We present a new class of reduced-complexity high-performance iterative receivers for single-user MIMO/OFDM systems with bit-interleaved coded modulation (BICM). The proposed inner-outer decoder structures rely on joint demappers which generate soft-output via an M-algorithm limited tree-search. A key element of the proposed designs is the way the M-algorithm chooses its survivor candidates during the tree search. In particular, at every depth in the tree the survivor list comprises the best M candidates as well as additional good candidates which are chosen to enable high-quality soft-output information for every bit. In the context of iterative inner/outer decoders, simulations show that the proposed survivor selection criteria result in superior performance/complexity trade-offs as compared to a conventional M-algorithm search.

In this paper we present reduced-complexity high-performance iterative receivers for single-user MIMO systems that employ OFDM with bit-interleaved coded modulation. The proposed inner-outer decoder structures exploit the Soft-Output M algorithm (SOMA) to calculate bit-likelihood estimates via a limited search on a tree. A key element of the proposed designs is the way the SOMA front-end adapts at each iteration to new extrinsic information. This front-end defines the tree, both in terms of the order in which symbols are considered, as well as in terms of the subspaces used in the likelihood calculations at each depth in the tree. The proposed SOMA front-ends are different from the conventional QR-decomposition front-ends and provide a systematic way to adapt both the order and the subspaces at each iteration in an iterative decoding structure. Simulations for 4 × 4 16 QAM systems show that the proposed iterative receivers can yield significant performance gains over receivers using non-adaptive conventional front-ends.

A low-complexity soft-output Max-log-MAP (maximum a posteriori probability) detector for N2-QAM is exemplified for a 64-QAM 2timesM multiple-input-multiple-output (MIMO) system, exhibiting the following novel features: (1) hierarchical formulation of the exhaustive metric calculation to reduce the number of candidate tests by a factor of N per received symbol, and (2) multiplier-free implementation of the exhaustive search with 8-fold parallelization. The computational complexity is reduced by a factor of about 250, resulting in a chip area of 0.031 mm2using 65 nm CMOS.

We consider forward-link multiuser MIMO transmission, whereby K users are served by a base station with a large number of (potentially distributed) transmit antennas. We address the problem of channel state information (CSI) mismatch between the transmitter and the receivers with a two-way training scheme. In a quasi-static setting, the proposed scheme requires only K pilot symbols for uplink training and as little as one symbol for downlink training. In particular, we show that the performance of the system where the receiver has perfect channel knowledge can be approached with a small value of downlink training symbols. We consider two variants of linear MMSE precoders that take into account the quality of the channel state information at the transmitter and demonstrate that robust high sum-rate systems can be designed that rely on single-antenna receivers, provided that a large enough number of antennas is used for transmission. Finally, we sketch an example of implementations for the equal rate case.

In this paper we present reduced-complexity high- performance receivers for single-user MIMO systems that employ coded OFDM transmission with bit-interleaved coded modulation (BICM). High data-rate versions of these systems have been proposed for 4G. The near-optimum inner-outer decoder structures for these MIMO/BICM/OFDM/QAM systems have complexity that grows exponentially fast with the number of multiplexed streams (number of transmit antennas) and the number of bits represented by the QAM constellations. We focus on reduced-complexity inner-outer decoder structures that exploit adaptive soft-output M algorithms for soft inner decoding. Our simulations show that these receivers can be systematically optimized to yield substantial complexity reductions without significant loss in performance.

The paper presents an approach to the design of layered BICM MIMO systems using multi-stage iterative decoding and Soft Output M-Algorithm (SOMA) based component decoders. The systems consider transmission based on multilevel coding linked to hierarchical QAM constellations. The receivers are iterative designs with a view to supporting high-rates. These receiver designs can also be used to obtain reduced complexity. The performance of the SOMA schemes are compared to achievable rate bounds for multi-level D-BLAST based schemes. The D-BLAST receivers illustrate general limitations of non-iterative approaches. The multi-layer transmission approach provides a natural support for unequal error protection (UEP), and can be used to balance tradeoffs between robust coverage vs quality in media broadcast applications. Rough predictions on such tradeoffs are given using layered MPEG2 video as a media example.

We consider space-time coding methods for cooperative narrowband and wideband downlink transmission from multiple base stations. The communication channels in multi base-station signaling differ from those involving collocated transmit-antenna systems, and, if properly used, can provide improved resistance to shadowing and extended range. One challenge, however, that arises in this context is asynchronous reception of the signal elements. In the narrowband case the proposed designs generate asynchrony robust space-time block codes (STBCs) via transformations of existing orthogonal STBCs. Subject to a maximum allowable relative delay between signals from distinct transmit antennas, the resulting received signal can be equivalently modeled as arising from synchronous STBC transmission with orthogonal or diagonal STBCs, implying that these designs provide full space diversity with low-complexity decoding in asynchronous settings. We also describe three system approaches for wideband transmission with throughput diversity receiver-complexity trade-offs. Common to all these systems are elements such as OFDM- type signaling, bit-interleaved coded modulation, and iterative decoding. The lowest data-rate lowest complexity system employs an inner orthogonal space-time block code with embedded OFDM-type transmission, while the highest data-rate highest complexity scheme does not employ an inner code. The latter group of schemes can also conveniently provide high data rates at the cost of reduced space diversity. All schemes can be readily extended to provide flexible unequal error protection for media transport.

We present techniques for simulcasting low-power digital data and analog FM over fading channels. Our methods have strong connections to what are referred to as dirty paper coding techniques in that a low-power digital data signal is modulo-added to the host analog FM signal. Due to the low power levels of the digital data and the suppression capability of analog FM, a standard analog FM receiver can be used to reliably recover the analog audio signal. We develop digital receivers that work reliably over fading channels given imperfect channel state information. Spread- response preceding is exploited to not only provide rate-1 temporal diversity benefits, but also to simplify the design of the modulo-precanceler and the receiver. Our theoretical and simulation-based performance analysis of the digital receivers and our MSE-based analog FM distortion analysis suggest that precoded modulo-precanceling schemes provide substantially higher data rates than existing precanceling strategies at the cost of transmission delay and transmitter and receiver complexity. The systems we present are also readily compatible with conventional channel coding techniques as well as with analog FM postcancelers, which can improve the digital receiver bit-error-rate performance at the expense of receiver complexity.

We present a method for network coding over time-varying networks with attractive tradeoffs between throughput and decoding-delay. We model the time-varying networks as a sequence of topology graphs. The method relies on designing a deterministic network code for a fixed virtual graph derived from the actual sequence of topologies, and on exploiting proper buffering in order to implement the code over the actual network. We show that, under certain conditions, this approach can achieve the maximum achievable throughput over the given time- varying network. We also present simulation results that validate the theoretical findings.

