Random Index Assignment Research Articles

On the Design of Optimal Noisy Channel Scalar Quantizer with Random Index Assignment

The general approach in a noisy channel scalar quantizer design is an iterative descent algorithm, which guarantees only a locally optimal solution. While sufficient conditions under which the local optimum becomes a global optimum are known in the noiseless channel case, such sufficient conditions were not derived for the noisy counterpart. Moreover, efficient globally optimal design techniques for general discrete distributions in the noiseless case exist; however, they seem not to extend to the noisy scenario when a fixed index assignment is assumed. Recently, the design of noisy channel scalar quantizer with random index assignment (RIA) was proposed using a locally optimal iterative algorithm. In this paper, we derive sufficient conditions for the uniqueness of a local optimum, which, thus, guarantee the global optimality of the solution. These sufficient conditions are satisfied for a log-concave probability density function which is, additionally, symmetric around its mean. Furthermore, we show that, assuming an RIA, the globally optimal design for general discrete sources can also be carried out efficiently.

Designing Optimal Multiresolution Quantizers with Error Detecting Codes

This paper investigates the design of optimal multiresolution vector quantizers for broadcast channels with cyclic redundancy checks (CRC). Given a CRC-coded broadcast system with multiresolution vector quantization (MRVQ), a closed-form formula for the weighted end-to-end distortion (EED) is first derived under random index assignment. The closed-form expression is then further utilized to identify necessary optimality conditions to minimize the EED, from which an iterative algorithm is proposed for quantization design. Experiments conducted under both the point-to-point and broadcast channels demonstrate that for a wide range of channel error probability, inclusion of CRC significantly reduces the EED without sacrificing bandwidth. Further analyses are conducted to determine the best tradeoff between bits allocated for source quantization and CRC error detection.

High-Rate Vector Quantization for Noisy Channels With Applications to Wideband Speech Spectrum Compression

This paper considers the high-rate performance of source coding for noisy discrete symmetric channels with random index assignment (IA). Accurate analytical models are developed to characterize the expected distortion performance of vector quantization (VQ) for a large class of distortion measures. It is shown that when the point density is continuous, the distortion can be approximated as the sum of the source quantization distortion and the channel-error induced distortion. Expressions are also derived for the continuous point density that minimizes the expected distortion. Next, for the case of mean squared error distortion, a more accurate analytical model for the distortion is derived by allowing the point density to have a singular component. The extent of the singularity is also characterized. These results provide analytical models for the expected distortion performance of both conventional VQ as well as for channel-optimized VQ. As a practical example, compression of the linear predictive coding parameters in the wideband speech spectrum is considered, with the log spectral distortion as performance metric. The theory is able to correctly predict the channel error rate that is permissible for operation at a particular level of distortion.

Design and Analysis of Optimal Noisy Channel Quantization With Random Index Assignment

This paper studies the design of vector quantization on noisy channels and its high rate asymptotic performance. Given a tandem source-channel coding system with vector quantization, block channel coding, and random index assignment, a closed-form formula is first derived for computing the average end-to-end distortion (EED) of the system, which reveals a structural factor called the scatter factor of a noisy channel quantizer. Based on this formula, we propose a noisy-channel quantization design method by minimizing the EED. Experiments and simulations show that quantizers jointly designed with channel conditions significantly reduce the EED when compared with quantizers designed separately without reference to channel conditions, which reveals a practical and effective design for noisy-channel quantization as to simplify the channel model by considering a random index assignment. Furthermore, we have presented the high rate asymptotic analysis of the EED for the tandem system, while convergence analysis of the iterative algorithm is included in the Appendix.

Performance of Quantized Equal Gain Transmission With Noisy Feedback Channels

In this paper, new results and insights are derived for the performance of multiple-input, single-output systems with beamforming at the transmitter, when the channel state information is quantized and sent to the transmitter over a noisy feedback channel. It is assumed that there exists a per-antenna power constraint at the transmitter, hence, the equal gain transmission (EGT) beamforming vector is quantized and sent from the receiver to the transmitter. The loss in received signal-to-noise ratio (SNR) relative to perfect beamforming is analytically characterized, and it is shown that at high rates, the overall distortion can be expressed as the sum of the quantization-induced distortion and the channel error-induced distortion, and that the asymptotic performance depends on the error-rate behavior of the noisy feedback channel as the number of codepoints gets large. The optimum density of codepoints (also known as the point density) that minimizes the overall distortion subject to a boundedness constraint is shown to be the same as the point density for a noiseless feedback channel, i.e., the uniform density. The binary symmetric channel with random index assignment is a special case of the analysis, and it is shown that as the number of quantized bits gets large the distortion approaches the same as that obtained with random beamforming. The accuracy of the theoretical expressions obtained are verified through Monte Carlo simulations.