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

This correspondence concerns the performance analysis of turbo-single-parity-check (SPC) codes based on the union bound of bit-error rate (BER). A treatment of the special interleavers used in turbo-SPC codes is discussed. It is shown that simple two- or four-state turbo-SPC codes with multiple component codes can perform comparably as (or even better than) the 16-state standard turbo codes. Using more complex trellis codes (with state number more than 4) appears unnecessary for such codes. Instead, performance improvement can be achieved by increasing the number of component codes, which maintains the low decoding complexity property of turbo-SPC codes.

A joint source-channel coding system for transmitting speech on a bandlimited additive white Gaussian noise (AWGN) channel is presented. The proposed method uses a hybrid of digital and analog modulation techniques. The digital part of the system consists of a Federal Standard 1016 code-excited linear predictive (FS 1016 CELP) speech coder followed by a rate-3/5 parallel concatenated (turbo) error correcting code. The analog part, which transmits the quantization error due to the FS 1016 CELP coder, consists of a linear encoder and decoder. The advantage of the proposed system is that it achieves excellent rate-distortion/capacity performance that is common in digital systems while maintaining a "graceful degradation" characteristic that is common in analog systems. Comparisons are made with three purely digital systems and an analog system-with all systems operating at the same overall rate. A formal listening test shows that, at high channel SNR, the improved performance of the proposed hybrid system (versus the purely digital systems) is noticeable to the average listener. Finally, an informal listening test indicates that at low channel SNR (where the error correcting code breaks down) the decoded speech of the hybrid system is still intelligible.

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.

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.

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.

A signal/noise KLT based approach for enhancing speech degraded by colored noise is proposed. The noisy speech frames are classified into speech-dominated frames and noise-dominated frames. In the speech-dominated frames, the signal KLT matrix is used and in the noise-dominated frames, the noise KLT matrix is used. The approach does not require noise whitening and hence works well even with narrowband noise. A two-dimensional objective measure which captures both the speech distortion and the noise shaping characteristics of the algorithm is proposed. This measure indicates that the proposed method performs better noise shaping than a modified version of the signal subspace approach proposed by Ephraim and Van Trees and the standard spectral subtraction method. Informal listening tests show that the proposed algorithm does not suffer from the problem of residual musical noise and performs better noise masking than the signal subspace approach.

A joint source-channel coding system for transmitting speech on a bandlimited additive white Gaussian noise (AWGN) channel is presented. The proposed method uses a hybrid of digital and analog modulation techniques. The digital part of the system consists of an FS-1016 CELP speech coder followed by a rate-3/5 parallel concatenated (turbo) error correcting code. The analog part, which transmits the quantization error due to the FS-1016 CELP coder consists of a linear encoder and decoder. The advantage of the proposed system is that it achieves excellent rate-distortion/capacity performance that is common in digital systems while maintaining a "graceful degradation" characteristic that is common in analog systems. Comparisons are made with three purely digital systems and two purely analog systems. A formal listening test shows that, at high channel SNR, the improved performance of the proposed hybrid system versus the purely digital systems is noticeable to the average listener.

A signal/noise Karhunen-Loeve transform (KLT) based approach for enhancing speech degraded by colored noise is proposed. The noisy speech frames are classified into speech-dominated frames and noise-dominated frames. In the speech-dominated frames, the signal KLT matrix is used and in the noise dominated frames, the noise KLT matrix is used. The approach does not require noise whitening and hence works well even with narrowband noise. A two-dimensional objective measure which captures both the speech distortion and the noise shaping characteristics of the algorithm is proposed. This measure indicates that the proposed method performs better noise shaping than a modified form of the signal subspace approach proposed by Ephraim and Van Trees (1995) and the standard spectral subtraction method. Informal listening tests show that the proposed algorithm does not suffer from the problem of residual musical noise and performs better noise masking than the signal subspace approach.

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.

We consider joint source-channel coding for a memoryless Gaussian source and an additive white Gaussian noise (AWGN) channel. For a given code defined by an encoder-decoder pair (/spl alpha/, /spl beta/), its dual code is obtained by interchanging the encoder and decoder: (/spl beta/, /spl alpha/). It is shown that if a code (/spl alpha/, /spl beta/) is optimal at rate p channel uses per source sample and if it satisfies a certain uniform continuity condition, then its dual code (/spl beta/, /spl alpha/) is optimal for rate 1//spl rho/ channel uses per source sample. Further, it is demonstrated that there is a code which is optimal but its dual code is not optimal. Finally, using random coding, we show that there is an optimal code which has an optimal dual. The duality concept is also presented for the cases of (i) binary memoryless equiprobable source and binary-symmetric channel (BSC), and (ii) colored Gaussian source and additive colored Gaussian noise (ACGN) channel.

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.

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 (1982) codes by approximately 1.1 dB (64-state code, 10/sup -5/ bit error probability). Furthermore, we compare the proposed SCO system to a more traditional tandem system consisting of a Huffman code, a convolutional code, an interleaver and an Ungerboeck trellis code. 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.

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.

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.

We consider the problem of reliably transmitting CELP-encoded speech over noisy communication channels. Our objective is to design efficient coding/decoding schemes for the transmission of the CELP line spectral parameters (LSPs) over very noisy channels. We begin by quantifying the amount of "residual redundancy" inherent in the LSPs of Federal Standard 1016 CELP. This is done by modeling the LSPs as first- and second-order Markov chains. Two models for LSP generation are proposed; the first model characterizes the intraframe correlation exhibited by the LSPs, while the second model captures both intraframe and interframe correlation. By comparing the entropy rates of the models thus constructed with the CELP rates, it is shown that as many as one-third of the LSP bits in every frame of speech are redundant. We next consider methods by which this residual redundancy can be exploited by an appropriately designed channel decoder. Before transmission, the LSPs are encoded with a forward error control (FEC) code; we consider both block (Reed-Solomon) codes and convolutional codes. Soft-decision decoders that exploit the residual redundancy in the LSPs are implemented assuming additive white Gaussian noise (AWGN) and independent Rayleigh fading environments. Simulation results employing binary phase-shift keying (BPSK) indicate coding gains of 2-5 dB over soft-decision decoders that do not exploit the residual redundancy.

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.

Describes a speech coder based on the intersymbol interference coded quantizer (ICQ). The ICQ is a structured vector quantizer that can realize both boundary and granular gains for sources with memory. It is the quantization dual of the intersymbol interference coder-a transmission scheme for channels with memory. The authors have studied two different suboptimal ICQ codebook search algorithms for speech coding and find that the performance of the ICQ based speech coder is very good at rates over 13 kbps but degrades rapidly at lower rates.

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.>

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.>

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.>

Several methods based on tree-searched vector quantization (TSVQ) are developed for the efficient encoding of speech line spectrum pair (LSP) parameters. The TSVQ effectively exploits the intraframe correlation of the LSP parameters. To make use of the interframe correlation, a differential coding scheme called interblock noiseless coding (IBNC) is used to encode the binary TSVQ codewords. Two possible applications of this coding scheme are studied: coding at very low bit rates ( approximately=5-10 bits/frame) and coding for high-quality speech (i.e., 1-dB/sup 2/ spectral distortion). In the first application, a frame repeat TSVQ scheme is used with IBNC to reduce the average bit rate. For the second application, in order to obtain the desired reproduction fidelity, the components of the TSVQ error vector are encoded using scalar quantizers. It is shown that, with only one frame encoding delay, a spectral distortion of 1 dB/sup 2/ can be obtained at approximately 20 bits/frame.>