New optimal partial unit memory codes

Dettmar, Uwe; Shavgulidze, Sergo

doi:10.1049/el:19921111

Cited by 17 publications

(17 citation statements)

References 3 publications

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“…In the following, we prove that decoding with Algorithm 1 is successful if the BRD condition (20) is fulfilled. The proof follows the proof of Dettmar and Sorger [22], [36]. Lemma 3 shows that the gaps between two correct results of Step 1 are not too big and Lemmas 4 and 5 show that the gap size after Steps 1 and 2 is at most one if the BRD condition (20) is fulfilled.…”

Section: B Proof Of Correctnessmentioning

confidence: 67%

“…(P)UM codes are a special class of convolutional codes with memory one. They can be constructed based on block codes, e.g., Reed-Solomon [14]- [16] or cyclic codes [17], [18]. The underlying block codes make an algebraic description of the convolutional code possible, enable us to estimate the distance properties and allow us to take into account existing efficient block decoders in order to decode the convolutional code.…”

Section: Introductionmentioning

confidence: 99%

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Convolutional Codes in Rank Metric With Application to Random Network Coding

Wachter-Zeh

Stinner

Sidorenko

2015

IEEE Trans. Inform. Theory

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Abstract-Random network coding recently attracts attention as a technique to disseminate information in a network. This paper considers a non-coherent multi-shot network, where the unknown and time-variant network is used several times. In order to create dependencies between the different shots, particular convolutional codes in rank metric are used. These codes are so-called (partial) unit memory ((P)UM) codes, i.e., convolutional codes with memory one. First, distance measures for convolutional codes in rank metric are shown and two constructions of (P)UM codes in rank metric based on the generator matrices of maximum rank distance codes are presented. Second, an efficient error-erasure decoding algorithm for these codes is presented. Its guaranteed decoding radius is derived and its complexity is bounded. Finally, it is shown how to apply these codes for error correction in random linear and affine network coding.

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Section: B Proof Of Correctnessmentioning

confidence: 67%

Section: Introductionmentioning

confidence: 99%

Convolutional Codes in Rank Metric With Application to Random Network Coding

Wachter-Zeh

Stinner

Sidorenko

2015

IEEE Trans. Inform. Theory

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“…contradicting (6). We prove this similarly for L (j) B without substracting in the limit of the sum, since we directly start left of the correct blocks on the right.…”

Section: Lemmamentioning

confidence: 70%

“…One approach is to define by G α a Maximum Distance Separable (MDS) code and d α = n−k−k 1 +1. This is basically the construction from [6], [10] which designs low-rate PUM codes since the (k +k 1 )×n matrix G α can define an MDS code only if k + k 1 ≤ n. Otherwise (as observed by [11]), there are linear dependencies between the rows of G α , what we have to consider when constructing PUM codes of arbitrary rate. In the following, we provide a construction of arbitrary k 1 < k and calculate its distance parameters.…”

Section: Constructing Pum Codes Of Arbitrary Rate a Constructionmentioning

confidence: 99%

“…Moreover, the existing efficient block decoders can be taken into account in order to decode the convolutional code. There are constructions of these so-called Partial Unit Memory (PUM) codes [1], [2] based on Reed-Solomon (RS) [3]- [5], BCH [6], [7] and -in rank metric -Gabidulin [8], [9] codes. Decoding of these PUM codes uses the algebraic structure of the underlying RS, BCH or Gabidulin codes.…”

Section: Introductionmentioning

confidence: 99%

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Efficient decoding of Partial Unit Memory codes of arbitrary rate

Wachter-Zeh

Stinner

Bossert

2012

2012 IEEE International Symposium on Information Theory Proceedings

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Partial Unit Memory (PUM) codes are a special class of convolutional codes, which are often constructed by means of block codes. Decoding of PUM codes may take advantage of existing decoders for the block code. The Dettmar-Sorger algorithm is an efficient decoding algorithm for PUM codes, but allows only low code rates. The same restriction holds for several known PUM code constructions. In this paper, an arbitraryrate construction, the analysis of its distance parameters and a generalized decoding algorithm for PUM codes of arbitrary rate are provided. The correctness of the algorithm is proven and it is shown that its complexity is cubic in the length.

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An Introduction to Generalized Concatenated Codes

Zyablov

Shavgulidze

Bossert

1999

Trans Emerging Tel Tech

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Abstract. This paper presents an introduction to the theory of generalized concatenated codes. We consider the encoding and decoding procedures of both ordinary concatenatedcodes, and generalized concatenatedcodes where block codes are used as inner codes. We give the main parameters of these codes, and by means of examples, show that under the same conditions the latter outperforms the former with respect to minimum code distance. We also heuristically describe the generalized concatenated decoding procedure. Then we show how the generalized concatenated coding ideas can be applied to encoded memoryless modulation. Such construction is often referred to as a multilevel code in literature. We consider the multilevel codes from the standpoint of generalized concatenated codes and with the help of a simple example, show how encoding and decoding procedures can be camed out. Ordinary concatenated and generalized concatenated coding schemes are considered next, using inner convolutional codes or inner modulation with memory. With the help of examples, we analyze the distance properties of such constructions.

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New optimal partial unit memory codes

Cited by 17 publications

References 3 publications

Convolutional Codes in Rank Metric With Application to Random Network Coding

Convolutional Codes in Rank Metric With Application to Random Network Coding

Efficient decoding of Partial Unit Memory codes of arbitrary rate

An Introduction to Generalized Concatenated Codes

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