Nam Phamdo

Robust and efficient quantization of speech LSP parameters using structured vector quantizers

Three robust algorithms based on the recently proposed concept of structured vector quantization have been developed for quantization of speech LSP (line spectrum pair) parameters. The first algorithm exploits interframe correlation of the LSP parameters and requires 24 bits per LSP vector to achieve 1 dB average spectral distortion. The second and third algorithms quantize each LSP vector independently and for 1 dB distortion require 29 and 25 bits per vector, respectively. The last two algorithms result in a considerably smaller fraction of frames with distortions greater than 2 dB as compared to other schemes proposed so far.<<ETX>>

Zigzag codes and concatenated zigzag codes

This paper introduces a family of error-correcting codes called zigzag codes. A zigzag code is described by a highly structured zigzag graph. Due to the structural properties of the graph, very low-complexity soft-in/soft-out decoding rules can be implemented. We present a decoding rule, based on the Max-Log-APP (MLA) formulation, which requires a total of only 20 addition-equivalent operations per information bit, per iteration. Simulation of a rate-1/2 concatenated zigzag code with four constituent encoders with interleaver length 65 536, yields a bit error rate (BER) of 10/sup -5/ at 0.9 dB and 1.3 dB away from the Shannon limit by optimal (APP) and low-cost suboptimal (MLA) decoders, respectively. A union bound analysis of the bit error probability of the zigzag code is presented. It is shown that the union bounds for these codes can be generated very efficiently. It is also illustrated that, for a fixed interleaver size, the concatenated code has increased code potential as the number of constituent encoders increases. Finally, the analysis shows that zigzag codes with four or more constituent encoders have lower error floors than comparable turbo codes with two constituent encoders.

Hybrid Digital&#8211;Analog Source&#8211;Channel Coding for Bandwidth Compression/Expansion

An approach to hybrid digital-analog (HDA) source-channel coding for the communication of analog sources over memoryless Gaussian channels is introduced. The HDA system, which exploits the advantages of both digital and analog systems, generalizes a scheme previously presented by the authors, and can operate for any bandwidth ratio (bandwidth compression and expansion). It is based on vector quantization and features turbo coding in its digital component and linear/nonlinear processing in its analog part. Simulations illustrate that, under both bandwidth compression and expansion modes of operation, the HDA system provides a robust and graceful performance with good reproduction fidelity for a wide range of channel conditions

A unified approach to tree-structured and multistage vector quantization for noisy channels

The large encoding complexity and sensitivity to channel errors of vector quantization (VQ) are discussed. The performance of two low-complexity VQs-the tree-structured VQ (TSVQ) and the multistage VQ (MSVQ)-when used over noisy channels are analyzed. An algorithm is developed for the design of channel-matched TSVQ (CM-TSVQ) and channel-matched MSVQ (CM-MSVQ) under the squared-error criterion. Extensive numerical results are given for the correlation coefficient 0.9. Comparisons with the ordinary TSVQ and MSVQ designed for the noiseless channel show substantial improvements when the channel is very noisy. The CM-MSVQ, which can be regarded as a block-structured combined source-channel coding scheme, is compared with a block-structured tandem source-channel coding scheme (with the same block length as the CM-MSVQ). For the Gauss-Markov source, the CM-MSVQ outperforms the tandem scheme in all cases that the authors have considered. It is demonstrated that the CM-MSVQ is fairly robust to channel mismatch. >

Quantization of memoryless and Gauss-Markov sources over binary Markov channels

Joint source-channel coding for stationary memoryless and Gauss-Markov sources and binary Markov channels is considered. The channel is an additive-noise channel where the noise process is an Mth-order Markov chain. Two joint source-channel coding schemes are considered. The first is a channel-optimized vector quantizer-optimized for both source and channel. The second scheme consists of a scalar quantizer and a maximum a posteriori detector. In this scheme, it is assumed that the scalar quantizer output has residual redundancy that can be exploited by the maximum a posteriori detector to combat the correlated channel noise. These two schemes are then compared against two schemes which use channel interleaving. Numerical results show that the proposed schemes outperform the interleaving schemes. For very noisy channels with high noise correlation, gains of 4-5 dB in signal-to-noise ratio are possible.

