71,736 research outputs found
On Multiple Decoding Attempts for Reed-Solomon Codes: A Rate-Distortion Approach
One popular approach to soft-decision decoding of Reed-Solomon (RS) codes is
based on using multiple trials of a simple RS decoding algorithm in combination
with erasing or flipping a set of symbols or bits in each trial. This paper
presents a framework based on rate-distortion (RD) theory to analyze these
multiple-decoding algorithms. By defining an appropriate distortion measure
between an error pattern and an erasure pattern, the successful decoding
condition, for a single errors-and-erasures decoding trial, becomes equivalent
to distortion being less than a fixed threshold. Finding the best set of
erasure patterns also turns into a covering problem which can be solved
asymptotically by rate-distortion theory. Thus, the proposed approach can be
used to understand the asymptotic performance-versus-complexity trade-off of
multiple errors-and-erasures decoding of RS codes.
This initial result is also extended a few directions. The rate-distortion
exponent (RDE) is computed to give more precise results for moderate
blocklengths. Multiple trials of algebraic soft-decision (ASD) decoding are
analyzed using this framework. Analytical and numerical computations of the RD
and RDE functions are also presented. Finally, simulation results show that
sets of erasure patterns designed using the proposed methods outperform other
algorithms with the same number of decoding trials.Comment: to appear in the IEEE Transactions on Information Theory (Special
Issue on Facets of Coding Theory: from Algorithms to Networks
Computing the Rate-Distortion Function of Gray-Wyner System
In this paper, the rate-distortion theory of Gray-Wyner lossy source coding
system is investigated. An iterative algorithm is proposed to compute
rate-distortion function for general successive source. For the case of jointly
Gaussian distributed sources, the Lagrangian analysis of scalable source coding
in [1] is generalized to the Gray-Wyner instance. Upon the existing
single-letter characterization of the rate-distortion region, we compute and
determine an analytical expression of the rate-distortion function under
quadratic distortion constraints. According to the rate-distortion function,
another approach, different from Viswanatha et al. used, is provided to compute
Wyner's Common Information. The convergence of proposed iterative algorithm, RD
function with different parameters and the projection plane of RD region are
also shown via numerical simulations at last.Comment: This work has been submitted to the IEEE for possible publication.
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Optimal parameter estimation for model-based quantization
We address optimal model estimation for model-based vector quan-tization for both the constrained resolution (CR) and constrained en-tropy (CE) cases. To this purpose we derive under high-rate (HR) theory assumptions the rate-distortion (RD) relations for these two quantization scenarios assuming a Gaussian model. Based on the RD relations we show that the maximum likelihood (ML) criterion leads to optimal performance for CE quantization, but not for CR quantization. We introduce a new model estimation criterion for CR quantization that is optimal (under HR theory assumptions) in terms of the RD relation. Our experiments confirm that the proposed cri-terion for model identification outperforms the ML criterion for a range of conditions. Index Terms — Constrained resolution, model-based quantiza-tion, model estimation, rate-distortion relation, high-rate theory
Geometric distortion measurement for shape coding: a contemporary review
Geometric distortion measurement and the associated metrics involved are integral to the rate-distortion (RD) shape coding framework, with importantly the efficacy of the metrics being strongly influenced by the underlying measurement strategy. This has been the catalyst for many different techniques with this paper presenting a comprehensive review of geometric distortion measurement, the diverse metrics applied and their impact on shape coding. The respective performance of these measuring strategies is analysed from both a RD and complexity perspective, with a recent distortion measurement technique based on arc-length-parameterisation being comparatively evaluated. Some contemporary research challenges are also investigated, including schemes to effectively quantify shape deformation
Rate control for HEVC intra-coding based on piecewise linear approximations
This paper proposes a rate control (RC) algorithm for intra-coded sequences (I-frames) within the context of block-based predictive transform coding (PTC) that employs piecewise linear approximations of the rate-distortion (RD) curve of each frame. Specifically, it employs information about the rate (R) and distortion (D) of already compressed blocks within the current frame to linearly approximate the slope of the corresponding RD curve. The proposed algorithm is implemented in the High-Efficiency Video Coding (HEVC) standard and compared with the current HEVC RC algorithm, which is based on a trained rate lambda (R-λ) model. Evaluations on a variety of intra-coded sequences show that the proposed RC algorithm not only attains the overall target bit rate more accurately than the current RC algorithm but is also capable of encoding each I-frame at a more constant bit rate according to the overall bit budget, thus avoiding high bit rate fluctuations across the sequence
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