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     

Detection of binary Markov sources over channels with additiveMarkov noise

We consider maximum a posteriori (MAP) detection of a binary asymmetric Markov source transmitted over a binary Markov channel. The MAP detector observes a long (but finite) sequence of channel outputs and determines the most probable source sequence. In some cases, the MAP detector can be implemented by simple rules such as the “believe what you see” rule or the “guess zero (or one) regardless of what you see” rule. We provide necessary and sufficient conditions under which this is true. When these conditions are satisfied, the exact bit error probability of the sequence MAP detector can be determined. We examine in detail two special cases of the above source: (i) binary independent and identically distributed (i.i.d.) source and (ii) binary symmetric Markov source. In case (i), our simulations show that the performance of the MAP detector improves as the channel noise becomes more correlated. Furthermore, a comparison of the proposed system with a (substantially more complex) traditional tandem source-channel coding scheme portrays superior performance for the proposed scheme at relatively high channel bit error rates. In case (ii), analytical as well as simulation results show the existence of a “mismatch” between the source and the channel (the performance degrades as the channel noise becomes more correlated). This mismatch is reduced by the use of a simple rate-one convolutional encoder     

Hybrid digital-analog (HDA) joint source-channel codes forbroadcasting and robust communications

We consider the problem of transmitting a band-limited Gaussian source on an additive band-limited Gaussian noise channel. The well-known "threshold effect" dictates that the more powerful a code is, the more sensitive it is to the exact knowledge of the channel noise. A code is said to be robust if it is asymptotically optimal for a wide range of channel noise. Thus, robust codes have a "graceful degradation" characteristic and are free of the threshold effect. It is demonstrated that robust codes exist whenever the source and channel bandwidths are equal. In the unequal-bandwidth case, a collection of nearly robust joint source-channel codes is constructed using a hybrid digital-analog (HDA) coding technique. For designing nearly robust codes, a matched tandem code whose channel encoder's output is partially/fully matched to its input is proposed and the existence of an asymptotically optimal matched tandem code is shown. The nearly robust codes achieve the Shannon limit (theoretically optimum distortion) and have a less severe threshold effect. Finally, for the case of two different noise conditions, the distortion regions of these codes are determined     

Soft-decision demodulation design for COVQ over white, colored, andISI 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=∞) 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     

Design and performance of VQ-based hybrid digital-analog jointsource-channel codes

A joint source-channel hybrid digital-analog (HDA) vector quantization (VQ) system is presented. The main advantage of the new VQ-based HDA system is that it achieves excellent rate-distortion-capacity performance at the design signal-to-noise ratio (SNR) while maintaining a "graceful improvement" characteristic at higher SNRs. It is demonstrated that, within the HDA framework, the parameters of the system can be optimized using an iterative procedure similar to that of channel-optimized vector quantizer design. Comparisons are made with three purely digital systems and one purely analog system. It is found that, at high SNRs, the VQ-based HDA system is superior to the other investigated systems. At low SNRs, the performance of the new scheme can be improved using the optimization procedure and using soft decoding in the digital part of the system. These results demonstrate that the introduced scheme provides an attractive method for terrestrial broadcasting applications     

Optimal detection of discrete Markov sources over discretememoryless channels-applications to combined source-channel coding

The authors consider the problem of detecting a discrete Markov source which is transmitted across a discrete memoryless channel. Two maximum a posteriori (MAP) formulations are considered: (i) a sequence MAP detection in which the objective is to determine the most probable transmitted sequence given the observed sequence and (ii) an instantaneous MAP detection which is to determine the most probable transmitted symbol at time n given all the observations prior to and including time n. The solution to the first problem results in a “Viterbi-like” implementation of the MAP detector (with Large delay) while the latter problem results in a recursive implementation (with no delay). For the special case of the binary symmetric Markov source and binary symmetric channel, simulation results are presented and an analysis of these two systems yields explicit critical channel bit error rates above which the MAP detectors become useful. Applications of the MAP detection problem in a combined source-channel coding system are considered. Here, it is assumed that the source is highly correlated and that the source encoder (a vector quantizer (VQ)) fails to remove all of the source redundancy. The remaining redundancy at the output of the source encoder is referred to as the “residual” redundancy. It is shown, through simulation, that the residual redundancy can be used by the MAP detectors to combat channel errors. For small block sizes, the proposed system beats Farvardin and Vaishampayan's channel-optimized VQ by wide margins. Finally, it is shown that the instantaneous MAP detector can be combined with the VQ decoder to form an approximate minimum mean-squared error decoder     

Analysis and design of trellis codes optimized for a binarysymmetric 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     

Quantization of memoryless and Gauss-Markov sources over binaryMarkov 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     

Source-channel optimized trellis codes for bitonal imagetransmission over AWGN channels

We consider the design of trellis codes for transmission of binary images over additive white Gaussian noise (AWGN) channels. We first model the image as a binary asymmetric Markov source (BAMS) and then design source-channel optimized (SCO) trellis codes for the BAMS and AWGN channel. The SCO codes are shown to be superior to Ungerboeck's codes by approximately 1.1 dB (64-state code, 10^-5 bit error probability), We also show that a simple “mapping conversion” method can be used to improve the performance of Ungerboeck's codes by approximately 0.4 dB (also 64-state code and 10 ^-5 bit error probability). We compare the proposed SCO system with a traditional tandem system consisting of a Huffman code, a convolutional code, an interleaver, and an Ungerboeck trellis code. The SCO system significantly outperforms the tandem system. Finally, using a facsimile image, we compare the image quality of an SCO code, an Ungerboeck code, and the tandem code, The SCO code yields the best reconstructed image quality at 4-5 dB channel SNR     

A unified approach to tree-structured and multistage vectorquantization 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