Based on known bounds for relative generalized Hamming weights of linear codes, we provide several new bounds for generalized column distances of convolutional codes, including the Griesmer-type bound for generalized ...
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Based on known bounds for relative generalized Hamming weights of linear codes, we provide several new bounds for generalized column distances of convolutional codes, including the Griesmer-type bound for generalized column distances. Then we construct several infinite families of convolutional codes such that the (1, 1)-Griesmer defect of these convolutional codes is small compared with the length of these convolutional codes by using cyclic codes, negacyclic codes and GRS codes. In particular, we obtain some convolutional codes such that the (1, 1)-Griesmer defect of these convolutional codes is zero or one. Next we prove that the 2-generalized column distance sequence {d(2,j)(C)}(infinity)(j=1)of any convolutional code C is increasing and bounded from above, and the limit of the sequence {d(2,j)(C)}(infinity)(j=1 )is related to the2-generalized Hamming weight of the convolutional code C. For i >= 3, we prove that the i-generalized column distance sequence {d(i,j)(C)}(infinity)(j=Gamma i/k-1 )of any convolutional code C is bounded above and below.
In this paper, we propose a new erasure decoding algorithm for convolutional codes using the generator matrix. This implies that our decoding method also applies to catastrophic convolutional codes in opposite to the ...
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In this paper, we propose a new erasure decoding algorithm for convolutional codes using the generator matrix. This implies that our decoding method also applies to catastrophic convolutional codes in opposite to the classic approach using the parity-check matrix. We compare the performance of both decoding algorithms. Moreover, we enlarge the family of optimal convolutional codes (complete-MDP) based on the generator matrix.
As maximum distance separable convolutional codes are known for their ability to achieve the generalized Singleton bound, they are highly suitable for correcting errors. Nevertheless, until now, these codes have prima...
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The accurate identification of channel-coding types plays a crucial role in wireless communication systems. The recognition of convolutional codes presents challenges, primarily due to their strong temporal dependenci...
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The accurate identification of channel-coding types plays a crucial role in wireless communication systems. The recognition of convolutional codes presents challenges, primarily due to their strong temporal dependencies, varying constraint lengths, and additional contamination from noise. However, existing algorithms often rely on manual feature extraction or are limited to a restricted number of coding types, rendering them inadequate for practical applications. To tackle this problem, we propose ConvLSTM-TFN (temporal feature network), an innovative blind-recognition network that integrates convolutional layers, long short-term memory (LSTM) networks, and a self-attention mechanism. The proposed approach enhances the acquisition of features from soft-decision sequence information, leading to improved recognition performance without necessitating prior knowledge of coding parameters, sequence starting positions, or other metadata. The experimental results demonstrate that our method is effective within a signal-to-noise ratio (SNR) range of 0 to 20 dB, achieving more than 90% recognition accuracy across 17 convolutional code types, with an average accuracy of 98.7%. Our method effectively distinguishes diverse coding features, surpassing existing models and establishing a new benchmark for channel-coding recognition.
convolutional codes are widely used in many applications. The encoders can be implemented with a simple circuit. Decoding is often accomplished by the Viterbi algorithm or the maximum a-posteriori decoder of Bahl et a...
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ISBN:
(数字)9798331522896
ISBN:
(纸本)9798331522902
convolutional codes are widely used in many applications. The encoders can be implemented with a simple circuit. Decoding is often accomplished by the Viterbi algorithm or the maximum a-posteriori decoder of Bahl et al. These algorithms are sequential in nature, requiring a decoding time proportional to the message length. For low latency applications this this latency might be problematic. This paper introduces a low latency decoder for tail-biting convolutional codes TBCCs that processes multiple trellis stages in parallel. The new decoder is designed for hardware with parallel processing capabilities. The overall decoding latency is proportional to the log of the message length. The new decoding architecture is modified into a list decoder, and the list decoding performance can be enhanced by exploiting linearity to expand the search space. Certain modifications to standard TBCCs are supported by the new architecture and improve frame error rate performance.
Identifying the unknown convolutional code corresponding to the given intercepted data is an important problem in military surveillance and in wireless communication. While a variety of code identification algorithms ...
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We define the bidirectional distance profile (BDP) of a convolutional code as the minimum of the distance profiles of the code and its corresponding "reverse" code. We present tables of codes with the optimu...
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We define the bidirectional distance profile (BDP) of a convolutional code as the minimum of the distance profiles of the code and its corresponding "reverse" code. We present tables of codes with the optimum BDP (OBDP), which minimize the average complexity of bidirectional sequential decoding algorithms. The computer search is accelerated by the facts that optimum distance profile (ODP) codes of larger memory must have ODP codes of smaller memory as their "prefixes", and that OBDP codes can be obtained by "concatenating" ODP and reverse ODP codes of smaller memory. We compare the performance of OBDP codes and other codes by simulation.
Maximum distance profile codes are characterized by the property that two trajectories which start at the same state and proceed to a different state will have the maximum possible minimum distance from each other rel...
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Maximum distance profile codes are characterized by the property that two trajectories which start at the same state and proceed to a different state will have the maximum possible minimum distance from each other relative to any other convolutional code of the same rate and degree. In this paper we use methods from systems theory to characterize maximum distance profile codes algebraically. The main result shows that maximum distance profile codes form a generic set inside the variety which parametrizes the set of convolutional codes of a fixed rate and a fixed degree. (C) 2004 Elsevier B.V. All rights reserved.
We construct a family of (n, k) convolutional codes with degree delta is an element of {k, n - k} that have a maximum distance profile. The field size required for our construction is Theta(n(2 delta)), which improves...
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We construct a family of (n, k) convolutional codes with degree delta is an element of {k, n - k} that have a maximum distance profile. The field size required for our construction is Theta(n(2 delta)), which improves upon the known constructions of convolutional codes with a maximum distance profile. Our construction is based on the theory of skew polynomials.
A new kind of convolutional codes generalizing Goppa codes is proposed. This provides a systematic method for constructing convolutional codes with prefixed properties. In particular, examples of Maximum-Distance Sepa...
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A new kind of convolutional codes generalizing Goppa codes is proposed. This provides a systematic method for constructing convolutional codes with prefixed properties. In particular, examples of Maximum-Distance Separable (MDS) convolutional codes are obtained.
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