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Coding problems involving values and their positions

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Many signal processing and coding problems involve objects that can be represented as a vector of sparse nonzero values. Examples include image coding (compression), sampling of non-bandlimited processes with finite rate of innovation, compressed sensing (aka compressive sampling) and error correction coding. Efficiency is gained through coding only the nonzero values and their positions. The challenge lies in constructing non-adaptive sampling/coding schemes that need not know the positions of the nonzero values, but only their number.

This talk will focus on the example of distributed source coding, where a source is compressed assuming that correlated side information is available at the decoder. Such systems fail if the correlation weakens intermittently. We present a general scheme that allows to “correct” such glitches and show how it can be implemented efficiently using LDPC codes. This illustrates that in certain cases, location can be encoded very efficiently, while in others, no methods with practical decoding complexity are known.

(Joint work with Francesca Bassi, Michel Kieffer and Gottfried Lechner)

This talk is part of the Signal Processing and Communications Lab Seminars series.

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