15,210 research outputs found
New Soft Set Based Class of Linear Algebraic Codes
In this paper, we design and develop a new class of linear algebraic codes defined as soft linear algebraic codes using soft sets. The advantage of using these codes is that they have the ability to transmit m-distinct messages to m-set of receivers simultaneously. The methods of generating and decoding these new classes of soft linear algebraic codes have been developed. The notion of soft canonical generator matrix, soft canonical parity check matrix, and soft syndrome are defined to aid in construction and decoding of these codes. Error detection and correction of these codes are developed and illustrated by an example
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
Information Theor
An Iteratively Decodable Tensor Product Code with Application to Data Storage
The error pattern correcting code (EPCC) can be constructed to provide a
syndrome decoding table targeting the dominant error events of an inter-symbol
interference channel at the output of the Viterbi detector. For the size of the
syndrome table to be manageable and the list of possible error events to be
reasonable in size, the codeword length of EPCC needs to be short enough.
However, the rate of such a short length code will be too low for hard drive
applications. To accommodate the required large redundancy, it is possible to
record only a highly compressed function of the parity bits of EPCC's tensor
product with a symbol correcting code. In this paper, we show that the proposed
tensor error-pattern correcting code (T-EPCC) is linear time encodable and also
devise a low-complexity soft iterative decoding algorithm for EPCC's tensor
product with q-ary LDPC (T-EPCC-qLDPC). Simulation results show that
T-EPCC-qLDPC achieves almost similar performance to single-level qLDPC with a
1/2 KB sector at 50% reduction in decoding complexity. Moreover, 1 KB
T-EPCC-qLDPC surpasses the performance of 1/2 KB single-level qLDPC at the same
decoder complexity.Comment: Hakim Alhussien, Jaekyun Moon, "An Iteratively Decodable Tensor
Product Code with Application to Data Storage
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
Iterative Algebraic Soft-Decision List Decoding of Reed-Solomon Codes
In this paper, we present an iterative soft-decision decoding algorithm for
Reed-Solomon codes offering both complexity and performance advantages over
previously known decoding algorithms. Our algorithm is a list decoding
algorithm which combines two powerful soft decision decoding techniques which
were previously regarded in the literature as competitive, namely, the
Koetter-Vardy algebraic soft-decision decoding algorithm and belief-propagation
based on adaptive parity check matrices, recently proposed by Jiang and
Narayanan. Building on the Jiang-Narayanan algorithm, we present a
belief-propagation based algorithm with a significant reduction in
computational complexity. We introduce the concept of using a
belief-propagation based decoder to enhance the soft-input information prior to
decoding with an algebraic soft-decision decoder. Our algorithm can also be
viewed as an interpolation multiplicity assignment scheme for algebraic
soft-decision decoding of Reed-Solomon codes.Comment: Submitted to IEEE for publication in Jan 200
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