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Multiple-Bases Belief-Propagation Decoding of High-Density Cyclic Codes
, 2009
"... We introduce a new method for decoding short and moderate length linear block codes with dense parity-check matrix representations of cyclic form, termed multiple-bases belief-propagation (MBBP). The proposed iterative scheme makes use of the fact that a code has many structurally diverse parity-che ..."
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We introduce a new method for decoding short and moderate length linear block codes with dense parity-check matrix representations of cyclic form, termed multiple-bases belief-propagation (MBBP). The proposed iterative scheme makes use of the fact that a code has many structurally diverse parity-check matrices, capable of detecting different error patterns. We show that this inherent code property leads to decoding algorithms with significantly better performance when compared to standard BP decoding. Furthermore, we describe how to choose sets of parity-check matrices of cyclic form amenable for multiple-bases decoding, based on analytical studies performed for the binary erasure channel. For several cyclic and extended cyclic codes, the MBBP decoding performance can be shown to closely follow that of maximum-likelihood decoders.
The Read Channel
, 2008
"... In this paper, we provide a survey of the novel read channel technologies that found their implementation in products over the past decade, and we outline possible technology directions for the future of read channels. Recently, magnetic recording read channels have undergone several changes. In ad ..."
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In this paper, we provide a survey of the novel read channel technologies that found their implementation in products over the past decade, and we outline possible technology directions for the future of read channels. Recently, magnetic recording read channels have undergone several changes. In addition to switching from longitudinal to perpendicular recording channels, detectors tuned to media noise sources are now readily implemented in read channel chips. Powerful numerical techniques have emerged to evaluate the capacity of the magnetic recording channel. Further, improved coding/decoding methods have surfaced both for the incumbent Reed-Solomon codes and the promising low-density parity-check (LDPC) codes. The paper is a tutorial-like survey of these emerging technologies with the aim to propel the reader to the forefront of research and development in the areas of signal processing and coding for magnetic recording channels.
Low-complexity soft decoding algorithms for Reed-Solomon codes
, 2006
"... Abstract—In this paper, we present a practical approach to the iterative decoding of Reed-Solomon (RS) codes. The presented methodology utilizes an architecture in which the output produced by steps of belief-propagation (BP) is successively applied to a legacy decoding algorithm. Due to the subopti ..."
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Abstract—In this paper, we present a practical approach to the iterative decoding of Reed-Solomon (RS) codes. The presented methodology utilizes an architecture in which the output produced by steps of belief-propagation (BP) is successively applied to a legacy decoding algorithm. Due to the suboptimal performance of BP conducted on the inherently dense RS parity-check matrix, a method is first provided for the construction of reduced-density, bi-nary, parity-check equations. Iterative decoding is then conducted utilizing a subset of a redundant set of parity-check equations to minimize the number of connections into the least-reliable bits. Simulation results show that performance comparable to (and exceeding) the best known practical RS decoding techniques is achievable with the presented methodology. The complexity of the proposed algorithm is significantly lower than these existing procedures and permits a practical implementation in hardware. Index Terms—Reed-Solomon (RS) codes, reduced-density parity-check matrices, belief propagation. I.
Adaptive Soft-Decision Iterative Decoding Using Edge Local Complementation
"... We describe an operation to dynamically adapt the structure of the Tanner graph used during iterative decoding. Codes on graphs– most importantly, low-density parity-check (LDPC) codes–exploit randomness in the structure of the code. Our approach is to introduce a similar degree of controlled rand ..."
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We describe an operation to dynamically adapt the structure of the Tanner graph used during iterative decoding. Codes on graphs– most importantly, low-density parity-check (LDPC) codes–exploit randomness in the structure of the code. Our approach is to introduce a similar degree of controlled randomness into the operation of the messagepassing decoder, to improve the performance of iterative decoding of classical structured (i.e., non-random) codes for which strong code properties are known. We use ideas similar to Halford and Chugg (IEEE Trans. on Commun., April 2008), where permutations on the columns of the parity-check matrix are drawn from the automorphism group of the code, Aut(C). The main contributions of our work are: 1) We maintain a graph-local perspective, which not only gives a low-complexity, distributed implementation, but also suggests novel applications of our work, and 2) we present an operation to draw from Aut(C) such that graph isomorphism is preserved, which maintains desirable properties while the graph is being updated. We present simulation results for the additive white Gaussian noise (AWGN) channel, which show an improvement over standard sum-product algorithm (SPA) decoding.
Efficient Box and Match Algorithm for Reliability-Based Soft-Decision Decoding of Linear Block
"... Abstract — In this paper, efficient methods to improve the box and matching algorithm (BMA) are presented. Firstly, an efficient approach is introduced to terminate the decoding if a local optimal candidate satisfies a probabilistic sufficient condition. The false alarm probability associated with t ..."
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Abstract — In this paper, efficient methods to improve the box and matching algorithm (BMA) are presented. Firstly, an efficient approach is introduced to terminate the decoding if a local optimal candidate satisfies a probabilistic sufficient condition. The false alarm probability associated with the use of the probabilistic sufficient condition is also derived. Secondly, by constructing a control band which is assumed error free, the matching capability of the BMA is enhanced. More precisely, the performance of BMA of order is nearly achieved with a small increase in complexity and no increase in memory with respect to the BMA of order. A tight performance analysis is derived based on the theory of order statistics. An error floor associated either with false alarms or with errors in the control band is introduced, but this error floor can be controlled using the analysis in both cases. Simulation results show that the performance of the enhanced BMA for the decoding of the RS(255,239) code with BPSK signaling over an AWGN channel is about 0.1 dB away from that of maximum likelihood decoding at the word error rate (WER). I.
