Fundamentals of Convolutional Coding

Johannesson, Rolf; Zigangirov, Kamil Sh.

doi:10.1109/9780470544693

Cited by 548 publications

(618 citation statements)

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“…In that case, we say that C has rate k/n, and that G(z) is a generator matrix of C. The free distance of C is given by A matrix G(z) ∈ F n×k [z] is called basic if it has a polynomial left inverse (see for example [20,21,36]). The degree or complexity δ of a rate k/n convolutional code C is the maximum degree of the k × k minors of any generator matrix (see [26,30]…”

Section: Preliminary Resultsmentioning

confidence: 99%

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Parallel concatenated convolutional codes from linear systems theory viewpoint

Climent

Herranz

Perea

2016

Systems & Control Letters

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The aim of this work is to characterize two models of concatenated convolutional codes based on the theory of linear systems. The problem we consider can be viewed as the study of composite linear system from the classical control theory or as the interconnection from the behavioral system viewpoint. In this paper we provide an input-state-output representation of both models and introduce some conditions for such representations to be both controllable and observable. We also introduce a lower bound on their free distances and the column distances.

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Section: Preliminary Resultsmentioning

confidence: 99%

“…A major parameter of a convolutional code is its free distance [21,30] since it determines the decoding capability of a code under maximum likelihood decoding. It depends on the collection of code sequences, not on the specific device that is used to generate those sequences.…”

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confidence: 99%

Parallel concatenated convolutional codes from linear systems theory viewpoint

Climent

Herranz

Perea

2016

Systems & Control Letters

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“…The extended row distance d r j is defined [11,24] to be the minimum Hamming weight of all paths in the minimal code trellis that diverge from the zero state and then return for the first time back in the zero state only after j branches. An UM code can be represented by a trellis [4][5][6] where the state at time t is u t−1 .…”

Section: Unit Memory Convolutional Codesmentioning

confidence: 99%

“…Hence, the notion of (extended) row distance is often used when more detailed knowledge of the distance structure of a convolutional code is needed [11]. One of the advantages of the row distance is that it is easy to calculate and serves as an excellent rejection rule when encoders are tested in search for convolutional code with large free distance.…”

Section: Introductionmentioning

confidence: 99%

“…In [23] the first concrete construction of an MDS convolutional code (over the finite field F) of rate k n and degree δ was presented for every given set of parameters (n, k, δ ), (with the characteristic of the finite field F and the length n of the code being coprime). Bounds and fundamental properties of the column distances of convolutional codes have also been thoroughly investigated, see for instance [7,8,11,18]. Convolutional codes having the largest columns distances for a given rate k n and degree δ are called maximum distance profile (MDP).…”

Section: Introductionmentioning

confidence: 99%

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On Optimal Extended Row Distance Profile

Almeida

Napp

Pinto

2017

Springer Proceedings in Mathematics &Amp; Statistics

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In this paper, we investigate extended row distances of Unit Memory (UM) convolutional codes. In particular, we derive upper and lower bounds for these distances and moreover present a concrete construction of a UM convolutional code that almost achieves the derived upper bounds. The generator matrix of these codes is built by means of a particular class of matrices, called superregular matrices. We actually conjecture that the construction presented is optimal with respect to the extended row distances as it achieves the maximum extended row distances possible. This in particular implies that the upper bound derived is not completely tight. The results presented in this paper further develop the line of research devoted to the distance properties of convolutional codes which has been mainly focused on the notions of free distance and column distance. Some open problems are left for further research.

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General Packet Radio Service (GPRS)

2001

GSM Switching, Services and Protocols

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he impressive growth of cellular mobile telephony as well as the number of Internet users promises an exciting potential for a market that combines both innovations: cellular wireless data services. Within the next few years, there will be an extensive demand for wireless data services. In particular, high-performance wireless Internet access will be requested by users.Existing cellular data services do not fulfill the needs of users and providers. From the user's point of view, data rates are too slow and the connection setup takes too long and is rather complicated. Moreover, the service is too expensive for most users. From the technical point of view, the drawback results from the fact that current wireless data services are based on circuit switched radio transmission. At the air interface, a complete traffic channel is allocated for a single user for the entire call period. In case of bursty traffic (e.g., Internet traffic), this results in a highly inefficient resource utilization. It is obvious that for bursty traffic, packet switched bearer services result in a much better utilization of the traffic channels. This is because a channel will only be allocated when needed and will be released immediately after the transmission of the packets. With this principle, multiple users can share one physical channel (statistical multiplexing).In order to address these inefficiencies, two cellular packet data technologies have been developed so far: cellular digital packet data (CDPD) (for AMPS, IS-95, and IS-136) and the General Packet Radio Service (GPRS). GPRS is the topic of this paper. It was originally developed for GSM, but will also be integrated within IS-136 (see [1]). We treat GPRS from the point of view of GSM.GPR S is a new bearer service for GSM that greatly improves and simplifies wireless access to packet data networks, e.g., to the Internet. It applies a packet radio principle to transfer user data packets in an efficient way between GSM mobile stations and external packet data networks. Packets can be directly routed from the GPRS mobile stations to packet switched networks. Networks based on the Internet Protocol (IP) (e.g., the global Internet or private/corporate intranets) and X.25 networks are supported in the current version of GPRS.Users of GPRS benefit from shorter access times and higher data rates. In conventional GSM, the connection setup takes several seconds and rates for data transmission are restricted to 9.6 kbit/s. GPRS in practice offers session establishment times below one second and ISDN-like data rates up to several ten kbit/s.In addition, GPRS packet transmission offers a more userfriendly billing than that offered by circuit switched services. In circuit switched services, billing is based on the duration of the connection. This is unsuitable for applications with bursty traffic. The user must pay for the entire airtime, even for idle periods when no packets are sent (e.g., when the user reads a Web page). In contrast to this, with packet switched services, billing can be ba...

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Fundamentals of Convolutional Coding

Cited by 548 publications

References 0 publications

Parallel concatenated convolutional codes from linear systems theory viewpoint

Parallel concatenated convolutional codes from linear systems theory viewpoint

On Optimal Extended Row Distance Profile

General Packet Radio Service (GPRS)

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