This paper considers the problem of designing bandwidth expansion zero-delay analog joint source-channel coding (JSCC) schemes for the transmission of memoryless Gaussian samples over additive white Gaussian noise (AW...
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ISBN:
(纸本)9781479930012
This paper considers the problem of designing bandwidth expansion zero-delay analog joint source-channel coding (JSCC) schemes for the transmission of memoryless Gaussian samples over additive white Gaussian noise (AWGN) channels when side information is present at the receiver (Wyner-Ziv scenario). We first propose a 1 : 1 scheme and a 1 : M scheme based on the use of Shannon-Kotel'nikov mappings in a periodic fashion. Then, we combine the two proposed mappings to construct a flexible rate bandwidth expansion mapping whose rate can be anywhere from 1 : 1 to 1 : M. Different from digital systems, the proposed scheme offers low delay, low complexity and high robustness. Simulation results show that the performance of the proposed 1 : 2 scheme is better than that of existing zero-delay systems for a wide range of signal to noise ratios, but especially for high signal to noise ratios and highly correlated side information. The proposed flexible rate bandwidth expansion system also offers satisfactory performance, specially when considering its great flexibleness in terms of rate.
The Welch (lower) Bound on the mean square cross correlation between n unit-norm vectors f(1), ... , f(n) in the m dimensional space (R-m or C-m), for n >= m, is a useful tool in the analysis and design of spread s...
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ISBN:
(纸本)9781538647813
The Welch (lower) Bound on the mean square cross correlation between n unit-norm vectors f(1), ... , f(n) in the m dimensional space (R-m or C-m), for n >= m, is a useful tool in the analysis and design of spread spectrum communications, compressed sensing and analog coding. Letting F = [f(1)vertical bar ... vertical bar f(n)] denote the m-by-n frame matrix, the Welch bound can be viewed as a lower bound on the second moment of F, namely on the trace of the squared Gram matrix (F' F)(2). We consider an erasure setting, in which a reduced frame, composed of a random subset of Bernoulli selected vectors, is of interest. We present the erasure Welch bound and generalize it to the d-th order moment of the reduced frame, for d = 2, 3, 4. We provide simple, explicit formulae for the generalized bound, which interestingly is equal to the d-th moment of Wachter's classical MANOVA distribution plus a vanishing term (as n goes to infinity with m/n held constant). The bound holds with equality if (and for d = 4 only if) F is an Equiangular Tight Frame (ETF). Hence, our results offer a novel perspective on the superiority of ETFs over other frames, and provide explicit characterization for their subset moments.
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