Design of sample adaptive product quantizers for noisy channels

Channel-optimized vector quantization (COVQ) has proven to be an effective joint source-channel coding technique that makes the underlying quantizer robust to channel noise. Unfortunately, COVQ retains the high encoding complexity of the standard vector quantizer (VQ) for medium-to-high quantization dimensions and moderate-to-good channel conditions. A technique called sample adaptive product quantization (SAPQ) was recently introduced by Kim and Shroff to reduce the complexity of the VQ while achieving comparable distortions. In this letter, we generalize the design of SAPQ for the case of memoryless noisy channels by optimizing the quantizer with respect to both source and channel statistics. Numerical results demonstrate that the channel-optimized SAPQ (COSAPQ) achieves comparable performance to the COVQ (within 0.2 dB), while maintaining considerably lower encoding complexity (up to half of that of COVQ) and storage requirements. Robustness of the COSAPQ system against channel mismatch is also examined.     

On Decoding Binary Perfect and Quasi-Perfect Codes over Markov Noise Channels

We study the decoding problem when a binary linear perfect or quasi-perfect code is transmitted over a binary channel with additive Markov noise. After examining the properties of the channel block transition distribution, we derive sufficient conditions under which strict maximum-likelihood decoding is equivalent to strict minimum Hamming distance decoding when the code is perfect. Additionally, we show a near equivalence relationship between strict maximum likelihood and strict minimum distance decoding for quasi-perfect codes for a range of channel parameters and the code's minimum distance. As a result, an improved (complete) minimum distance decoder is proposed and simulations illustrating its benefits are provided.     

A Model for Correlated Rician Fading Channels Based on a Finite Queue

We study the problem of approximating the family of hard-decision frequency-shift keying demodulated correlated flat Rician fading channels via a recently introduced queue-based channel (QBC) model for binary communication channels with memory. For a given ldquodiscretizedrdquo fading channel, we construct a QBC whose noise process is statistically ldquocloserdquo in the Kullback-Leibler sense to the error or noise process that is generated by the fading channel, and the modeling accuracy is evaluated in terms of noise autocorrelation function (ACF) and channel capacity. Numerical results indicate that the QBC provides a good approximation of the fading channels for a wide range of channel conditions. Furthermore, it estimates the noise ACF more accurately than the finite-state Markov models that have been recently studied by Pimentel , while, at the same time, remaining mathematically tractable.     

Tight error bounds for space-time orthogonal block codes under slow Rayleigh flat fading

The performance of space-time orthogonal block (STOB) codes over slow Rayleigh fading channels and maximum-likelihood (ML) decoding is investigated. Two Bonferroni-type bounds (one upper bound and one lower bound) for the symbol error rate (SER) and bit error rate (BER) of the system are obtained. The bounds are expressed in terms of the pairwise error probabilities (PEPs) and the two-dimensional pairwise error probabilities (2-D PEPs) of the transmitted symbols. Furthermore, the bounds can be efficiently evaluated and they hold for arbitrary (nonstandard) signaling schemes and mappings. Numerical results demonstrate that the bounds are very accurate in estimating the performance of STOB codes. In particular, the upper and lower bounds often coincide even at low channel signal-to-noise ratios, large constellation sizes, and large diversity orders.     

Random-Coding Lower Bounds for the Error Exponent of Joint Quantization and Watermarking Systems

We establish random-coding lower bounds to the error exponent of discrete and Gaussian joint quantization and private watermarking systems. In the discrete system, both the covertext and the attack channel are memoryless and have finite alphabets. In the Gaussian system, the covertext is memoryless Gaussian and the attack channel has additive memoryless Gaussian noise. In both cases, our bounds on the error exponent are positive in the interior of the achievable quantization and watermarking rate region.     

