Iterative joint design of source codes and multiresolution channel codes

We propose an iterative design algorithm for jointly optimizing source and channel codes. The joint design combines channel-optimized vector quantization (COVQ) for the source code with rate-compatible punctured convolutional (RCPC) coding for the channel code. Our objective is to minimize the average end-to-end distortion. For a given channel SNR and transmission rate, our joint source and channel code design achieves an optimal allocation of bits between the source and channel coders. This optimal allocation can reduce distortion by up to 6 dB over suboptimal allocations for the source data set considered. We also compare the distortion of our joint iterative design with that of two suboptimal design techniques: COVQ optimized for a given channel bit-error-probability, and RCPC channel coding optimized for a given vector quantizer. We conclude by relaxing the fixed transmission rate constraint and jointly optimizing the transmission rate, source code, and channel code

Multiresolution vector quantization

Multiresolution source codes are data compression algorithms yielding embedded source descriptions. The decoder of a multiresolution code can build a source reproduction by decoding the embedded bit stream in part or in whole. All decoding procedures start at the beginning of the binary source description and decode some fraction of that string. Decoding a small portion of the binary string gives a low-resolution reproduction; decoding more yields a higher resolution reproduction; and so on. Multiresolution vector quantizers are block multiresolution source codes. This paper introduces algorithms for designing fixed- and variable-rate multiresolution vector quantizers. Experiments on synthetic data demonstrate performance close to the theoretical performance limit. Experiments on natural images demonstrate performance improvements of up to 8 dB over tree-structured vector quantizers. Some of the lessons learned through multiresolution vector quantizer design lend insight into the design of more sophisticated multiresolution codes

Network vector quantization

We present an algorithm for designing locally optimal vector quantizers for general networks. We discuss the algorithm's implementation and compare the performance of the resulting "network vector quantizers" to traditional vector quantizers (VQs) and to rate-distortion (R-D) bounds where available. While some special cases of network codes (e.g., multiresolution (MR) and multiple description (MD) codes) have been studied in the literature, we here present a unifying approach that both includes these existing solutions as special cases and provides solutions to previously unsolved examples

Joint design of vector quantizers and RCPC channel codes for Rayleigh fading channels

We study the performance of joint source and channel codes designed to minimize end-to-end distortion over a Rayleigh fading channel. We consider two joint code designs. The first joint code uses a sequential design: a standard vector quantizer (VQ) source code is designed for a perfect channel (noiseless and distortionless) and then an RCPC channel code is optimized relative to the VQ and the channel statistics. The second design jointly optimizes a channel optimized VQ (COVQ) and an RCPC channel code through an iterative design process. We consider both hard-decision and soft-decision decoding for the channel codes. In both designs the bit allocation between the source and channel codes is optimized. At this optimal bit allocation, the performance of the iterative joint design and the simpler sequential design are nearly the same over the range of SNR values that we considered. Both code designs outperform standard COVQ and by up to 6 dB, and this performance improvement is most pronounced at low SNRs

Optimal Multiresolution Quantization for Broadcast Channels with Random Index Assignment

Shannon's classical separation result holds only in the limit of infinite source code dimension and infinite channel code block length. In addition, Shannon theory does not address the design of good source codes when the probability of channel error is nonzero, which is inevitable for finite-length channel codes. Thus, for practical systems, a joint source and channel code design could improve performance for finite dimension source code and finite block length channel code, as well as complexity and delay. Consider a multicast system over a broadcast channel, where different end users typically have different capacities. To support such user or capacity diversity, it is desirable to encode the source to be broadcasted into a scalable bit stream along which multiple resolutions of the source can be reconstructed progressively from left to right. Such source coding technique is called multiresolution source coding. In wireless communications, joint source channel coding (JSCC) has attracted wide attention due to its adaptivity to time-varying channels. However, there are few works on joint source channel coding for network multicast, especially for the optimal source coding over broadcast channels. In this work, we aim at designing and analyzing the optimal multiresolution vector quantization (MRVQ) in conjunction with the subsequent broadcast channel over which the coded scalable bit stream would be transmitted. By adopting random index assignment (RIA) to link MRVQ for the source with superposition coding for the broadcast channel, we establish a closed-form formula of end-to-end distortion for a tandem system of MRVQ and a broadcast channel. From this formula we analyze the intrinsic structure of end-to-end distortion (EED) in a communication system and derive two necessary conditions for optimal multiresolution vector quantization over broadcast channels with random index assignment. According to the two necessary conditions, we propose a greedy iterative algorithm for jointly designed MRVQ with channel conditions, which depends on the channel only through several types of average channel error probabilities rather than the complete knowledge of the channel. Experiments show that MRVQ designed by the proposed algorithm significantly outperforms conventional MRVQ designed without channel information. By building an closed-form formula for the weighted EED with RIA, it also makes the computational complexity incurred during the performance analysis feasible. In comparison with MRVQ design for a fixed index assignment, the computation complexity for quantization design is significantly reduced by using random index assignment. In addition, simulations indicate that our proposed algorithm shows better robustness against channel mismatch than MRVQ design with a fixed index assignment, simply due to the nature of using only the average channel information. Therefore, we conclude that our proposed algorithm is more appropriate in both wireless communications and applications where the complete knowledge of the channel is hard to obtain. Furthermore, we propose two novel algorithms for MRVQ over broadcast channels. One aims to optimize the two corresponding quantizers at two layers alternatively and iteratively, and the other applies under the constraint that each encoding cell is convex and contains the reconstruction point. Finally, we analyze the asymptotic performance of weighted EED for the optimal joint MRVQ. The asymptotic result provides a theoretically achievable quantizer performance level and sheds light on the design of the optimal MRVQ over broadcast channel from a different aspect

Extended object reconstruction in adaptive-optics imaging: the multiresolution approach

We propose the application of multiresolution transforms, such as wavelets (WT) and curvelets (CT), to the reconstruction of images of extended objects that have been acquired with adaptive optics (AO) systems. Such multichannel approaches normally make use of probabilistic tools in order to distinguish significant structures from noise and reconstruction residuals. Furthermore, we aim to check the historical assumption that image-reconstruction algorithms using static PSFs are not suitable for AO imaging. We convolve an image of Saturn taken with the Hubble Space Telescope (HST) with AO PSFs from the 5-m Hale telescope at the Palomar Observatory and add both shot and readout noise. Subsequently, we apply different approaches to the blurred and noisy data in order to recover the original object. The approaches include multi-frame blind deconvolution (with the algorithm IDAC), myopic deconvolution with regularization (with MISTRAL) and wavelets- or curvelets-based static PSF deconvolution (AWMLE and ACMLE algorithms). We used the mean squared error (MSE) and the structural similarity index (SSIM) to compare the results. We discuss the strengths and weaknesses of the two metrics. We found that CT produces better results than WT, as measured in terms of MSE and SSIM. Multichannel deconvolution with a static PSF produces results which are generally better than the results obtained with the myopic/blind approaches (for the images we tested) thus showing that the ability of a method to suppress the noise and to track the underlying iterative process is just as critical as the capability of the myopic/blind approaches to update the PSF.Comment: In revision in Astronomy & Astrophysics. 19 pages, 13 figure