Transmission efficiency in radio channels can be considerably improved by using multiple transmit and receive antennas and employing a family of schemes called space-time (ST) coding. Both extended range and/or improved bandwidth efficiency can be achieved, compared with a radio link with a single transmit and receive antenna. Bit-interleaved coded modulation schemes give diversity gains on fading channels with higher order modulation constellations combined with conventional binary convolutional codes also for the case of a single transmit and receive antenna radio link. In this paper, we study a family of flexible bandwidth-efficient ST coding schemes which combine these two ideas in a narrowband flat-fading channel and single-carrier modems. We address receiver complexity for the case of a large number of transmit antennas and higher order modulation constellations. Especially, we focus on practical configurations, where the number of transmit antennas is greater than that of receive antennas. Simplified receivers using tentative decisions are proposed and evaluated by means of simulations. Tradeoffs between complexity reduction and performance loss are presented. We emphasize systems that are of particular interest in applications where the number of transmit antennas exceeds the number of receive antennas. A system with four transmit antennas with an eight-fold complexity reduction and a performance loss of about 1 dB is demonstrated

Transmission efficiency in radio channels can be considerably improved by using multiple transmit and receive antennas, and employing a family of schemes called space–time coding. Both extended range and/or improved bandwidth efficiency can be achieved, compared with a radio link with a single transmit and receive antenna. Bit-interleaved coded modulation schemes give diversity gains on fading channels with higher order modulation constellations combined with conventional binary convolutional codes, also for the case of a single transmit and receive antenna radio link. In this paper, we study a family of flexible bandwidth-efficient space–time coding schemes which combine these two ideas in a narrowband flat-fading channel and single-carrier modems. We address receiver complexity for the case of a large number of transmit antennas and higher order modulation constellations. Especially, we focus on practical configurations where the number of transmit antennas is greater than that of receive antennas. Simplified receivers using tentative decisions are proposed and evaluated by means of simulations. Tradeoffs between complexity reduction and performance loss are presented. We emphasize systems that are of particular interest in applications where the number of transmit antennas exceeds the number of receive antennas. A system with four transmit antennas with an eight-fold complexity reduction and a performance loss of about 1 dB is demonstrated.

Efficient transmission methods for fading radio channels often require an iterative decoder. This is for example the case for systems using turbo codes. Receiver decoder iterations could potentially lead to a latency problem which impacts the performance of the medium access control protocol. In this paper, we present modifications based on the carrier sense multiple access with collision avoidance (CSMA/CA) medium access control (MAC) protocol to accommodate the increased latency in the iterative processing. One area of applications is wireless local area networks (WLANs) with high data rate. The simulation results performed in the IEEE 802.11a WLAN environment by replacing the 802:11a's convolutional coding with turbo coding demonstrate that the proposed algorithm provides a throughput gain over the conventional method.

We present techniques for simulcasting low-power digital data and analog FM over fading channels. Our methods have strong connections to "writing on dirty paper" techniques in that a low-power digital data signal is modulo-added to the host analog FM signal, so as to minimize the distortion on the analog FM signal. We develop digital receivers that work reliably over fading channels given partial channel state information. Spread-response preceding is exploited to provide rate-1 temporal diversity benefits and simplify the digital receiver design. Our theoretical and simulation-based performance analysis of the digital receivers and our MSE-based analog FM distortion analysis suggest that the proposed schemes provide higher data rates than existing precanceling strategies at the cost of transmission delay and transceiver complexity.

List-sequence (LS) decoding has the potential to yield significant coding gain additional to that of conventional single-sequence decoding, and it can be implemented with full backward compatibility in systems where an error-detecting code is concatenated with an error-correcting code. LS maximum-likelihood (ML) decoding provides a list of estimated sequences in likelihood order. For convolutional codes, this list can be obtained with the serial list Viterbi algorithm (SLVA). Through modification of the metric increments of the SLVA, an LS maximum a posteriori (MAP) probability decoding algorithm is obtained that takes into account bitwise a priori probabilities and produces an ordered list of sequence MAP estimates. The performance of the resulting LS-MAP decoding algorithm is studied in this paper. Computer simulations and approximate analytical expressions, based on geometrical considerations of the decision domains of LS decoders, are presented. We focus on the frame-error performance of LS-MAP decoding, with genie-assisted error detection, on the additive white Gaussian noise channel. It is concluded that LS-MAP decoding exploits a priori information more efficiently, in order to achieve performance improvements, than does conventional single-sequence MAP decoding. Interestingly, LS-MAP decoding can provide significant improvements at low signal-to-noise ratios, compared with LS-ML decoding. In this environment, it is furthermore observed that feedback convolutional codes offer performance improvements over their feedforward counterparts. Since LS-MAP decoding can be implemented in existing systems at a modest complexity increase, it should have a wide area of applications, such as joint source-channel decoding and other kinds of iterative decoding.

We present a soft decoding algorithm for convolutional codes that simultaneously yields soft-sequence output, i.e., list sequence (LS) decoding, and soft-symbol output. The max-log list algorithm (MLLA) introduced in this paper provides near-optimum soft-symbol output equal to that of the max-log maximum a posteriori (MAP) probability algorithm. Simultaneously, the algorithm produces an ordered list containing LS-MAP estimates. The MLLA exists in an optimum and a suboptimum version that are different in that the optimum version produces optimum LS-MAP decoding for arbitrary list lengths, while the suboptimum low-complexity version only provides the MAP, the second-order MAP, and the third-order MAP sequence estimates. For lists with more than three elements, MAP decoding is not guaranteed, but the LS decoding is close to the optimal. It is demonstrated that the suboptimum/optimum MLLA can be used to obtain the combination of soft-symbol and soft-sequence outputs at lower complexity than a previously published algorithm. Furthermore, the suboptimum MLLA is well suited for operation in an iterative list (turbo) decoder, since it is obtained by only minor modifications of the well-known Max-Log-MAP algorithm frequently used for decoding of the component codes of turbo codes. Another potential area of application for the suboptimum/optimum MLLA is joint source-channel LS decoding. Estimates of complexity and memory use, as well as performance evaluations of the suboptimum/optimum MLLA, are provided in this paper.

An algorithm for decoding Turbo codes that combines conventional Turbo decoding and list sequence maximum a posteriori probability decoding is presented and evaluated. Compared to previous results on this theme, performance improvements in the order of 0.7 dB are obtained for Turbo codes with 514-b pseudorandom interleaving at a frame error rate of 10/sup -4/ on the additive white Gaussian noise channel.

Bit-interleaved coded modulation schemes give diversity gains on fading channels with higher order modulation constellations combined with conventional binary convolutional codes. By employing multiple transmit and receive antennas, both extended range and/or improved bandwidth efficiency can be achieved in space-time bit-interleaved coded modulation schemes. In this paper, we analyze the performance of this space-time coding scheme in a narrow band flat fading channel and single carrier modems. We give constructive binary codes that yield maximum diversity. We also show that the puncturing mechanism in general fails to achieve the full diversity in such a scheme.

An algorithm for decoding turbo codes that combines conventional turbo decoding and list sequence (LS) maximum a posteriori probability (MAP) decoding is presented and evaluated. Compared to previous results on this theme, a reduction in the order of 0.7 dB of the signal-to-noise ratio (SNR) is obtained for turbo codes with 514-bit pseudo-random interleaving at frame error rate (FER) 10/sup -4/ on the additive white Gaussian noise (AWGN) channel.

