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In this thesis, I present bounds on the performance of a variety of network source codes. These rate loss bounds compare the rates achievable by each network code to the rate-distortion bound R(D) 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 M-resolution code with M>=2, the rate loss at the ith resolution with distortion D_i is defined as L_i=R_i-R(D_i), where R_i is the rate achievable by the MRSC at stage i. 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 (L_1=0); (iii) when the rate loss at the second resolution is 0 (L_2=0). 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 M-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 sour

In this paper, we first define and bound the rate loss of source codes for broadcast channels. Our broadcast channel model comprises one transmitter and two receivers; the transmitter is connected to each receiver by a private channel and to both receivers by a common channel. The transmitter sends a description of source (X, Y) through these channels, receiver 1 reconstructs X with distortion D1, and receiver 2 reconstructs Y with distortion D2. Suppose the rates of the common channel and private channels 1 and 2 are R0, R1, and R2, respectively. The work of Gray and Wyner gives a complete characterization of all achievable rate triples (R0,R1,R2) given any distortion pair (D1,D2). In this paper, we define the rate loss as the gap between the achievable region and the outer bound composed by the rate-distortion functions, i.e., R0+R1+R2 ≥ RX,Y (D1,D2), R0 + R1 ≥ RX(D1), and R0 + R2 ≥ RY (D2). We upper bound the rate loss for general sources by functions of distortions and upper bound the rate loss for Gaussian sources by constants, which implies that though the outer bound is generally not achievable, it may be quite close to the achievable region. This also bounds the gap between the achievable region and the inner bound proposed by Gray and Wyner and bounds the performance penalty associated with using separate decoders rather than joint decoders. We then construct such source codes using entropy-constrained dithered quantizers. The resulting implementation has low complexity and performance close to the theoretical optimum. In particular, the gap between its performance and the theoretical optimum can be bounded from above by constants for Gaussian sources.

In this paper, we build multiresolution source codes using entropy constrained dithered scalar quantizers. We demonstrate that for n-dimensional random vectors, dithering followed by uniform scalar quantization and then by entropy coding achieves performance close to the n-dimensional optimum for a multiresolution source code. Based on this result, we propose a practical code design algorithm and compare its performance with that of the set partitioning in hierarchical trees (SPIHT) algorithm on natural images.

The rate loss of a multi-resolution source code (MRSC) describes the difference between the rate needed to achieve distortion D/sub i/ in resolution i and the rate-distortion function R(D/sub i/). We generalize the rate loss definition and bound the rate losses of multiple description source codes (MDSCs) and additive MRSCs (AMRSCs). For a 2-description MDSC (2DSC), the rate loss of description i with distortion D/sub i/ is defined as L/sub i/=R/sub i/-R(D/sub i/), i=1, 2, where R/sub i/ is the rate of the ith description; the rate loss associated with decoding the two descriptions together to achieve central distortion D/sub 0/ is measured as L/sub 0/=R/sub 1/+R/sub 2/-R(D/sub 0/) or as L/sub 12/=L/sub 1/+L/sub 2/. We show that given an arbitrary source with variance /spl sigma//sup 2/, there exists a 2DSC with L/sub 1//spl les/0.5 and (a) L/sub 0//spl les/1 if D/sub 0//spl les/D/sub 1/+D/sub 2/-/spl sigma//sup 2/, (b) L/sub 12//spl les/1 if 1/D/sub 0//spl les/1/D/sub 1/+1/D/sub 2/-1//spl sigma//sup 2/, (c) L/sub 0//spl les/L/sub G0/+1.5 and L/sub 12//spl les/L/sub G12/+1 otherwise, where L/sub G0/ and L/sub G12/ are the joint rate losses of a normal (0, /spl sigma//sup 2/) source. An AMRSC is an MRSC with the kth-resolution reconstruction equal to the sum of the first k side reproductions of an MDSC. We obtain one bound on the rate loss of an AMRSC.

We demonstrate inconsistencies in prior results on the achievable region for multiple description (MD) source codes on i.i.d. Gaussian sources with the squared error distortion measure. We then describe the complete region.

We examine the performance of the KLT for transform coding applications. The KLT has long been viewed as the best available block transform for transform coding. This paper treats fixed-rate and variable-rate transform codes. The fixed-rate approach uses an optimal fixed-rate scalar quantizer followed by an optimal entropy code. Earlier work shows that for the variable-rate case there exist sources on which the KLT is not unique and the optimal transform code matched to a "worst" KLT yields performance as much as 1.5 dB worse than the optimal transform code matched to a "best" KLT. In this paper, we strengthen that result to show that in both the fixed-rate and the variable-rate coding frameworks there exist sources for which the performance penalty for a "worst" KLT can be made arbitrarily large. Further, we demonstrate in both frameworks that there exist sources for which even a best KLT gives suboptimal performance. Finally, we show that even for vector sources where the KLT yields independent coefficients, the KLT can be suboptimal for fixed-rate coding.

Assuming the squared error distortion measure, we bound the performance achieved by using scalar entropy constrained dithered quantization (SECDQ) [1] to build multi-resolution (MR), multiple access (MA), and broadcast system (BS) source codes.

In this paper, we present new bounds for the rate loss of multi-resolution source codes. Consider an M-resolution code with ith-resolution rate and distortion Ri and Di. The ith-resolution rate loss, defined as Li=Ri-R(Di), describes the performance degradation of the multi-resolution code compared to the best single-resolution code with the same distortion. For 2-resolution codes, there are three scenarios of particular interest: (i) both resolutions are equally important; (ii) the rate loss at the first resolution is 0; (iii) the rate loss at the second resolution is 0. Lastras and Berger (see IEEE Trans. Inform. Theory, vol.47, no.3, p.918-26, March 2001) give constant upper bounds for the rate loss of an arbitrary i.i.d. source in scenarios (i) and (ii) and an asymptotic bound for scenario (iii) as D2→0. In this paper, we: (a) prove that L2 ⩽1.1610 for all D2