codeword based on the received vector, we propose a new branch-evaluation-
search-on-the-code-tree (BESOT) algorithm, which is powerful
enough to approach the ML performance for all linear block
codes.
To maximise the recovery capability of the In-place algorithm in
network transmissions, we propose the product packetisation structure
to reconcile the computational complexity of the In-place algorithm.
Combined with the proposed product packetisation structure,
the computational complexity is less than the quadratic complexity
bound. We then extend this to application of the Rayleigh fading
channel to solve the errors and erasures. By concatenating an outer
code, such as BCH codes, the product-packetised RS codes have the
performance of the hard-decision In-place algorithm significantly better
than that of the soft-decision iterative algorithms on optimally
designed LDPC codes
Error-Correction Coding and Decoding: Bounds, Codes, Decoders, Analysis and Applications
Coding; Communications; Engineering; Networks; Information Theory; Algorithm
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
JTIT
kwartalni