An improved bidirectional search algorithm for computing the weight spectrum of convolutional codes is presented. This algorithm does not employ the column distance function of a code which plays an important role in ...
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An improved bidirectional search algorithm for computing the weight spectrum of convolutional codes is presented. This algorithm does not employ the column distance function of a code which plays an important role in the original bidirectional search algorithm. We show the proposed algorithm can reduce computaion time for obtaining the weigth spectrum of convolutional codes significantly compared with that of the bidirectional search algorithm.
In this letter, we propose tight performance upper bounds for convolutional codes terminated with an input sequence of finite length. To obtain the upper bounds, a weight enumerator is defined to represent the relatio...
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In this letter, we propose tight performance upper bounds for convolutional codes terminated with an input sequence of finite length. To obtain the upper bounds, a weight enumerator is defined to represent the relation between the Hamming distance of the coded output and the Hamming distance of the input bits of the code. The upper bounds on frame error rate (FER) and average bit error rate (BER) are obtained from the weight enumerator. A simple method is presented to compute the weight enumerator of a terminated convolutional code based on a modified trellis diagram.
Nested convolutional codes are a set of convolutional codes that is derived from a given generator matrix. The structural properties of nested convolutional codes and nested generator matrices are studied. A method to...
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Nested convolutional codes are a set of convolutional codes that is derived from a given generator matrix. The structural properties of nested convolutional codes and nested generator matrices are studied. A method to construct the set of all minimal (rational) generator matrices of a given convolutional code is presented. As an example, two different sets of nested convolutional codes are derived from two equivalent minimal generator matrices. The significant difference in their free-distance profiles emphasizes the importance of being careful when selecting the generator matrices that determine the nested convolutional codes. As an application of nested convolutional codes, woven codes with outer warp, and inner nested convolutional codes are considered. The free-distance profile of the inner generator matrix is shown to be an important design tool.
Error rate performances of free-space optical communication are analyzed for irradiance modulation and direct detection systems using subcarrier intensity modulation with binary phase-shift keying and convolutional co...
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Error rate performances of free-space optical communication are analyzed for irradiance modulation and direct detection systems using subcarrier intensity modulation with binary phase-shift keying and convolutional code. The analysis is carried out for Gamma-Gamma turbulence channels. For bit-by-bit interleaved channels, a highly accurate series solution is developed for the pairwise error probability, and this solution is used to formulate a simplified upper bound on the average bit-error rate (BER). We also study the BER performance for quasi-static fading channels of a convolutional coded system using block interleaving where each block experiences independent fading.
This letter presents a method to find convolutional codes with good translation properties by modifying the generator matrix of existing codes and using a bit modifier. Applying the method causes no loss in the error ...
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This letter presents a method to find convolutional codes with good translation properties by modifying the generator matrix of existing codes and using a bit modifier. Applying the method causes no loss in the error correcting performance and only slight modifications to the architecture of existing encoders and decoders.:The new codes' maximal runs of both zeros and ones are constrained. It is shown that some of the new line codes are dc-free.
We study multidimensional analogues of quasi-twisted codes from different points of view. Their concatenated structure allows us to characterize self-dual and complementary-dual classes of such codes as well as to sho...
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We study multidimensional analogues of quasi-twisted codes from different points of view. Their concatenated structure allows us to characterize self-dual and complementary-dual classes of such codes as well as to show that multidimensional quasi-twisted (QT) codes are asymptotically good, together with their self-dual and complementary-dual subclasses. They are naturally related to nD convolutional codes as well. It is known that the minimum distance of quasi-cyclic codes provides a lower bound on the free distance of convolutional codes. An analogous result was shown for certain 1-generator 2D convolutional codes by using quasi-2D-cyclic codes. We prove a similar relation between convolutional codes and the related QT codes first, and then generalize the relation further to certain product convolutional codes and the related product QT codes, which improves the previous result in terms of dimension and number of generators. We also provide two-dimensional ternary and binary codes of modest lengths which yield good parameters.
In this paper, we construct a class of new group character codes with parameters [2(n), 2(n) - 2S(n)(r - 1), 2(r)] based on Ding et al. (IEEE Trans Inf Theory 46(1):280-284, 2000). Moreover, we use the new group chara...
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In this paper, we construct a class of new group character codes with parameters [2(n), 2(n) - 2S(n)(r - 1), 2(r)] based on Ding et al. (IEEE Trans Inf Theory 46(1):280-284, 2000). Moreover, we use the new group character codes to construct a family of unit memory convolutional codes with parameters [2(n), 2(n) - 2S(n)(r - 1), S-n(r - 1);1, 2(r)], which the free distances of these convolutional codes are exact values.
The structure of an SST Viterbi decoder for general rate (n-1)/n convolutional codes is investigated in the Light of syndrome decoding. Since the input to the main decoder is expressed as S (H-1)(T) (S: syndrome, H: d...
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The structure of an SST Viterbi decoder for general rate (n-1)/n convolutional codes is investigated in the Light of syndrome decoding. Since the input to the main decoder is expressed as S (H-1)(T) (S: syndrome, H: dual encoder of G) for a general non-systematic convolutional code G if the inverse encoder G(-1) is used as a pre-decoder, SST Viterbi decoding can be regarded as searching for the most likely error sequence through an extended syndrome trellis. We show that searching based on the extended syndrome trellis is equivalent to the original syndrome decoding by applying the invariant-factor theorem.
This paper considers a method for constructing good highrate punctured convolutional codes through dual codes. A low-rate R = 1/n convolutional code has a dual code identical to a punctured convolutional code with rat...
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This paper considers a method for constructing good highrate punctured convolutional codes through dual codes. A low-rate R = 1/n convolutional code has a dual code identical to a punctured convolutional code with rate R = (n - 1)/n. This implies that a low-rate R = 1/n convolutional code encoder can help the search of punctured convolutional code encoders. This paper provides the procedures that obtain all the useful dual code encoders to a given CC with rate R = 1/n easily, and the best PCC encoder with rate R = (n - 1)/n among the encoders we derive from all the obtained dual code encoders. This paper also shows an example of the PCC the procedures obtain from some CC.
The circular decoding algorithm for tail-biting convolutional codes is executed using a fixed number of computations and is suitable for DSP/ASIC implementations. This letter presents the performance and complexity tr...
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The circular decoding algorithm for tail-biting convolutional codes is executed using a fixed number of computations and is suitable for DSP/ASIC implementations. This letter presents the performance and complexity trade-off in the circular decoding algorithm using an analytic bound on the error probability. An incremental performance improvement is shown as the complexity increases from O(L) to O(L + 10 K) where L is the length of the decoding trellis and K is the constraint length. The decoding complexity required to produce the maximum-likelihood performance is presented, which is applicable to many codes of practical interest.
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