We present a new class of systematic, time-invariant, convolutional encoders suitable for low delay burst erasure correction. Specifically, we show that the new encoders have the shortest possible decoding delay required to correct all bursts of a given length with a fixed redundancy. By comparing the new encoders to maximum distance separable (MDS) codes, we show that the latter generally require either more redundancy or more delay to correct bursts of a given length. In addition, we show that the new encoders can achieve better performance than MDS codes on a simple two-state Markov erasure channel. Thus, we demonstrate the advantages of using cross packet coding for delay-sensitive applications such as Voice over Internet Protocol, video-conferencing, etc., on bursty packet networks. Finally, we discuss suitable performance measures for encoders designed to correct both burst and random erasures and report the results of a computer search for such hybrid encoders.

Space-time coding techniques are methods to improve transmission efficiency in radio channels by using multiple transmit and/or receive antennas. Bit-interleaved coded modulation gives good diversity gains with higher order modulation schemes using well known binary convolutional codes. By using orthogonal frequency division multiplexing (OFDM), wideband transmission can be achieved over frequency selective fading radio channels. In this paper, we combine these three ideas into a family of flexible space-time coding methods where modulation order and coding rates as well as the number of transmit and receive antennas can be changed without drastic redesign of the space-time codes. Near optimum iterative decoders are evaluated in terms of simulation for slowly varying wireless LAN type channels. Significant performance gains over the 802.11a standard system are reported.

In this work, anew approach of designing channel codes for partial band interference channels based on "hidden puncturing" is introduced that is not requiring explicit estimation of the interferer. We investigate the performance of specially designed rate 1/2 Viterbi decoding of convolutional codes and rate 1/2 turbo codes in an example scenario with partial band FM interference. We show by means of simulations that for Gaussian as well as for a variety of multipath fading profiles, a significant channel coding gain compared to a conventional system can be achieved. Thereby the performance of optimal combining, that is requiring optimal estimation of the interferer, can be approached very closely in various scenarios.

We consider simultaneous broadcasting of low-power digital data and analog FM and present reliable receivers for the digital data. Due to the relatively low power level of the digital data and the interference suppression capability of analog FM, standard analog FM receivers can reliably recover the analog FM audio signal. To recover the digital data, an extended Kalman filter front end is developed that exploits the capture capability of analog FM to reconstruct and postcancel the analog FM component from the received composite signal. Simulations are conducted with artificial analog FM signals, suggesting that postcanceling schemes can provide higher data rates than their precanceling counterparts, at a lower transmission delay penalty but higher digital receiver complexity. For analog FM to digital signal power level ratios in the range of 30-50 dB, the postcanceler digital signal recovery appears fairly robust, providing digital signal-to-noise ratios of 2-7.5 dB. The corresponding uncoded bit error rates strongly depend on the power level difference between the host analog FM and the digital data signal. In particular, at 260 kb/s and E/sub b//N/sub o/=10 dB they range between 1% to about 15%, and can be reduced to acceptable levels using standard channel coding techniques.

The strict delay constraints of real-time communication applications in packet networks limit the use of automatic repeat request (ARQ) (retransmission systems) and error correction codes with extensive interleaving and decoding over long intervals. Since packet losses can introduce significant impairments, we study the effectiveness of low delay channel coding techniques to increase transmission quality across links with bursty losses. Specifically, we consider the benefits of the newly discovered class of low delay convolutional codes known as maximally short codes. By analyzing a Gaussian source transmitted over a Gilbert-Elliott channel, we demonstrate that these codes can achieve significant gains in comparison to uncoded transmission schemes or traditional coded schemes employing Reed-Solomon block codes. To complement and validate the theoretical analysis we also present results from informal listening tests with a voice-over-IP application.

A list sequence (LS) maximum a posteriori probability (MAP) decoding algorithm for convolutional codes, that takes into account bitwise a priori probabilities and produces a rank ordered list of /spl Lscr/ sequence MAP estimates, can be obtained by modification of the metric increments of the serial list Viterbi algorithm. In this paper, we study the performance of LS-MAP decoding with genie-assisted error detection on the additive white Gaussian noise channel. Computer simulations and approximate analytical expressions, based on geometrical considerations are presented. We focus on the frame error rate and it is concluded that LS-MAP decoding with /spl Lscr/ > 1 often exploits a priori information more efficiently than conventional single sequence MAP decoding (/spl Lscr/ = 1). This leads in many cases to larger relative gains with LS-MAP than LS-ML decoding as /spl Lscr/ increases.

In this paper we investigate the application of Unequal Error Protection (UEP) channel coding schemes to the Transform Predictive Coding (TPC) audio coding paradigm. The TPC paradigm has natural perceptual ordering of the bitstream that provides a good match with the UEP concept. Also introduced is the general idea of Mode Adaptive UEP schemes that adapt to the differing bit-error sensitivity profiles of signal adaptive multimode source-coders. By doing this the decoded signal quality is optimized jointly over the input signal, the channel conditions and the bit-error sensitivity profile of the source coder.

In a variety of networks, packet losses occur in bursts. Conventional application of error correction codes for packet recovery often requires interleaving and long decoder delays. These long delays are usually unacceptable in real-time multimedia communication applications such as voice over IP (VoIP). Consequently, erasure correction codes with severe limits on delay are desirable. We present various codes suitable for correcting bursts of lost packets. In addition, we show that these codes have the shortest possible decoding delay. To demonstrate the practical benefits of these codes for VoIP, we present results of informal mean opinion score listening tests conducted with various codes.

We evaluate the performance of list sequence (LS) maximum a posteriori probability (MAP) decoding on the additive white Gaussian noise (AWGN) channel and the fully interleaved flat Rayleigh fading channel. In particular, we focus on the frame error rate (FER) of LS-MAP decoding with genie-assisted error detection. It is demonstrated that LS-MAP decoding yields significant performance improvements relative to single sequence MAP decoding on the AWGN channel as well as the fully interleaved flat Rayleigh fading channel. Furthermore, feedback convolutional codes have been observed to have the potential to yield improved FER performance with both single sequence MAP and IS-MAP decoding, compared to feedforward convolutional codes. Based on these performance improvements, we propose a joint source-channel IS decoding scheme. The scheme is based on the max-log list algorithm for simultaneous soft symbol and IS decoding of convolutional codes. In existing systems where a cyclic redundancy check for error mitigation is concatenated with a convolutional code for error correction, this scheme can be implemented in a fully backward compatible receiver.

The move to digital is a natural progression taking place in all aspects of broadcast media applications from document processing in newspapers to video processing in television distribution. This is no less true for audio broadcasting which has taken a unique development path in the United States. This path has been heavily influenced by a combination of regulatory and migratory requirements specific to the U.S. market. In addition, competition between proposed terrestrial and satellite systems combined with increasing consumer expectations have set ambitious, and often changing, requirements for the systems. The result has been a unique set of evolving requirements on source coding, channel coding, and modulation technologies to make these systems a reality. This paper outlines the technical development of the terrestrial wireless and satellite audio broadcasting systems in the U.S., providing details on specific source and channel coding designs and adding perspective on why specific designs were selected in the final systems. These systems are also compared to other systems such as Eureka-147, DRM, and Worldspace, developed under different requirements.