Sequence MAP decoding of trellis codes for Gaussian and Rayleighchannels

This paper considers the use of sequence maximum a posteriori (MAP) decoding of trellis codes. A MAP receiver can exploit any “residual redundancy” that may exist in the channel encoded signal in the form of memory and/or a nonuniform distribution, thereby providing enhanced performance over very noisy channels, relative to maximum likelihood (ML) decoding. The paper begins with a first-order two-state Markov model for the channel encoder input. A variety of different systems with different source parameters, different modulation schemes, and different encoder complexities are simulated. Sequence MAP decoding is shown to substantially improve performance under very noisy channel conditions for systems with low-to-moderate redundancy, with relative gain increasing as the rate increases. As a result, coding schemes with multidimensional constellations are shown to have higher MAP gains than comparable schemes with two-dimensional (2-D) constellations. The second part of the paper considers trellis encoding of the code-excited linear predictive (CELP) speech coder's line spectral parameters (LSPs) with four-dimensional (4-D) QPSK modulation. Two source LSP models are used. One assumes only intraframe correlation of LSPs while the second one models both intraframe and interframe correlation. MAP decoding gains (over ML decoding) as much as 4 dB are achieved. Also, a comparison between the conventionally designed codes and an I-Q QPSK scheme shows that the I-Q scheme achieves better performance even though the first (sampler) LSP model is used     

The Kullback-Leibler divergence rate between Markov sources

In this work, we provide a computable expression for the Kullback-Leibler divergence rate lim/sub n/spl rarr//spl infin//1/nD(p/sup (n)//spl par/q/sup (n)/) between two time-invariant finite-alphabet Markov sources of arbitrary order and arbitrary initial distributions described by the probability distributions p/sup (n)/ and q/sup (n)/, respectively. We illustrate it numerically and examine its rate of convergence. The main tools used to obtain the Kullback-Leibler divergence rate and its rate of convergence are the theory of nonnegative matrices and Perron-Frobenius theory. Similarly, we provide a formula for the Shannon entropy rate lim/sub n/spl rarr//spl infin//1/nH(p/sup (n)/) of Markov sources and examine its rate of convergence.     

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     

Hybrid Digital-Analog Coding with Bandwidth Compression for Gaussian Source-Channel Pairs

Three hybrid digital-analog (HDA) systems, denoted by HDA-I, HDA* and HDA-II, for the coding of a memoryless discrete-time Gaussian source over a discrete-time additive memoryless Gaussian channel under bandwidth compression are studied. The systems employ simple linear coding in their analog component and superimpose their analog and digital signals before channel transmission. Information-theoretic upper bounds on the asymptotically optimal mean squared error distortion of the systems are obtained under both matched and mismatched channel conditions. Allocation schemes for distributing the channel input power between the analog and the digital signals are also examined. It is shown that systems HDA* and HDA-II can asymptotically achieve the optimal Shannon-limit performance under matched channel conditions. Low-complexity and low-delay versions of systems HDA-I and HDA-II are next designed and implemented without the use of error correcting codes. The parameters of these HDA systems, which employ vector quantization in conjunction with binary phase-shift keying modulation in their digital part, are optimized via an iterative algorithm similar to the design algorithm for channel-optimized vector quantizers. Both systems have low complexity and low delay, and guarantee graceful performance improvements for high CSNRs. For memoryless Gaussian sources the designed HDA-II system is shown to be superior to the HDA-I designed system. When applied to a Gauss-Markov source under Karhunen-Loeve processing, the HDA-I system is shown to provide considerably better performance.     

Error analysis for nonuniform signaling over Rayleigh fading channels

We investigate the error performance of a communication system where a nonuniform memoryless binary source is transmitted via Gray-mapped M-ary phase-shift keying or quadrature amplitude modulation over memoryless Rayleigh fading channels, and demodulated via optimal maximum a posteriori detection. Using recently derived upper and lower bounds on the probability of a general union of events, which are tight and can be efficiently computed, the system symbol-error (P/sub s/) and bit-error (P/sub b/) rates are evaluated for a wide range of channel conditions. Since for nonuniform signaling, Gray mapping is not necessarily optimal for minimizing P/sub s/ or P/sub b/ (as was recently shown by Takahara et al.), we also evaluate the system performance under the map obtained by Takahara et al. and compare it with a Gray-mapped system.