Soft-decision demodulation design for COVQ over white, colored, and ISI Gaussian channels

In this work, the design of a q-bit (scalar and vector) soft-decision demodulator for Gaussian channels with binary phase-shift keying modulation is investigated. The demodulator is used in conjunction with a soft-decision channel-optimized vector quantization (COVQ) system. The COVQ is constructed for an expanded (q>1) discrete channel consisting of the concatenation of the modulator, the Gaussian channel, and the demodulator. It is found that as the demodulator resolution q increases, the capacity of the expanded channel increases, resulting in an improvement of the COVQ performance. Consequently, the soft-decision demodulator is designed to maximize the capacity of the expanded channel. Three Gaussian channel models are considered as follows: (1) additive white Gaussian noise channels; (2) additive colored Gaussian noise channels; and (3) Gaussian channels with intersymbol interference. Comparisons are made with (a) hard-decision COVQ systems, (b) COVQ systems which utilize interleaving, and (c) an unquantized (q=/spl infin/) soft-decision decoder proposed by Skoglund and Hedelin (1999). It is shown that substantial improvements can be achieved over COVQ systems which utilize hard decision demodulation and/or channel interleaving. The performance of the proposed COVQ system is comparable with the system by Skoglund and Hedelin-though its computational complexity is substantially less.

Soft-decision COVQ for Rayleigh-fading channels

A channel-optimized vector quantizer (COVQ) scheme that exploits the channel soft-decision information is proposed. The scheme is designed for stationary memoryless Gaussian and Gauss-Markov sources transmitted over BPSK-modulated Rayleigh-fading channels. It is demonstrated that substantial coding gains of 2-3 dB in channel signal-to-noise ratio (SNR) and 1-1.5 dB in source signal-to-distortion ratio (SDR) can be achieved over COVQ systems designed for discrete (hard-decision demodulated) channels.

Turbo decoders which adapt to noise distribution mismatch

This article investigates the sensitivity of turbo decoder performance to mismatch of the noise distribution, and proposes a simple on-line procedure for estimating the unknown noise distribution from each block of received signal. This procedure consists of: (1) quantization of the received signal and (2) estimation of the noise distribution from the histogram of the quantized received signal. For Gaussian and Laplacian noise, the proposed procedure leads to decoder performances which are comparable (within 0.1 dB at bit-error rate of 10/sup -4/) to the case where the noise distribution is known exactly.

BER bounds on parallel concatenated single parity check arrays and zigzag codes

A union bound analysis of the bit error probability of parallel concatenated single parity check (SPC) array and zigzag code is presented. It is shown that the union bounds for these codes can be generated very efficiently. It is also shown that the simple codes studied can achieve comparable performances as the turbo codes (yet has much lower decoding costs as discussed in an earlier paper). It illustrates that, for a fixed interleaver size, the concatenated code has increased code potential as its dimension, i.e., the number of interleavers, increases (which raises decoding costs linearly, not exponentially as for increased constraint length). Finally, the analysis shows that the zigzag codes with dimension greater than three have lower error floors than comparable two-dimensional turbo codes.

Analysis and design of trellis codes optimized for a binary symmetric Markov source with MAP detection

We consider the problem of transmitting a binary symmetric Markov source (BSMS), over the additive white Gaussian noise (AWGN) channel. The coding technique considered is trellis-coded modulation (TCM), where we utilize decoders which implement the maximum-likelihood (ML) and maximum a posteriori (MAP) criteria. Employing 8-PSK Ungerboeck codes on a BSMS with state transition probability 0.1, we first show that the MAP decoder realizes a 0.8-2.1-dB coding gain over the ML decoder. Motivated by these gains, we consider the design of trellis codes optimized for the BSMS/AWGN/MAP system. An approximate union bound is established for this system. Using this bound, we found codes which exhibit additional 0.4-1.1-dB gains over Ungerboeck codes. Finally, we compare the proposed TCM system with a tandem coding system. At normalized signal-to-noise ratio (SNR) of 10.8 dB and below, the proposed system significantly outperforms the tandem system.