We investigate the performance of rate 1/2 turbo codes for multipath fading channels in a hybrid in band on channel (HIBOC) digital audio broadcasting (DAB) system in the FM band. An orthogonal frequency division multiplexing (OFDM) modem with differential quadrature phase shift keying (DQPSK) modulation is used. We show by means of simulations that for a variety of multipath fading profiles and vehicle speeds, we obtain a channel coding gain of about 3 dB in channel signal-to-noise ratio (SNR) compared to a conventional system with a memory 6 convolutional code with Viterbi decoding.

Hybrid in band on channel (IBOC) digital audio broadcasting (DAB) simultaneously with analog amplitude modulation (AM) has been proposed as a hybrid solution to digital audio broadcasting in the AM band. Adding digital transmission in the crowded AM band is a challenging proposition. To achieve FM like audio quality, an audio coder rate of 32-64 kbit/s may be required. One of the currently proposed hybrid IBOC-AM systems is 30 kHz wide. Severe second adjacent interference may occur in certain geographical areas. For coping with such harsh transmission conditions, we present a solution based on embedded/multi-descriptive audio coding with matched multistream transmission in separate frequency bands. With loss of one frequency band, the embedded system blends to a lower audio coder rate with still a better quality than analog AM. The non-embedded system without multi-stream transmission fails catastrophically causing a severe discontinuity in quality while blending directly to analog AM.

The conventional list Viterbi algorithm (LVA) produces a list of the L best output sequences over a certain block length in decoding a terminated convolutional code. We show in this paper that the LVA with a sufficiently long list is an optimum maximum-likelihood decoder for the concatenated pair of a convolutional code and a cyclic redundancy check (CRC) block code with error detection. The CRC is used to select the output. New LVAs for continuous transmission are proposed and evaluated, where no termination bits are required for the convolutional code for every CRC block. We also present optimum and suboptimum LVAs for tailbiting convolutional codes. Convolutional codes with Viterbi decoding were proposed for so-called hybrid in band on channel (hybrid IBOC) systems for digital audio broadcasting compatible with the frequency modulation band. For high-quality audio signals, it is beneficial to use error concealment/error mitigation techniques to avoid the worst type of channel errors. This requires a reliable error flag mechanism (error detection feature) in the channel decoder. A CRC on a block of audio information bits provides this mechanism. We demonstrate how the LVA can significantly reduce the flag rate compared to the regular Viterbi algorithm (VA) for the same transmission parameters. At the expense of complexity, a receiver optional LVA can reduce the flag rate by more than an order of magnitude. The difference in audio quality is dramatic. The LVA is backward compatible with a VA.

A low-complexity method of linearly combining an analog frequency-modulation (FM) signal with a low-level multitone signal for simultaneous broadcasting of digital data and analog FM is proposed and evaluated. The analog FM signal can be recovered with a standard FM receiver. The digital multitone signal is added symmetrically at the band edges of the 200-kHz FM signal in contiguous bands with variable width. To maximize the data rate, the digital bandwidth is maximized subject to a maximum allowed distortion of the demodulated analog FM signal. The impact of the analog FM signal on, digital reception is cancelled by means of transmitter precanceling techniques. Conditions for precanceling techniques for multipath channels are formulated. The main advantage of the contiguous band insertion method is that the rate of the control channel is considerably lower compared to previously proposed methods of carrier insertion without significant reduction in data rate. We present a number of numerical results for acoustical signals.

Hybrid in-band on-channel (IBOC) broadcasting systems for digital audio radio have the capability of simultaneously transmitting analog FM and digital audio of CD-like quality. Due to fading and interference in the already-crowded FM band, the signal design for the hybrid IBOC system is very challenging. It has been proposed to use a method of double sideband transmission where the digital information is transmitted by means of orthogonal frequency-division multiplexing (OFDM) on both sides of the analog host FM and where the digital information can be recovered when one sideband is partially or even totally lost. This leads to an interesting channel coding problem, where we search for optimal pairs of high-rate codes that form good combined low-rate codes, which are better than classic code combining techniques. Furthermore, we also search for rate-compatible punctured convolutional codes which can be used for two-level unequal error protection (UEP) of digital audio. Since some of the tones in the multitone modem (OFDM) are more exposed to interference than others, optimal assignments of convolutional code bits to tones depending on their spectral position are also found. A large number of new codes with memory 6 and 8 are presented both for equal error protection and UEP.

In most source coded bit streams certain bits can be much more sensitive to transmission errors than others. Unequal error protection (UEP) offers a mechanism for matching error protection capability to sensitivity to transmission errors. A UEP system typically has the same average transmission rate as a corresponding equal error protection (EEP) system but offers an improved perceived signal quality at equal channel signal to noise ratio. In this work we introduce methods of UEP to the perceptual audio coder (PAC). An error sensitivity classifier divides the bits in classes of different sensitivity. Different channel codes are then applied to each class. We show how punctured convolutional codes can be used for UEP of the PAC bitstream. Experimental results for channels with uniform as well as non-uniform noise/interference level indicate that the systems with UEP exhibit graceful degradation and extended range for applications such as digital audio broadcasting (DAB).

Simultaneous broadcasting of digital data and existing analog FM is investigated. A suboptimum method of linearly combining the analog FM signal with a low level multitone signal is proposed and evaluated. The analog FM signal is to be recovered with a standard FM receiver. The digital multitone signal is added symmetrically at the band edges of the 200 kHz FM signal in contiguous bands with variable width. To maximize the data rate, the digital bandwidth is maximized subject to a maximum allowed distortion of the analog FM signal. The impact of the analog FM signal on digital reception is cancelled by means of transmitter precancelling techniques. Conditions for precancelling techniques for multipath channels are formulated. The main advantage of the contiguous band insertion (CBI) method is that the rate of the control channel is considerably lower compared to previous near optimum methods of carrier insertion without significant reduction in data rate. We present a number of numerical results for acoustical signals.

A reliable method for broadcasting digital audio simultaneously with existing analog FM radio is presented. According to this linear combining scheme, the digital data sequence is adaptively modulated so as to achieve high data rates while ensuring that the interference incurred on the analog FM signal remains at acceptably low levels. The digital transmission is based on adaptive orthogonal frequency division multiplexing. Implementable, near optimum algorithms for insertion of the maximum number of carriers at all times are presented, which incur negligible distortion on the analog FM signal. The digital receiver response of the analog FM signal (known to the transmitter) is computed and canceled from the aggregate signal prior to signal transmission. As a result of this precanceling process the digital transmission is free from analog FM interference. We present simulation results on acoustic signals where the average digital data use up to 50% of the 200 kHz power spectrum with digital signal power levels 25-35 dB below the analog signal. A control channel is used for the positions of the modem carriers.

