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On a class of convolutional codes
IEEE Transactions on Information Theory, 1983Summary: For the case when \(k\) divides \(n\), we introduce a special class of \((n,k)\) \(F\)-ary convolutional codes, \(F= \mathrm{GF}(q)\) a finite field, by considering the input to an \((n,k)\) encoder as a sequence over \(\mathrm{GF}(q^k)\), the output as a sequence over \(\mathrm{GF}(q^n)\), and then considering encoders which correspond to ...
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A MacWilliams formula for Convolutional Codes
2007 IEEE International Symposium on Information Theory, 2007Regarding convolutional codes as polynomial analogues of arithmetic lattices, we derive a Poisson–Jacobi formula for their trivariate weight enumerator. The proof is based on harmonic analysis on locally compact abelian groups as developed in Tate's thesis to derive the functional equation of the zeta function.
Patrick Solé, Dmitrii V. Zinoviev
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Recursive convolutional codes for time-invariant LDPC convolutional codes
2010 IEEE International Symposium on Information Theory, 2010In this paper we present an attractive alternative to construct time-invariant Low-Density Parity-Check Convolutional Codes (LDPC-CC) of coding rate-b/c from a simple recursive systematic convolutional encoder design. The proposed Recursive Convolutional Doubly-Orthogonal (RCDO) encoders have a corresponding Tanner graph for which the girth is ...
Eric Roy +2 more
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Signal Codes: Convolutional Lattice Codes
IEEE Transactions on Information Theory, 2011The coded modulation scheme proposed in this paper has a simple construction: an integer sequence, representing the information, is convolved with a fixed, continuous-valued, finite impulse response (FIR) filter to generate the codeword - a lattice point. Due to power constraints, the code construction includes a shaping mechanism inspired by precoding
Ofir Shalvi, Naftali Sommer, Meir Feder
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Strongly-MDS convolutional codes [PDF]
IEEE Transactions on Information Theory, 2006 33 ...
Joachim Rosenthal
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Every Convolutional Code is a Goppa Code
IEEE Transactions on Information Theory, 2013Convolutional Goppa codes (CGC) were defined in Appl. Algebra Eng. Comm. Comput., vol. 15, pp. 51-61, 2004 and IEEE Trans. Inf. Theory, vol. 52, 340-344, 2006. In this paper, we prove that every convolutional code is a CGC defined over a smooth curve over \BBF q(z) and we give an explicit construction of convolutional codes as CGC over the projective ...
José Ignacio Iglesias Curto +3 more
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2008
Die vorliegende Arbeit befasst sich mit verkoppelten Faltungscodes - Codes die durch Verkettung von mehreren systematischen äusseren Faltungscodes und mehreren systematischen inneren Blockcodes konstruiert sind, wobei die einzelnen Eingangssequenzen der äusseren Codes verschachtelt werden, bevor sie in die inneren Codes hineingehen.
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Die vorliegende Arbeit befasst sich mit verkoppelten Faltungscodes - Codes die durch Verkettung von mehreren systematischen äusseren Faltungscodes und mehreren systematischen inneren Blockcodes konstruiert sind, wobei die einzelnen Eingangssequenzen der äusseren Codes verschachtelt werden, bevor sie in die inneren Codes hineingehen.
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On Tail Biting Convolutional Codes
IEEE Transactions on Communications, 1986In this paper, we introduce generalized tail biting encoding as a means to ameliorate the rate deficiency caused by zero-tail convolutional encoding. This technique provides an important link between quasi-cyclic block and convolutional codes. Optimum and suboptimum decoding algorithms for these codes are described and their performance determined by ...
Howard H. Ma, Jack K. Wolf
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On the structure of convolutional and cyclic convolutional codes
IEEE Transactions on Information Theory, 1979Algebraic convolutional coding theory is considered. It is shown that any convolutional code has a canonical direct decomposition into subcodes and that this decomposition leads in a natural way to a minimal encoder. Considering cyclic convolutional codes, as defined by Piret, an easy application of the general theory yields a canonical direct ...
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Syndrome Decoding of Convolutional Codes
IEEE Transactions on Communications, 1975The classical Viterbi decoder recursively finds the trellis path (code word) closest to the received data. Given the received data, the syndrome decoder first forms a syndrome, instead. A recursive algorithm like Viterbi's is used to determine the noise sequence of minimum Hamming weight that can be a possible cause of this syndrome. Given the estimate
Joost Schalkwijk, A. J. Han Vinck
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