Frame-Theoretic Analysis of DFTCodes With Erasures

Rath, Gagan; Guillemot, Christine

doi:10.1109/tsp.2003.821106

Cited by 65 publications

(50 citation statements)

References 18 publications

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“…As it can be observed, the PSNR is good if the erasure patterns are not bursty. This is similar to the trend observed in the case of block transforms [11]. From the theory developed, we note that the bursty erasure reconstruction capability of the code depends on the length of the analysis filters.…”

Section: B Image Coding Using Uniform Ofb For the Image Subbandssupporting

confidence: 85%

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Tree-Structured Oversampled Filterbanks as Joint Source-Channel Codes: Application to Image Transmission Over Erasure Channels

Motwani

Guillemot²

2004

IEEE Trans. Signal Process.

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This paper studies oversampled filterbanks for robust transmission of multimedia signals over erasure channels. Oversampled filterbanks implement frame expansions of signals in 2 ( ). The dependencies between the expansion coefficients introduced by the oversampled filterbank are first characterized both in the -domain and in the time-domain. Conditions for recovery of some typical erasure patterns like bursty erasure patterns are derived. The analysis leads to the design of two erasure recovery algorithms that are first studied without quantization noise. The reconstruction algorithm derived from the time-domain analysis exploits the fact that an oversampled filterbank represents signals with more than one set of basis functions. The erased samples are first reconstructed from the received ones, and then, signal space projection is applied. The effect of quantization noise on the reconstructed signal is studied for both algorithms. Using image signals, the theoretical results are validated for a number of erasure patterns, considering unequal error protection enabled tree-structured decompositions.

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Section: B Image Coding Using Uniform Ofb For the Image Subbandssupporting

confidence: 85%

“…DFT codes can be also regarded as joint source-channel block codes to obtain robustness to erasures [17], [18]. It is shown in [11] that DFT codes are actually a special class of frames. Filterbank frame expansions have also been studied to achieve resilience to erasures [1], [6], [20], [22].…”

Section: Introductionmentioning

confidence: 99%

Tree-Structured Oversampled Filterbanks as Joint Source-Channel Codes: Application to Image Transmission Over Erasure Channels

Motwani

Guillemot²

2004

IEEE Trans. Signal Process.

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“…2 and 3). These OFBs were designed with analysis polyphase matrix E(z) = EcP(z) where Ec is an N × K real-valued DFT code [12] and P(z) is the K × K polyphase matrix of an FIR UFB. One of the downside of time domain method for designing filter banks is the large number of free parameters that should be optimized.…”

Section: Design Examplesmentioning

confidence: 99%

Design of high order FIR Unimodular Filter Banks and its application in combatting instantaneous erasures

Akbari

Labeau

2011

2011 Digital Signal Processing and Signal Processing Education Meeting (DSP/SPE)

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FIR Unimodular Filter Banks (UFBs) offer the minimum possible delay among all the filter banks with the same downsampling rate. Although Order-one UFBs can be factorized into degree-one unimodular matrices, this factorization is not possible for higher order UFBs. This is unfavorable because in most applications, banks with longer length filters result in better performance. In this paper, we investigate the design of high order FIR UFBs using a time domain approach. We show that due to the flexibility of this method, long filters with decent frequency responses are achievable. We also propose a special factorization for high order UFBs which reduces the large number of free parameters of time domain approach. Although this factorization is not complete, we show that it can give reasonably good filters. Finally we use the designed filters in the application of reconstructing the output of an Oversampled FB in the case of instantaneous erasure in sub-band domain. Instantaneous erasure accounts for a situation where the sub-band samples are erased based on different patterns in each time instance and the minimum delay of the OFB is crucial for reconstructing the output.

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“…1 In that work, the detection and correction of codes has been applied to impulse noise cancellation for pulse amplitude modulation transmission. More recently, Rath and Guillemot [140] clearly make the connection between frames and DFT codes by taking a frame-theoretic approach to study DFT codes with erasures. They show that DFT codes are a special class of frames and use lowpass DFT codes to provide robustness to channel erasures.…”

Section: Coding Theorymentioning

confidence: 99%