A method for broadcasting digital audio simultaneously with existing analog frequency modulation (FM) radio is presented. The method is based on precomputing the response of the host analog FM signal at the digital receiver and precanceling it at the transmitter. As a result, the digital transmission is free from interference from analog FM. We select the rate and power level of the digital transmission in a manner that the interference the digital data incur on the analog FM signal remains at acceptably low levels. The digital transmission is based on adaptive orthogonal frequency-division multiplexing (OFDM) (adaptive multicarrier). The frequencies and number of carriers of the digital multicarrier modem are judiciously selected in a time-varying fashion so as to cause a negligible distortion in a standard receiver for analog FM. Simulations based on conservative nonoptimized signal design indicate that data rates up to about 130 kb/s inside the 200-kHz FM channel are achievable for acoustic test signals. We present a number of numerical examples where the average digital data use up to 50% of the 200-kHz power spectrum with digital signal power levels 25-35 dB below the analog signal. Due to the resulting variable-rate digital transmission, a control channel is required. A method of precanceling with multiple orthogonal direct-sequence spread-spectrum schemes is also presented.

The Viterbi algorithm (VA) is the maximum likelihood decoding algorithm for convolutionally encoded data. Improvements in the performance of a concatenated coding system that uses VA decoding (inner decoder) can be obtained when, in addition to the standard VA output, an indicator of the reliability of the VA decision is delivered to the outer stage of processing. Two different approaches of extending the VA are considered. In the first approach, the VA is extended with a soft output (SOVA) unit that calculates reliability values for each of the decoded output information symbols. In the second approach, coding gains are obtained by delivering a list of the L best estimates of the transmitted data sequence, namely the list Viterbi decoding algorithm (LVA). Our main interest is to evaluate the LVA and the SOVA in comparison with each other, determine suitable applications for both algorithms and to construct extended versions of the LVA and the SOVA with low complexity that perform the task of the other algorithm. We define a list output VA using the output symbol reliability information of the SOVA to generate a list of size L and that also has a lower complexity than the regular LVA for a long list size. We evaluate the list-SOVA in comparison to the LVA. Further, we introduce a low complexity soft symbol output viterbi algorithm that accepts the (short) list output of the LVA and calculates for each of the decoded information bits a reliability value. The complexity and the performance of the soft-LVA (LVA and soft decoding unit) is a function of the list size L. The performance of the soft-LVA and the SOVA are compared in a concatenated coding system. A new software implementation of the iterative serial version of the LVA is also included.>

Previously, we (see Wong, Sundberg and Seshadri, GLOBECOM '93, p.1649-1653, 1993) proposed a low-delay multiple access scheme, called shared time-division duplexing (STDD). This scheme allows both the up-link and downlink traffic to share a common channel, thereby achieving high statistical multiplexing gain even with a low population of simultaneous conversations. Here, we focus on transmitting speech using this multiple access scheme by a suitable choice of speech coder, channel coder and modulation. In particular, we consider low delay, high quality speech coding and digital modulation systems based on adaptive DPCM, with QDPSK or pseudo-analog transmission (skewed DPSK). The choice of the alternative systems depends on required end-to-end delay, recovered speech quality and bandwidth efficiency. Typically, with a total capacity of 1 MBaud, 2 ms frame and 8 kBaud speech coding rate, low delay STDD is able to support 48 pairs of users compared to 38, 35 and 16 for TDMA with speech activity detection, basic TDMA and PRMA respectively. This corresponds to respective gains of 26%, 37% and 200%.>

A list Viterbi decoding algorithm (LVA) produces a rank ordered list of the L globally best candidates after a trellis search. The authors present two such algorithms, (i) a parallel LVA that simultaneously produces the L best candidates and (ii) a serial LVA that iteratively produces the k/sup th/ best candidate based on knowledge of the previously found k-1 best paths. The application of LVA to a concatenated communication system consisting of an inner convolutional code and an outer error detecting code is considered in detail. Analysis as well as simulation results show that significant improvement in error performance is obtained when the inner decoder, which is conventionally based on the Viterbi algorithm (VA), is replaced by the LVA. An improvement of up to 3 dB is obtained for the additive white Gaussian noise (AWGN) channel due to an increase in the minimum Euclidean distance. Ever larger gains are obtained for the Rayleigh fading channel due to an increase in the time diversity. It is also shown that a 10% improvement in throughput is obtained along with significantly reduced probability of a decoding failure for a hybrid FEC/ARQ scheme with the inner code being a rate compatible punctured convolutional (RCPC) code.>

The authors present coded 8-phase-shift-keyed (8-PSK) modulations for the Rayleigh fading channel. The schemes are based on multilevel trellis-coded-modulation constructions and utilize maximum free Hamming distance binary convolutional codes as building blocks. A suboptimal multistage decoder that utilizes interstage interleaving and iterative decoding is proposed and evaluated. Examples are constructed to show that the proposed schemes outperform the best modified codes of the Ungerboeck type due to significantly higher implicit time diversity, yielding seven branches of built-in time diversity, whereas the Ungerboeck code yields four branches of time diversity for a 64-state system. The transmission delay is higher, however. The new schemes can provide three levels of unequal error protection when 8-PSK or 8-differential-phase-shift-keying (8-DPSK) modulations are used. They provide 10-14-dB channel signal-to-noise ratio gain over uncoded 4-DPSK at a bit error rate of 10/sup -3/ for a modest decoding complexity.>

The unequal error protection capabilities of convolutional codes belonging to the family of rate-compatible punctured convolutional codes (RCPC codes) are studied. The performance of these codes is analyzed and simulated for the first fading Rice and Rayleigh channels with differentially coherent four-phase modulation (4-DPSK). To mitigate the effect of fading, interleavers are designed for these unequal error protection codes, with the interleaving performed over one or two blocks of 256 channel bits. These codes are decoded by means of the Viterbi algorithm using both soft symbol decisions and channel state information. For reference, the performance of these codes on a Gaussian channel with coherent binary phase-shift keying (2-CPSK) is presented. A number of examples are provided to show that it is possible to accommodate widely different error protection levels within short information blocks. Unequal error protection codes for a subband speech coder are studied in detail. A detailed study of the effect of the code and channel parameters such as the encoder memory, the code rate, interleaver depth, fading bandwidth, and the contrasting performance of hard and soft decisions on the received symbols is provided.>

By using codes of rate 2/3 followed by 8-PSK modulation, a gain of 3-6 dB is obtained over uncoded 4-PSK, for an ideal coherent transmission on the white Gaussian channel. In the presence of carrier phase offset, it has been shown that trellis-coded 8-PSK systems are more sensitive than uncoded 4-PSK. A more robust performance can be achieved by using rate 2/3 trellis-coded 8-PSK signals and 4-PSK signals in a time-varying manner. Only the mapper from the output of the binary convolutional code to the signal point number to be transmitted has to be periodically time-varying. In its simplest form, trellis-coded 8-PSK and 4-PSK signals alternate in time. An examination has also been made of systems where the mixture of 8-PSK and 4-PSK signals varies, with a short periodic sequence of time-varying mapping rules. The distance spectra and error probability are evaluated with and without phase offset. Simulation results of bit error rate (BER) and performance of the recovery loop (S curve) are presented. It is concluded that systems which are more robust against jitter can be achieved by means of time-varying hybrid trellis-coded 8/4-PSK systems.>

