2019/05/29 by Charalambos D. Charalambous, Charalambous, Charalambos D., Jan H. van Schuppen +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · #94-A15 #94-A34 #Cooperative Communication and Network Coding #DNA and Biological Computing #Distributed Sensor Networks and Detection Algorithms #FOS: Computer and information sciences #Information Theory (cs.IT) #Wireless Communication Security Techniques
paper · pdf · doi:10.48550/arxiv.1905.12695
openalex publication_date 2019/05/29 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28
The classical Gray and Wyner source coding for a simple network for sources\nthat generate a tuple of multivariate, correlated Gaussian random variables\n(Y1,Y2) is re-examined using the geometric approach of Gaussian random\nvariables, and the weak stochastic realization of correlated Gaussian random\nvariables. New results are: (1) The formulation, methods and algorithms to\nparametrize all random variables W : \Ω \→ mathbb Rn which\nmake the two components of the tuple (Y1,Y2) conditionally independent,\naccording to the weak stochastic realization of (Y1, Y2). (2) The\ntransformation of random variables (Y1,Y2) via non-singular transformations\n(S1,S2), into their canonical variable form. (3) A formula for Wyner's\nlossy common information for joint decoding with mean-square error distortions.\n(4) The methods are shown to be of fundamental importance to the\nparametrization of the lossy rate region of the Gray and Wyner source coding\nproblem, and the calculation of the smallest common message rate R0 on the\nGray and Wyner source problem, when the sum rate R0+R1+R2 is arbitrary\nclose to the joint rate distortion function RY1, Y2(\Δ1, \Δ2)\nof joint decoding. The methods and algorithms may be applicable to other\nproblems of multi-user communication, such as, the multiple access channel,\netc. The discussion is largely self-contained and proceeds from first\nprinciples; basic concepts of weak stochastic realization theory of\nmultivariate correlated Gaussian random variables are reviewed, while certain\nresults are developed to meet the requirement of results (1)-(4).\n