On the DPCM compression of Gaussian autoregressive sequences

Abstract

Differential Pulse-Coded Modulation (DPCM) encoding of Gaussian Auto-Regressive sequences is considered. It is pointed out that DPCM is rate-distortion inefficient at low bit rates. Simple filtering modifications are proposed and incorporated into DPCM. A rate-distortion optimization framework that results in optimal filters is presented. It is shown that the designed filters take advantage of "less significant" process spectral components in order to achieve superior rate-distortion performance. Design equations are derived, issues related to optimization and complexity addressed. It is shown that simple DPCM systems with the proposed modifications significantly outperform their standard counterparts.

Multi-frame optimized quantization for high efficiency video coding

“…The latter observation is also as expected, because for a large value of µ, all the u(n) will be equal to zero. The low-pass characteristic of the residual signal for intermediate values of µ is consistent with the ideas presented by Guleryuz and Orchard in [GO01] for rate distortion optimized DPCM encoding of autoregressive sources at low bit rates.…”

“…Using this set-up, the rate distortion performance can be even further improved. Other than the previously discussed method described in [GO01], this inevitably comes along with modifications at the decoder side, because the downsampling has again to be inversed by upsampling and low-pass filtering.…”

“…In [GO01], DPCM encoding of Gaussian autoregressive (AR) sequences at low bit rates is studied. It is shown that using DPCM, the process innovation of the AR sequence plus a feedback quantization error term is encoded.…”

On Constrained Randomized Quantization

“…Although this assumption is satisfied at asymptotically high rates [9], such systems are mostly useful for very low rate applications. For example, in [8], it is stated that the assumptions made in the paper are not satisfied by deterministic quantizers, and that dithered quantizers satisfy the assumptions exactly. However, conventional (uniform) dithered quantization suffers from suboptimal compression performance.…”

“…Many filter/system optimization problems in practical compression settings, such as the "ratedistortion optimal filterbank design" problem [7], or low rate filter optimization for DPCM compression of Gaussian autoregressive processes [8], assume quantization noise that is independent of (or uncorrrelated with) the source. Although this assumption is satisfied at asymptotically high rates [9], such systems are mostly useful for very low rate applications.…”