On trellis codes with a delay processor and a signal mapper

It is already known that a trellis code T, which is constructed by using the encoder of a convolutional code C with short constraint length followed by a delay processor and a signal mapper, is equivalent to a trellis code with large constraint length. In this paper, we derive a new lower bound on the free distance of T, which, in some cases, is better than the previously derived bound. Moreover, instead of the decoding used in earlier publications, we apply iterative decoding on both tailbiting and zero-tail representations of T to take advantage of the new lower bound and, in the meantime, to decrease the associated error coefficient caused by the decoding used in earlier publications. Comparisons among various designs of such a trellis code and some well-known coding methods are also provided.     

A trellis coded modulation scheme constructed from block codedmodulation with interblock memory

Proposes a new trellis coded modulation scheme which is constructed by combining a convolutional code and a variation of block coded modulation called block coded modulation with interblock memory. In the proposed scheme, each coded multidimensional signal point has a kind of two-fold dependency on other coded multidimensional signal points. In addition to the dependency on other coded multidimensional signal points described by the trellis of a convolutional code, each coded multidimensional signal point has another form of dependency on one previously coded multidimensional signal point. The additional dependency comes from the design of block coded modulation with interblock memory     

Assembled space-time turbo trellis codes

A novel full rate space-time turbo trellis code, referred to as an assembled space-time turbo trellis code (ASTTTC), is presented in this paper. For this scheme, input information binary sequences are first encoded using two parallel concatenated convolutional encoders. The encoder outputs are split into four parallel streams and each of them is modulated by a QPSK modulator. The modulated symbols are assembled by a predefined linear function rather than punctured as in the standard schemes. This results in a lower code rate and a higher coding gain over time-varying fading channels. An extended two-dimensional (2-D) log-MAP (maximum a posteriori probability) decoding algorithm, which simultaneously calculates two a posteriori probabilities (APP), is developed to decode the proposed scheme. Simulation results show that, under the same conditions, the proposed code considerably outperforms the conventional space-time turbo codes over time-varying fading channels.     

A geometric construction procedure for geometrically uniformtrellis codes

The problem of maximizing the minimum free squared Euclidean distance of a trellis code is developed from a geometric point of view. This approach provides a new way of constructing constellations for trellis coding. A decomposition of the trellis topology leads to a systematic construction of signal sets and generators for geometrically uniform trellis codes. An algorithm is proposed to construct geometrically uniform trellis codes, and examples show how to obtain large free distance trellis codes. This approach unifies the construction of convolutional codes over the binary field and trellis codes over the real field     

Joint Source and Channel Coding using Punctured Ring Convolutional Coded CPM

In this paper, a novel trellis source encoding scheme based on punctured ring convolutional codes is presented. Joint source and channel coding (JSCC) using trellis coded continuous phase modulation (CPM) with punctured convolutional codes over rings is investigated. The channels considered are the additive white gaussian noise (AWGN) channel and the Rayleigh fading channel. Optimal soft decoding for the proposed JSCC scheme is studied. The soft decoder is based on the a posteriori probability (APP) algorithm for trellis coded CPM with punctured ring convolutional codes. It is shown that these systems with soft decoding outperform the same systems with hard decoding especially when the systems operate at low to medium signal-to-noise ratio (SNR). Furthermore, adaptive JSCC approaches based on the proposed source coding scheme are investigated. Compared with JSCC schemes with fixed source coding rates, the proposed adaptive approaches can achieve much better performance in the high SNR region. The novelties of this work are the development of a trellis source encoding method based on punctured ring convolutional codes, the use of a soft decoder, the APP algorithm for the combined systems and the adaptive approaches to the JSCC problem.     

AMR的信道编码设计及其DSP实现

对于超短波移动通信系统中AMR语音业务的传输，提出了基于码率兼容的删余卷积码和码率兼容的删余Turbo码这2种可变的不等差错保护信道编码方案。通过设计最优的删余方案和合适的速率匹配方法，这2种不等差错保护方案都可达到类内不等保护的目的，将对具有不同重要性的信源比特的作更精确不等保护。并基于DSP芯片TMS320C6416实时实现了这2种方案对AMR语音的不等差错保护。实验结果表明，这种方法具有合理的系统复杂度和很短的处理延时，适合于语音业务的应用。     

Interblock memory for turbo coding

We investigate a binary code, which is implemented by serially concatenating a multiplexer, a multilevel delay processor, and a signal mapper to a binary turbo encoder. To achieve improved convergence behavior, we modify the binary code by passing only a fraction of the bits in the turbo code through the multilevel delay processor and the signal mapper. Two decoding methods are discussed and their performances are evaluated.     

Turbo coded multiple-antenna systems for near-capacity performance

For a turbo coded BLAST (Bell LAbs Space-Time architecture) system with N_t transmit antennas and N_r receive antennas, there is a significant gap between its detection threshold and the capacity in case N_t > N_r. In this paper, we show that by introducing a convolutional interleaver with block delay between the BLAST mapper and the turbo encoder, the threshold can be improved. Near-capacity thresholds can be achieved for some cases. To take advantage of the low detector complexity in Alamouti STBC (space-time block code), we also investigate a STBC system, which is the concatenation of the Alamouti STBC with a turbo trellis coded modulation. By using a proper labelling and adding a convolutional interleaver with block delay to such a STBC system, we achieve both lower error floors and lower thresholds.     