The effects of capture on the average system throughput and delay performance of slotted ALOHA were analyzed for slow and fast Rayleigh fading radio channels. A short-range multipoint-to-base station packet radio network is considered. It is shown that larger capture effects and thus improved network performance can be achieved with proper choice of modulation. It is also shown that the use of simple error-correcting codes improves capture. The use of selection diversity also improves the capture effect both for fast and slow fading. It is concluded that the inverse distance variability of the received signal is the main reason for the capture effect. The Rayleigh fading alone yields a very small contribution in terms of throughput; nonetheless, it helps to stabilize the system. Numerical results are presented for a slotted ALOHA system with 50 users. It is found that the maximum average throughput can be increased from about 36% to almost 60% by using channel coding and space diversity.>

The coder is a dynamic bit allocation sub-band coder of the type first proposed by Ramstad (1982). It is structured in such a way that the relative importance of all bits is established as a byproduct of the dynamic bit allocation. It is shown that there is a difference in error sensitivity of four orders of magnitude between the most and the least important bits of the bit stream on average. A very flexible unequal error protection scheme is used to match the error sensitivity of the sub-band coder bit stream. This is accomplished using the concept of rate compatible punctured convolutional coding. The resulting coder gives robust performance over a simulated noisy channel. Its nominal bit rate is 16 kb/s, with 12 kb/s assigned for speech coding and 4 kb/s assigned for error correction. The entire encoder and decoder have been implemented on a single AT&T DSP-32 digital signal processor.>

The bit error probability properties of signals consisting of convolutional coding combined with partial-response multilevel continuous phase modulation (CPM) are studied. It is assumed that the channel is an additive white Gaussian noise channel and that the receiver performs coherent maximum-likelihood sequence detection by means of the Viterbi algorithm. An upper bound on the bit error probability is derived, using the average generating function technique, and evaluated numerically for a number of coded multilevel full-response CPM schemes. Simulation results are also presented. It is concluded that the free Euclidean distance is the best one-parameter description of the error probability for the considered class of signals for high signal-to-noise ratios. However, the upper bound results show that the free distance alone yields pessimistic bit error probability behavior for some interesting cases.>

Convolutionally encodedM-ary quadrature amplitude modulation (M-QAM) systems operated over multidimensional channels, for example dual-polarized radio systems, are considered in this paper. We have derived upper bounds on the average bit-error probability for 4QAM (QPSK) with conventional convolutional coding by means of a truncated union bound technique and averaging over the cross-polarization interference by means of the method of moments. By modifying this technique, we have found approximate upper bounds on the average biterror probability for bandwidth efficient trellis-coded QAM systems. This is an extension of our previous work [1] that was based on one dominating error event probability as a performance measure. Our evaluations seem to indicate that bandwidth efficient trellis-codedMQAM schemes offer much larger coding gains in an interference environment, e.g., a cross-coupled interference channel, than in a Gaussian noise channel. In general, our findings point out that optimum codes for a Gaussian channel are not optimum when applied in an interference environment. We note that a rate 1/2 convolutional code for example, with a code memory greater than two, if applied to two of the bits in each signal point representation, can be utilized with a simple decoder to greatly improve the performance of a QAM signal in interference. Also, we have introduced a new concept referred to as dualchannel polarization hopping in this paper which can improve the system performance significantly for systems with nonsymmetrical interference.

The performance of cross-coupled,M-ary quadrature amplitude modulation (QAM) systems is determined when bandwidth efficient trellis codes are used to combat interference. Performance with and without compensation for cross-coupled interference is presented. It is found that simple trellis codes can maintain the error probability at an acceptable level for cross-coupling parameters that render uncoded systems unusable. Up to two-dimensional trellis codes are considered for four-dimensional QAM signals, and possibilities of obtaining diversity advantages in the form of higher total system throughput by prolonged availability of the two signals are explored. This is accomplished through joint coding over two different constellations. The probability of the most likely error events is calculated by using the method of moments. The results are applicable to any digital communication system using multidimensional quadrature amplitude modulation, e.g., voiceband modems, cross-polarized radio systems and, to some extent, optical systems. In the paper the analysis is restricted to nondispersive cross-coupling models. In most cases the coding gain is larger than in the absence of cross-coupling interference. Specifically, it is found that simple codes have coding gains increased by at least 2 dB with cross-coupling interference relative to that obtained on the additive white Gaussian noise channel.

Error correcting codes have two opposite effects on the efficiency of cellular mobile-radio systems. Although they increase the bandwidth per channel, the codes also make signals more robust and thereby reduce the required distance between users of the same frequency band. This paper reports a mathematical study of the interactions of these two effects in determining the efficiencies of a large number of sourcecode and channel-code combinations. Within a statistical performance objective (basebandSNR \geq 11dB for 90 percent of the users), the most efficient scheme in this study has an embedded differential pulse code modulation (DPCM) source code and a rate 1/2 channel code that protects 2 bits of each 4 bit DPCM code word. Based on a conservative model of cellular transmission, we estimate that the bandwidth efficiency is 3 users/cell/MHz of system bandwidth. By contrast, there are only 1.2 users/cell/MHz with uncoded transmission and 4.5 users/cell/MHz with a rather complicated variable-rate scheme. We also observe that the embedded source code, originally devised for variable-rate operation, has a higher baseband SNR than conventional DPCM in certain fixed-rate environments.

Partial response continuous phase modulation (CPM) schemes have a high spectrum utilization and also a high immunity to nonlinear distortion, since they have a constant envelope. Schemes with high power efficiency can also be designed when they are coherently detected with a Viterbi detector. These schemes are sometimes complex, however. In this paper two minimum-shift-keyed (MSK)type receivers are studied. The MSK-type receiver can be implemented as a serial receiver and as a parallel receiver. Both receivers are useful for binary modulation schemes with modulation indexh = 1/2. Only coherent detection of signals transmitted over an additive white Gaussian noise channel is considered. The serial receiver can be implemented with only two filters and simple decision logic. The decisions are made serially in one decision eye pattern. Two types of receiver filters are considered. Error probability results are presented for the receiver, both with and without phase and timing errors present in the receiver. It is shown that, assuming perfect phase and time synchronization, the serial and parallel receivers have equal performances. The advantages of the serial receiver over the parallel receiver are the same for partial response continuous phase modulation as for classical MSK; i.e., both in implementation aspects and in the reduced sensitivity to phase errors.

Partial response continuous phase modulation (CPM) gives constant envelope digital modulation schemes with excellent power spectra. Both narrow main lobe and low spectral tails can be achieved. When these signals are detected in an optimum coherent maximum likelihood sequence detector (Viterbi detector), power efficient schemes can also be designed, sometimes at the expense of receiver complexity. This paper describes a general class of simple Viterbi detectors with reduced complexity compared to the optimum case. The key idea is that the approximate receiver is based on a less complex CPM scheme than the transmitted scheme. The asymptotically optimum reduced-complexity receiver is found for a variety of transmitted schemes and various complexity reduction factors, for a specific class of receivers and modulation indexes. A new distance measure is introduced for the performance analysis. Smooth schemes based on raised cosine pulses are analyzed and simulated for the case of simplified reception. A graceful performance degradation occurs with the reduction of complexity.

