Convolutional codes
From 1D convolutional codes to 2D convolutional codes of rate 1/n
... (2D) convolutional codes with finite support. These codes are of rate 1/n and degree δ with n ≥ δ + 1 and achieve the maximum possible distance among all 2D convolutional codes with ...
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Periodic state-space representations of periodic convolutional codes
... that convolutional codes and linear sys- tems defined over a finite field are essentially the same objects, see for instance [16] and references ...with convolutional codes, see [10, ...on ...
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A new class of superregular matrices and MDP convolutional codes
... The convolutional codes whose column distances increase as rapidly as possible for as long as possible are called maximum distance profile (MDP) ...These codes are specially appealing for the ...
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Decoding of 2D convolutional codes over an erasure channel
... 1D convolutional codes, called (reverse and complete) MDP, that have the maximum possible column distances (for a given set of parameters) and therefore perform particularly well over an erasure ...2D ...
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Minimal state-space realizations of 2D convolutional codes
... 1D convolutional codes, and some necessary background such as properties of equivalent encoders are ...1D convolutional codes and their encoders is considered for the 2D ...
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Input-state-output representations of concatenated 2D convolutional codes
... two codes (an inner code and an outer code) form an important class of error-correcting codes called concatenated ...concatenated codes used block codes, NASA started to use a ...
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Distance properties of convolutional codes over Z pr
... of convolutional codes, namely, the free distance and the column ...free codes these parameters have special values and then our bound coincides with the bound given in ...
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Column Rank Distances of Rank Metric Convolutional Codes
... for convolutional codes, two encoders of C differ by left multiplication by a unimodular matrix and therefore C always admits minimal ...metric convolutional code C is the sum of the row degrees of a ...
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Column distances of convolutional codes over Z_p^r
... a convolutional code that admits a noncatastrophic p-encoder a noncatastrophic convolutional ...noncatastrophic convolutional codes contain the class of convolutional codes that ...
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Concatenation of convolutional codes and rank metric codes for multi-shot network coding
... It is important to note that the conditions of Lemma 3 may not be satisfied at time instant s − 1 but hold true at instant s. Therefore one may need to wait until these conditions are satisfied in order to proceed with ...
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Input-state-output representations and constructions of finite-support 2D convolutional codes
... support convolutional codes by means of linear ...2D convolutional codes, whereas such constructions are not known for the representations used in ...2D convolutional codes and ...
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Realization of 2D convolutional codes of rate 1/n by separable Roesser models
... When considering 2D processes, there exist several state-space models [1, 4,18]. While in the 1D case there exists a characterization of minimality for realization via state-space models, the same does not happen in the ...
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Series concatenation of 2D convolutional codes by means of input-state-output representations
... Convolutional codes are one dimensional (1D) convolutional codes and can be seen as a general- ization of block codes in the sense that a block code is a convolutional code with ...
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On duals and parity-checks of convolutional codes over Z p r
... on convolutional codes over a finite ring, we consider an approach in which code sequences are semi-infinite Laurent series, ...i.e., convolutional codes constituted by left compact sequences ...
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On Minimality of ISO Representation of Basic 2D Convolutional Codes
... One of the most important problems studied in the theory of convolutional codes is the minimality of representations of these codes, i.e., the determination of ISO representations with minimal ...
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MDS 2D convolutional codes with optimal 1D horizontal projections
... the upperbound (1). In other words, the existence of optimal convolutional codes for any given set of Forney indices was left as an open question. In [2], it was considered a special class of matrices that ...
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Separation set distance for 2D Convolutional Codes
... In this paper we address the problem of extending the well-known no- tion of column distance of one-dimensional (1D) convolutional codes to the context of multidimensional (nD) convolutional ...
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MDP periodically time-varying convolutional codes
... time-varying convolutional codes and find necessary and sufficient conditions on the subcodes to obtain a (n, 2, 1) MDP time-varying convolutional code combin- ing (possibly) non MDP ...
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Maximum distance separable 2D convolutional codes
... 2D convolutional codes (Section ...2D convolutional codes that achieve such a bound are called MDS 2D convolutional ...2D convolutional codes (Section ...
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Generalized column distances for convolutional codes
... block codes to introduce the novel concept of generalized column distances for convolutional ...MDP convolutional code. The problem of constructing convolu- tional codes with design ...
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