Rate loss of network source codes

• Main Author: Feng, Hanying
• Format: Others
• Published: 2002
• Online Access: https://thesis.library.caltech.edu/1965/1/thesis.pdf; Feng, Hanying (2002) Rate loss of network source codes. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/GVDP-7248. https://resolver.caltech.edu/CaltechETD:etd-05232002-173821 <https://resolver.caltech.edu/CaltechETD:etd-05232002-173821>

In this thesis, I present bounds on the performance of a variety of network source codes. These <em>rate loss</em> bounds compare the rates achievable by each network code to the rate-distortion bound <em>R(D)</em> at the corresponding distortions. The result is a collection of optimal performance bounds that are easy to calculate. I first present new bounds for the rate loss of multi-resolution source codes (MRSCs). Considering an <em>M</em>-resolution code with <em>M</em>>=2, the rate loss at the <em>i</em>th resolution with distortion <em>D_i</em> is defined as <em>L_i=R_i-R(D_i)</em>, where <em>R_i</em> is the rate achievable by the MRSC at stage <em>i</em>. For 2-resolution codes, there are three scenarios of particular interest: (i) when both resolutions are equally important; (ii) when the rate loss at the first resolution is 0 (<em>L_1=0</em>); (iii) when the rate loss at the second resolution is 0 (<em>L_2=0</em>). The work of Lastras and Berger gives constant upper bounds for the rate loss in scenarios (i) and (ii) and an asymptotic bound for scenario (iii). In this thesis, I show a constant bound for scenario (iii), tighten the bounds for scenario (i) and (ii), and generalize the bound for scenario (ii) to <em>M</em>-resolution greedy codes. I also present upper bounds for the rate losses of additive MRSCs (AMRSCs), a special MRSC. I obtain two bounds on the rate loss of AMRSCs: one primarily good for low rate coding and another which depends on the source entropy. I then generalize the rate loss definition and present upper bounds for the rate losses of multiple description source codes. I divide the distortion region into three sub-regions and bound the rate losses by small constants in two sub-regions and by the joint rate losses of a normal source with the same variance in the other sub-region. Finally, I present bounds for the rate loss of multiple access source codes (MASCs). I show that lossy MASCs can be almost as good as codes based on joint source encoding.