Continuous phase frequency shift keying (CPFSK) is a constant amplitude modulation method with good spectral sidelobe properties. Good error probability properties can be obtained with coherent maximum-likelihood detection. In this paper we study the Euclidean distance properties of signals formed by a conventional rate1/2convolutional encoder followed by a binary or4-level CPFSK modulator. The minimum Euclidean distance is calculated for these signal sets as a function of the modulation index and the observation interval length. The optimum detector is discussed for rational modulation index values. The best obtainable codes are found for the case of short rate1/2codes with binary or4-level CPFSK modulation. Lists of the best codes are given. Among the results are that the noncatastrophic rate1/2convolutional codes with optimum free Hamming distance do not in general give the best Euclidean distance with CPFSK.

Recently bandwidth efficient constant envelope digital modulation schemes have been shown also to be power efficient, if detected coherently. In this paper the performance of such systems is analyzed for an optimum noncoherent or partially coherent detector, at large signal-to-noise ratios. The considered schemes are M-ary with arbitrary pulse shaping over one symbol interval (full response). The performance is analyzed by means of a parameter called equivalent minimum Euclidean distance, mathematically playing the same role as the minimum Euclidean distance used for coherent detectors. It is shown that noncoherent detectors perform as well as coherent, although the observation interval must be increased.

In sharp contrast to the task of calculating the power spectrum for a general digital FM scheme, the autocorrelation can easily be obtained. By considering a class of FM schemes having a time-limited autocorrelation function, truncation is avoided and, applying a Fourier transformation, power spectral densities are easily obtained. A method is applied taking these properties into account. Thus, a powerful tool is available for investigation of different parameters within the considered digital FM modulation format.

A class of smoothed phase modulation codes is analyzed in terms of power spectral density and error probability for large signal-to-noise ratios. The signals have constant envelope and the information-carrying phase function is of multi-hpartial response continuous phase type. A cyclic variation of modulation index from symbol time interval to symbol time interval is introduced. Coherent transmission and an additive white Gaussian channel are assumed. Both power- and bandwidth-efficient signals are to be found in the above class. Comparisons are made between fixed-hand multi-hsystems both for the binary and multilevel cases. Tradeoff is performed between bandwidth and error probability performance for large signal-to-noise ratios. It is concluded that quaternary and octal systems always seem preferable. Increasing the number of modulation indexes from one in the fixed-hcase to two in the simplest multi-hcase gives performance advantages at the expense of increased system complexity.

The problem of calculating accurate power spectral densities for an extended class of digital FM schemes is considered. This extended class includes partial response as well as multilevel schemes. A method suitable for numerical calculation using a computer is developed. This new method consists of two parts. First, the spectral main lobe is calculated. Then, the spectral tail is calculated by a different approach. The accuracy of the spectral tail is that of a correction term to an analytical asymptotic tail formula. This method yields accurate power spectra down to a level considerably below -100 dB. Numerical results obtained from calculations are given. The power spectra can be calculated for an arbitrary modulation index value.

The minimum Euclidean distance for a class of constant envelope phase modulation codes is studied. Bandwidth and power efficient signals with continuous phase are considered. The information carrying phase varies piecewise linearly and the slopes are cyclically changed for successive symbol time intervals, yielding the so-called multi-hsignals. It has previously been shown that this class of signals contains bandwidth and power efficient signals when coherent maximum likelihood sequence detection is used. Bounds on the achievable Euclidean distance for signals in the above class are given. Upper bounds are calculated as well as minimum distance results for specific multilevel multi-hsignals. It is concluded that quaternary and octal muiti-hschemes considerably outperform the binary schemes. Furthermore in the important small modulation index region,2-hcodes gain the maximum 3 dB. Larger gains are not available by increasing the number ofhvalues.

Constant envelope phase varying sinusoids of the form\sqrt{2E/T} \cos(\omega_{c}t + \phi(t))are studied, in which the phase function\phi(t)follows some coded pattern in response to data. Power and bandwidth performance are studied for such patterns. The patterns depend on a phase shaping function, a modulation index (h), and a sequence ofM-ary underlying changes in phase which are chosen at random. A cutoff rate-like parameter R0is computed, which guarantees existence of codes at all ratesR < R_{0}bits/T-interval whose error performance varies as exp[-N(R_{0} - R)], whereNis the code word length inT-intervals. Plots of R0are given as a function of interval energyE, the shaping functionhandM. Extensive spectral calculations give the spectra of these phased sinusoids, and their performance is plotted in the power-bandwidth plane. The results give strong evidence that phase codes can approximate any power-bandwidth combination consistent with Shannon's Gaussian channel capacity, and that linear channels are not required for narrow-band transmission.

An analysis of constant envelope digital partial response continuous Phase modulation (CPM) systems is reported. Coherent detection is assumed and the channel is Gaussian. The receiver observes the received signal over more than one symbol interval to make use of the correlative properties of the transmitted signal. The Systems areM-ary, and baseband pulse shaping over several symbol intervals is considered. An optimum receiver based on the Viterbi algorithm is presented. Constant envelope digital modulation schemes with excellent spectral tail properties are given. The spectra have extremely low sidelobes. It is concluded that partial response CPM systems have spectrum compaction properties. Furthermore, at equal or even smaller bandwidth than minimum shift keying (MSK), a considerable gain in transmitter power can be obtained. This gain increases withM. Receiver and transmitter configurations are presented.

The continuous phase modulation (CPM) signaling scheme has gained interest in recent years because of its attractive spectral properties. Data symbol pulse shaping has previously been studied with regard to spectra, for binary data and modulation index 0.5. In this paper these results have been extended to theM-ary case, where the pulse shaping is over a one symbol interval, the so-called full response systems. Results are given for modulation indexes of practical interest, concerning both performance and spectrum. Comparisons are made with minimum shift keying (MSK) and systems have been found which are significantly better inE_{b}/N_{0}for a large signal-to-noise ratio (SNR) without expanded bandwidth. Schemes with the same bit error probability as MSK but with considerably smaller bandwidth have also been found. Significant improvement in both power and bandwidth are obtained by increasing the number of levelsMfrom 2 to 4.

Expressions are derived for the average probability of block errorP_{f}(M, N), i.e., the probability of more thanMerrors in a block ofNsymbols. The average is formed over the inatantaneous receiver signal-to-noise ratio after combining. Binary frequency-shift keying with noncoherent detection is transmitted over a very slow nonselective Rayleigh fading channel and received in additive Gaussian noise. Diversity is used and the branch fading is assumed independent. Formulas forP_{f}(M, N)are derived for both ideal selection combining and maximal ratio combining.

A class of perfect block codes are found for the binary channel associated with differentially encoded phase shift keying signals with coherent detection (DCPSK). The codes are shown to correct all double adjacent errors and single errors in the first and last word positions. Such codes are found for which the number of available different syndromes equals the number of most probable channel errors. A construction algorithm is given for this class of codes. Computer search results for shortened codes are presented.