Turbo decoding of product codes based on the modified adaptive belief propagation algorithm
- in Proc. of ISIT
, 2007
"... Abstract—This paper introduces the Modified Adaptive Belief Propagation (m-ABP) algorithm, an innovative method for the turbo decoding of product codes based on BCH component codes. The Adaptive Belief Propagation algorithm of Jiang and Narayanan is simplified by moving the matrix adaptation step ou ..."
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Abstract—This paper introduces the Modified Adaptive Belief Propagation (m-ABP) algorithm, an innovative method for the turbo decoding of product codes based on BCH component codes. The Adaptive Belief Propagation algorithm of Jiang and Narayanan is simplified by moving the matrix adaptation step outside of the iteration loop, significantly reducing the complexity. Performance in terms of the biterror-rate (BER) of the novel turbo decoding algorithm is given. Simulation results for the turbo decoding of product codes show that compared to the Chase-Pyndiah algorithm no significant BER deviation is observed while the highlyparallelizable graph-based structure of the algorithm enables high-throughput decoding. Index Terms — iterative decoding of product codes, Adaptive Belief Propagation, BCH codes, parity check matrix. I.
Information-Dispersion-Entropy-Based Blind Recognition of Binary BCH Codes in Soft Decision Situations
, 2013
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1 Iterative Decoding of a Class of Cyclic Codes
"... Abstract — Among the classes of LDPC codes that have been constructed and designed, the only class of LDPC codes that are cyclic is the class of codes constructed based on the incidence vectors of lines of finite geometries, called finite geometry LDPC codes. Cyclic finite geometry LDPC codes are kn ..."
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Abstract — Among the classes of LDPC codes that have been constructed and designed, the only class of LDPC codes that are cyclic is the class of codes constructed based on the incidence vectors of lines of finite geometries, called finite geometry LDPC codes. Cyclic finite geometry LDPC codes are known to have large minimum distances and can provide good error performance with very low error-floors using iterative decoding based on belief propagation. Their cyclic structure allows them to be efficiently and systematically encoded with simple shift-registers in linear time with linear complexity. An obvious question is whether, besides cyclic finite geometry LDPC codes, there are other cyclic codes with large minimum distances that can be efficiently decoded iteratively using channel soft information. In this paper, we present one such class of cyclic codes. Codes in this class are two-step majority-logic decodable and they are also constructed based on finite geometries. Two iterative decoding algorithms are devised for this class of cyclic codes and they provide significant coding gain over the two-step majority-logic decoding of codes in this class. I.
Turbo decoding of product codes using adaptive belief propagation
- Communications, IEEE Transactions on
, 2009
"... Abstract — The Adaptive Belief Propagation (ABP) algorithm was recently proposed by Jiang and Narayanan for the soft decoding of Reed-Solomon (RS) codes. In this paper, simplified versions of this algorithm are investigated for the turbo decoding of product codes. The complexity of the Turbo-oriente ..."
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Abstract — The Adaptive Belief Propagation (ABP) algorithm was recently proposed by Jiang and Narayanan for the soft decoding of Reed-Solomon (RS) codes. In this paper, simplified versions of this algorithm are investigated for the turbo decoding of product codes. The complexity of the Turbo-oriented Adaptive Belief propagation (TAB) algorithm is significantly reduced by moving the matrix adaptation step outside of the belief propagation iteration loop. A reduced-complexity version of the TAB algorithm that offers a trade-off between performance and complexity is also proposed. Simulation results for the turbo decoding of product codes show that belief propagation based on adaptive parity check matrices is a practical alternative to the currently very popular Chase-Pyndiah algorithm. Index Terms — Product codes, BCH codes, Reed-Solomon codes, iterative decoding, adaptive belief propagation.
On the Performance of Short Forward Error-Correcting Codes
"... Abstract — This letter investigates the performance of short forward error-correcting (FEC) codes. Reed-Solomon (RS) codes and concatenated zigzag codes are chosen as representatives of classical algebraic codes and modern simple iteratively decodable codes, respectively. Additionally, random binary ..."
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Abstract — This letter investigates the performance of short forward error-correcting (FEC) codes. Reed-Solomon (RS) codes and concatenated zigzag codes are chosen as representatives of classical algebraic codes and modern simple iteratively decodable codes, respectively. Additionally, random binary linear codes are used as a baseline reference. Our main results (demonstrated by simulations and ensemble distance spectrum analysis) are as follows: 1) Short RS codes are as good as random binary linear codes; 2) Carefully designed short low-density paritycheck (LDPC) codes are almost as good as random binary linear codes; 3) Low complexity belief propagation decoders incur considerable performance loss at short coding lengths. Thus, future work could focus on developing low-complexity (near) optimal decoders for RS codes and/or LDPC codes. Index Terms — Reed-Solomon (RS) codes, concatenated zigzag (CZ) codes, adaptive belief propagation. I.
