869 research outputs found
The Euclidean Algorithm for Generalized Minimum Distance Decoding of Reed-Solomon Codes
This paper presents a method to merge Generalized Minimum Distance decoding
of Reed-Solomon codes with the extended Euclidean algorithm. By merge, we mean
that the steps taken to perform the Generalized Minimum Distance decoding are
similar to those performed by the extended Euclidean algorithm. The resulting
algorithm has a complexity of O(n^2)
A New Chase-type Soft-decision Decoding Algorithm for Reed-Solomon Codes
This paper addresses three relevant issues arising in designing Chase-type
algorithms for Reed-Solomon codes: 1) how to choose the set of testing
patterns; 2) given the set of testing patterns, what is the optimal testing
order in the sense that the most-likely codeword is expected to appear earlier;
and 3) how to identify the most-likely codeword. A new Chase-type soft-decision
decoding algorithm is proposed, referred to as tree-based Chase-type algorithm.
The proposed algorithm takes the set of all vectors as the set of testing
patterns, and hence definitely delivers the most-likely codeword provided that
the computational resources are allowed. All the testing patterns are arranged
in an ordered rooted tree according to the likelihood bounds of the possibly
generated codewords. While performing the algorithm, the ordered rooted tree is
constructed progressively by adding at most two leafs at each trial. The
ordered tree naturally induces a sufficient condition for the most-likely
codeword. That is, whenever the proposed algorithm exits before a preset
maximum number of trials is reached, the output codeword must be the
most-likely one. When the proposed algorithm is combined with Guruswami-Sudan
(GS) algorithm, each trial can be implement in an extremely simple way by
removing one old point and interpolating one new point. Simulation results show
that the proposed algorithm performs better than the recently proposed
Chase-type algorithm by Bellorado et al with less trials given that the maximum
number of trials is the same. Also proposed are simulation-based performance
bounds on the MLD algorithm, which are utilized to illustrate the
near-optimality of the proposed algorithm in the high SNR region. In addition,
the proposed algorithm admits decoding with a likelihood threshold, that
searches the most-likely codeword within an Euclidean sphere rather than a
Hamming sphere
Decoding of Repeated-Root Cyclic Codes up to New Bounds on Their Minimum Distance
The well-known approach of Bose, Ray-Chaudhuri and Hocquenghem and its
generalization by Hartmann and Tzeng are lower bounds on the minimum distance
of simple-root cyclic codes. We generalize these two bounds to the case of
repeated-root cyclic codes and present a syndrome-based burst error decoding
algorithm with guaranteed decoding radius based on an associated folded cyclic
code. Furthermore, we present a third technique for bounding the minimum
Hamming distance based on the embedding of a given repeated-root cyclic code
into a repeated-root cyclic product code. A second quadratic-time probabilistic
burst error decoding procedure based on the third bound is outlined. Index
Terms Bound on the minimum distance, burst error, efficient decoding, folded
code, repeated-root cyclic code, repeated-root cyclic product cod
Iterative Soft Input Soft Output Decoding of Reed-Solomon Codes by Adapting the Parity Check Matrix
An iterative algorithm is presented for soft-input-soft-output (SISO)
decoding of Reed-Solomon (RS) codes. The proposed iterative algorithm uses the
sum product algorithm (SPA) in conjunction with a binary parity check matrix of
the RS code. The novelty is in reducing a submatrix of the binary parity check
matrix that corresponds to less reliable bits to a sparse nature before the SPA
is applied at each iteration. The proposed algorithm can be geometrically
interpreted as a two-stage gradient descent with an adaptive potential
function. This adaptive procedure is crucial to the convergence behavior of the
gradient descent algorithm and, therefore, significantly improves the
performance. Simulation results show that the proposed decoding algorithm and
its variations provide significant gain over hard decision decoding (HDD) and
compare favorably with other popular soft decision decoding methods.Comment: 10 pages, 10 figures, final version accepted by IEEE Trans. on
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