This correspondence deals with the problem of selecting optimal shortened d = 3 Hamming codes and d = 4 extended Hamming codes. The studied codes are transparent codes, minimum column weight codes, and codes with a minimum number of codewords of minimum weight. It is concluded that a shortened code normally does not combine the properties of being transparent, being of minimum column weight type and having a minimum number of codewords of minimum weight. Furthermore, it is concluded that the weight distribution of a shortened code depends on the selected set of shortened information symbols for a given fixed number of shortened symbols. The correspondence also gives examples of good 22, 16 codes.

A program for the development of a highly reliable memory has been underway for a number ofyears at ESTEC. Plated wire and ferrite core spaceborne memories have been developed and qualified, and the more recent advent of low power LSI memory devices has made the semiconductor memory an attractive proposition for spaceborne applications. These technologies are briefly discussed and compared. However, in common with the previous solutions, the reliability of a semiconductor memory even when protected by a conventional single error correction scheme, did not meet the requirements of long duration space missions.

Simple analytical upper bounds, approximations and lower bounds on the error functionQ(x)are presented and analyzed. A class of functions are given, where the choice of two parameters result in good upper bounds, lower bounds and approximations onQ(x). The results are given in formulas, parameter tables and graphs. The approximations are suitable for programmable pocket calculators.

In this paper we introduce and evaluate error correction methods which takes into account the special properties of failure modes in semiconductor memories. We assume that the memory faults are of the type stuck-to 1 or 0. Thus the fault, once it has occurred, is located to a specific position in a memory word. The position may be found and this fact makes it convenient to use erasure correction, rather than random error correction.

The effect of digital errors in PCM systems for speech signals depends on the PCM code used. The standard binary folded PCM code is superior to the natural binary code but it is not optimum. This paper considers PCM codes especially designed to be insensitive to the double error patterns produced by DPSK. It is concluded that the dynamic range with especially designed PCM codes is considerably extended compared to standard binary folded PCM. Special simplified interleaving schemes and optimum PCM codes for coherent PSK are also considered. The dynamic behavior of various PCM codes is calculated and compared, e.g., asymptotically optimum PCM codes for DPSK, binary folded PCM with and without interleaving, asymptotically optimum PCM codes for coherent PSK, etc. We conclude that the best scheme for DPSK is simplified interleaving and an optimum PCM code for PSK. This paper also gives analytical formulas for double errorA-factors for standard PCM systems.

The effect of digital errors in PCM encoded speech signals transmitted over a noisy channel is reduced by using soft decision demodulation at the receiver. The reliability information supplied by the soft decision demodulator is used to point out likely transmission errors, especially in the most significant PCM bits. When a likely transmission error is identified, the corresponding PCM word is rejected by the receiver and replaced by a predictor estimate or an interpolation estimate if delayed decisions are used. We have analyzed soft decision demodulation schemes for standard PCM encoded speech signals transmitted over the Gaussian channel with coherent PSK (phase shift keying). A signal to noise ratio gain inE_{b}/N_{0}of the order of 1-2 dB is Obtained at low input signal levels. The gain depends on the performance of the predictor or, alternatively, the interpolator. No modifications of the transmitter are required to obtain this improvement. The suggested soft decision schemes are optional at the receiver. The comparisons are made with hard decision demodulation.

Weighted digital modulation schemes which provide bit error probabilities matched to the PCM bits with respect to their sensitivity to digital errors are analyzed. The channel is additive, white Gaussian. The PCM system has arbitrary code, companding law and input signal density function. Especially optimum weighted PSK/PCM and QAM/PCM are given for speech signals. The average channel signal to noise ratio is kept constant when schemes are compared. We obtain a channel signal to noise ratio gain in threshold extension of 2 dB for standard 8 bit PCM. The performance of suboptimum schemes, where the number of different bit error probability levels are smaller than the number of PCM bits are also studied. Two levels per 8 bit PCM word yield more than half of the achievable gain (in dB) and 4 levels is almost equal to optimum.

The effect of digital errors in linear pulse code modulation (PCM) systems has been considered by several authors for channels with independent errors. In this paper we present a general approach of analyzing digital errors in linear and nonlinear PCM systems with arbitrary channels. The examples given in this paper cover the different standard nonlinear PCM systems and independent channel errors. The technique used for the analysis leads to the conclusion that there are PCM codes less sensitive to digital errors than the standard binary folded PCM code. An example of such a PCM code is given in this paper.

The main idea of this concise paper is to use symbol reliability information for improving the performance of error detectors. A class of soft decision error detectors (SDED's) is presented, where low weight error patterns are selectively corrected. The reliability numbers govern which error pattern to correct. Asymptotic performance and bounds are derived for the Gaussian channel. It is shown that singleerror correcting SDED's without thresholds have an exponentially lower repeat request probability than the hard decision error detector, but the same exponent in the probability of undetected errors. Detectors with thresholds are also considered. In this case it is possible to contruct an error detector with both better probability of undetected errors and better probability of repeat request than for the hard decision error detector (HDED). Bounds and computer simulations are presented and SDED's are compared to HDED's.

This correspondence is an extension of the work in [1] and [2]. We present two new classes of error detectors which utilize symbol reliability information (i.e., soft decision error detectors). First, a simple class of selectively single error correcting error detectors is discussed where the syndrome information is used and where just one single reliability number is compared to a threshold value. These error detectors are simpler than those in [1] and [2], but less powerful. Second, a class of soft decision error detectors with low probability of undetected errors is considered. The reliability information is used to reduce the probability of undetected errors without increasing the repeat request probability (compared to the hard decision error detector). Exponential properties for large signal-to-noise ratios and bounds are calculated for both classes of error detectors. Computer simulations are also presented.

The effects of independent bit errors are calculated for nonlinear PCM systems. General simplified computer formulas are given for natural binary and binary folded PCM codes. Analytical formulas are produced for μ-quantization, binary folded PCM, and speech-like input signal density functions.

This paper deals with soft decision as a means to bridge the gap in performance between a receiver using hard decision symbol estimation followed by an algebraic decoder and a maximum-likelihood receiver. A measure of the reliability of the code symbol estimates is introduced to facilitate the decoding process. The decoding operation studied erases the least reliable received symbols and then applies an algorithm capable of correcting errors and erasures. This procedure, termed successive-erasure decoding (SED), was introduced by G. D. Forney in connection with general minimum-distance decoding (GMD). It is studied for binary and nonbinary transmission using polyphase signals on the additive white Gaussian noise (AWGN) channel. The exponential behavior of the error probability at high signal-to-noise ratio (SNR) is calculated and is supplemented by computer simulations. The results indicate that soft decision by successive erasures for binary transmission has properties not present in the nonbinary case. In the binary case the procedure is asymptotically optimum for increasing SNR's. On the nonbinary channel, however, the procedure is only capable of bridging part of the gap in performance between maximum-likelihood decoding (MLD) and hard decision decoding (HDD).

A method of using reliability information in one-step majority-logic decoders is presented. The idea is, basically, that the received binary digits are corrected in an order such that the least reliable digit is first corrected. With this method the error correction capability of the decoder is extended for large signal-to-noise ratios (SNR's). Different decoding algorithms are used when the number of orthogonal parity-check sums are even and odd, respectively. Computer simulations are presented for some short codes with binary antipodal signals on the additive white Gaussian noise channel.