TY - GEN
T1 - Analog coding of a source with erasures
AU - Haikin, Marina
AU - Zamir, Ram
N1 - Publisher Copyright:
© 2016 IEEE.
PY - 2016/8/10
Y1 - 2016/8/10
N2 - Analog coding decouples the tasks of protecting against erasures and noise. For erasure correction, it creates an 'analog redundancy' by means of band-limited discrete Fourier transform (DFT) interpolation, or more generally, by an over-complete expansion based on a frame. We examine the analog coding paradigm for the dual setup of a source with 'erasure' side-information (SI) at the encoder. The excess rate of analog coding above the rate-distortion function (RDF) is associated with the energy of the inverse of submatrices of the frame, where each submatrix corresponds to a possible erasure pattern. We give a partial theoretical as well as numerical evidence that a variety of structured frames, in particular DFT frames with difference-set spectrum and more general equiangular tight frames (ETFs), with a common MANOVA limiting spectrum, minimize the excess rate over all possible frames. However, they do not achieve the RDF even in the limit as the dimension goes to infinity.
AB - Analog coding decouples the tasks of protecting against erasures and noise. For erasure correction, it creates an 'analog redundancy' by means of band-limited discrete Fourier transform (DFT) interpolation, or more generally, by an over-complete expansion based on a frame. We examine the analog coding paradigm for the dual setup of a source with 'erasure' side-information (SI) at the encoder. The excess rate of analog coding above the rate-distortion function (RDF) is associated with the energy of the inverse of submatrices of the frame, where each submatrix corresponds to a possible erasure pattern. We give a partial theoretical as well as numerical evidence that a variety of structured frames, in particular DFT frames with difference-set spectrum and more general equiangular tight frames (ETFs), with a common MANOVA limiting spectrum, minimize the excess rate over all possible frames. However, they do not achieve the RDF even in the limit as the dimension goes to infinity.
KW - DFT
KW - Data compression
KW - Jacobi/MANOVA distribution
KW - Welch bound
KW - analog codes
KW - difference set
KW - equiangular tight frames
KW - frames
KW - side information
KW - signal amplification
UR - http://www.scopus.com/inward/record.url?scp=84985953079&partnerID=8YFLogxK
U2 - 10.1109/ISIT.2016.7541664
DO - 10.1109/ISIT.2016.7541664
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AN - SCOPUS:84985953079
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 2074
EP - 2078
BT - Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2016 IEEE International Symposium on Information Theory, ISIT 2016
Y2 - 10 July 2016 through 15 July 2016
ER -