We look at graphical descriptions of block, codes known as trellises, which illustrate connections between algebra and graph theory, and can be used to develop powerful decoding algorithms. Trellises for linear block ...
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We look at graphical descriptions of block, codes known as trellises, which illustrate connections between algebra and graph theory, and can be used to develop powerful decoding algorithms. Trellises for linear block codes are known to grow exponentially with the code parameters and hence decoding on such objects is often infeasible. Of considerable interest to coding theorists therefore, are more compact descriptions called tail-biting trellises which in some cases can be much smaller than any ordinary trellis for the same code. We derive some interesting properties of tail-biting trellises and present an optimal maximum-likelihood decoding algorithm that performs rather well in terms of decoding complexity even at low signal-to-noise ratios.
A novel soft-decision decoding algorithm for Reed-Solomon codes over GF(2 (m) ) is proposed, which is based on representing them as polar codes with dynamic frozen symbols and applying the successive cancellation meth...
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A novel soft-decision decoding algorithm for Reed-Solomon codes over GF(2 (m) ) is proposed, which is based on representing them as polar codes with dynamic frozen symbols and applying the successive cancellation method. A further performance improvement is obtained by exploiting multiple permutations of codewords which are taken from the automorphism group of Reed-Muller codes. It is also shown that the proposed algorithm can be simplified in the case of decoding a binary image of the Reed-Solomon code.
This paper proposes a new approximation to be used for the correction function in the turbo decoding algorithm, called Linear-Constant-log Map. Max-log Map, Linear-log Map and Constant-log Map are the well known simpl...
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This paper proposes a new approximation to be used for the correction function in the turbo decoding algorithm, called Linear-Constant-log Map. Max-log Map, Linear-log Map and Constant-log Map are the well known simplified versions of Jacobi-log Map (Maximum a Posteriori) algorithm already in use but they cannot meet a proper performance in term of output BER and clock consumption of the CPU decoding encoded bits. The proposed algorithm first breaks the correction function domain of the Jacobi logarithm to three subsections by determining the border points between these sections and then uses a linear function and two constant values as an approximation of this function. Using an AWGN channel model, simulation results show that the new algorithm is almost more than six times faster than Jacobi-log Map algorithm with a Bit Error Rate (BER) very close to it. (C) 2012 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
Neural spike train decoding algorithms are important tools for characterizing how ensembles of neurons represent biological signals. We present a Bayesian neural spike train decoding algorithm based on a point process...
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Neural spike train decoding algorithms are important tools for characterizing how ensembles of neurons represent biological signals. We present a Bayesian neural spike train decoding algorithm based on a point process model of individual neurons, a linear stochastic state-space model of the biological signal, and a temporal latency parameter. The latency parameter represents the temporal lead or lag between the biological signal and the ensemble spiking activity. We use the algorithm to study Whether the representation of position by the ensemble spiking activity of pyramidal neurons in the CA1 region of the rat hippocampus is more consistent with prospective coding, i.e., future position, or retrospective coding, past position. Using 44 simultaneously recorded neurons and an ensemble delay latency of 400 ms, the median decoding error was 5.1 cm during 10 min of foraging in an open circular environment. The true coverage probability for the algorithm's 0.95 confidence regions was 0.71. These results illustrate how the Bayesian neural spike train decoding paradigm may be used to investigate spatio-temporal representations of position by an ensemble of hippocampal neurons.
A modification of the decoding q-ary Sum Product Algorithm (q-SPA) was proposed for the nonbinary codes with small check density based on the permutation matrices. The algorithm described has a vector realization and ...
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A modification of the decoding q-ary Sum Product Algorithm (q-SPA) was proposed for the nonbinary codes with small check density based on the permutation matrices. The algorithm described has a vector realization and operates over the vectors defined on the field GF(q), rather than over individual symbols. Under certain code parameters, this approach enables significant speedup of modeling.
A latency reduced method is proposed based on the modified successive cancellation (MSC) decoder for decoding polar codes. In the MSC decoder, it was shown that latencies for both the rate-zero and the rate-one nodes ...
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A latency reduced method is proposed based on the modified successive cancellation (MSC) decoder for decoding polar codes. In the MSC decoder, it was shown that latencies for both the rate-zero and the rate-one nodes can be reduced. By redistributing the information bits, the proposed method can obtain a good rate-zero and rate-one nodes distribution, in which decoding latency can be further reduced under the MSC decoder. Simulation results show that the new polar code (obtained by the proposed method) achieves 8.5% latency reduction with neglected error performance loss compared with the original polar code. Furthermore, it is easy to adjust the trade-off between the error performance and decoding latency by the proposed method.
A successive cancellation stack (SCS) decoding algorithm is proposed to improve the performance of polar codes. Unlike the conventional successive cancellation decoder which determines the bits successively with a loc...
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A successive cancellation stack (SCS) decoding algorithm is proposed to improve the performance of polar codes. Unlike the conventional successive cancellation decoder which determines the bits successively with a local optimal strategy, the SCS algorithm stores a number of candidate partial paths in an ordered stack and tries to find the global optimal estimation by searching along the best path in the stack. Simulation results in the binary-input additive white Gaussian noise channel show that the SCS algorithm has the same performance as the successive cancellation list (SCL) algorithm and can approach that of the maximum likelihood algorithm. Moreover, the time complexity of the SCS decoder is much lower than that of the SCL and can be very close to that of the SC in the high SNR regime.
Early termination techniques are widely used in low-density party-check (LDPC) decoding since the decoding operations can be tremendously reduced. A layer stopping criterion is proposed to reduce further the operation...
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Early termination techniques are widely used in low-density party-check (LDPC) decoding since the decoding operations can be tremendously reduced. A layer stopping criterion is proposed to reduce further the operations within iterative layered LDPC decoding. The proposed criterion detects the high reliability of the soft log-likelihood ratio with a threshold in each layer. Then the layer operations can be stopped when the reliable layers are detected. The proposed criterion combined with early termination techniques can efficiently reduce the layer operations by up to 60% with a negligible loss of coding gain at E-b/N-0 of 3.2 dB.
We first present a memory-efficient array data structure to represent the Huffman tree. We then present a fast Huffman decoding algorithm. (C) 1997 Elsevier Science B.V.
We first present a memory-efficient array data structure to represent the Huffman tree. We then present a fast Huffman decoding algorithm. (C) 1997 Elsevier Science B.V.
A list successive cancellation (LSC) decoding algorithm to boost the performance of polar codes is proposed. Compared with traditional successive cancellation decoding algorithms, LSC simultaneously produces at most L...
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A list successive cancellation (LSC) decoding algorithm to boost the performance of polar codes is proposed. Compared with traditional successive cancellation decoding algorithms, LSC simultaneously produces at most L locally best candidates during the decoding process to reduce the chance of missing the correct codeword. The complexity of the proposed algorithm is O(LNlog N), where N and L are the code length and the list size, respectively. Simulation results of LSC decoding in the binary erasure channel and binary-input additive white Gaussian noise channel show a significant performance improvement.
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