2012/03/28 by Erik Johannesson, Johannesson, Erik, Anders Rantzer +5
Computer Science · Engineering · Mathematics · #Cooperative Communication and Network Coding #Error Correcting Code Techniques #FOS: Computer and information sciences #Information Theory (cs.IT) #Wireless Communication Security Techniques #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1203.6318
Submitted to IEEE Transactions on Information Theory on March 28th 2012
arxiv created 2012/03/28 · openalex publication_date 2012/03/28 · arxiv updated 2012/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The problem of joint source-channel coding is considered for a stationary remote (noisy) Gaussian source and a Gaussian channel. The encoder and decoder are assumed to be causal and their combined operations are subject to a delay constraint. It is shown that, under the mean-square error distortion metric, an optimal encoder-decoder pair from the linear and time-invariant (LTI) class can be found by minimization of a convex functional and a spectral factorization. The functional to be minimized is the sum of the well-known cost in a corresponding Wiener filter problem and a new term, which is induced by the channel noise and whose coefficient is the inverse of the channel's signal-to-noise ratio. This result is shown to also hold in the case of vector-valued signals, assuming parallel additive white Gaussian noise channels. It is also shown that optimal LTI encoders and decoders generally require infinite memory, which implies that approximations are necessary. A numerical example is provided, which compares the performance to the lower bound provided by rate-distortion theory.