Coded QAM using a binary convolutional code

As an alternative to trellis coding, a binary convolutional code is considered for use with such nonbinary modulation schemes as quadrature amplitude modulation (QAM). A Gray code is used to map the encoder output to the M-ary QAM constellation. The focus is on the design of 16-ary coded QAM with a rate 3/4 punctured convolutional code of a constraint length 7. A quantized binary metric generation method is proposed and shown to be suboptimum as compared to the direct use of a M-ary unquantized metric. Impressive coding gains and bandwidth efficiency are shown in comparison with uncoded systems     

On Trellis Coded Noncoherent Space-Time Modulation

Unitary space-time modulation (USTM) is well-tailored for noncoherent space-time modulation. Trellis coded USTM (TC-USTM) can obtain significant coding gains over uncoded USTM for the noncoherent block fading channel. Conventional TC-USTM schemes expand the signal set of uncoded USTM by a factor of two. In this letter, we propose a new TC-USTM scheme in which the size of USTM set is not limited to be just double for uncoded USTM. However, in TC-USTM schemes, because signals of the same trellis branch are transmitted over the same fading coefficients, one trellis branch can only obtain one temporal diversity. In this letter, we also propose a new trellis coded noncoherent space-time modulation scheme by interleaving space-time signals. The proposed scheme can enlarge temporal diversity at the price of increased complexity and delay. Simulation results demonstrate the excellent error performances of codes found by computer searches for both schemes.     

Space–Time Trellis Codes Based on Channel-Phase Feedback

Space-time coding (STC) has been proposed recently for multiple-antenna wireless communication systems. Most of the proposed STC schemes use the assumption that either no channel-state information, or the channel mean/covariance information, is available at the transmitter. In this paper, we propose a new STC scheme for a closed-loop transmission system, where quantized channel-phase information is available at the transmitter. A new performance criterion is derived for the quasi-static fading channel. This design criterion is then used to construct a new class of space-time trellis codes (STTCs). The proposed code construction is based on the concatenation of a standard multiple trellis-coded modulation outer code with an inner code. The inner code is selected from a series of inner codes using the channel-phase feedback. The series of inner codes are constructed based on the systematic set partitioning of several classes of space-time signal designs. Simulation results show significant performance improvement over the other STTCs in the literature. In addition, the proposed coding scheme enjoys low peak-to-average-power ratio, simple decoding, and power-efficient low-cost implementation     

Diagonal block space-time code design for diversity and coding advantage over flat fading channels

The potential promised by multiple transmit antennas has raised considerable interest in space-time coding for wireless communications. In this paper, we propose a systematic approach for designing space-time trellis codes over flat fading channels with full antenna diversity and good coding advantage. It is suitable for an arbitrary number of transmit antennas with arbitrary signal constellations. The key to this approach is to separate the traditional space-time trellis code design into two parts. It first encodes the information symbols using a one-dimensional (M,1) nonbinary block code, with M being the number of transmit antennas, and then transmits the coded symbols diagonally across the space-time grid. We show that regardless of channel time-selectivity, this new class of space-time codes always achieves a transmit diversity of order M with a minimum number of trellis states and a coding advantage equal to the minimum product distance of the employed block code. Traditional delay diversity codes can be viewed as a special case of this coding scheme in which the repetition block code is employed. To maximize the coding advantage, we introduce an optimal construction of the nonbinary block code for a given modulation scheme. In particular, an efficient suboptimal solution for multilevel phase-shift-keying (PSK) modulation is proposed. Some code examples with 2-6 bits/s/Hz and two to six transmit antennas are provided, and they demonstrate excellent performance via computer simulations. Although it is proposed for flat fading channels, this coding scheme can be easily extended to frequency-selective fading channels.     

Two 16-state, rate R=2/4 trellis codes whose free distances meetthe Heller bound

For rate R=1/2 convolutional codes with 16 states there exists a gap between Heller's (1968) upper bound on the free distance and its optimal value. This article reports on the construction of 16-state, binary, rate R=2/4 nonlinear trellis and convolutional codes having d _free=8; a free distance that meets the Heller upper bound. The nonlinear trellis code is constructed from a 16-state, rate R=1/2 convolutional code over Z₄ using the Gray map to obtain a binary code. Both convolutional codes are obtained by computer search. Systematic feedback encoders for both codes are potential candidates for use in combination with iterative decoding. Regarded as modulation codes for 4-PSK, these codes have free squared Euclidean distance d_{E, free}²=16     

Trellis-coded constant-envelope modulations with linear receivers

We present two multilevel constant-envelope continuous-phase modulation (CPM) schemes with four-dimensional (4-D) trellis coding. The receiver is composed of a simple quadrature demodulator, followed by a symbol-rate sampler and a Viterbi decoder matched to the code trellis. The first modulation is a quaternary CPM scheme whose phase transitions over a symbol interval are those of π/4-shift quaternary phase-shift keying (QPSK). The demodulator filter is optimized so as to minimize the combined effect of intersymbol interference (ISI) and noise at the decision instants. We use Wei's (1987) 16-state 4-D trellis code, and redefine the set partitioning tree so as to maintain the same minimum distance between parallel transitions as in quadrature amplitude modulation (QAM) signal sets. The resulting modulation outperforms minimum-shift keying (MSK) by as much as 3.5 dB, in addition to reducing the 30-dB signal bandwidth by 20%. Next, we introduce an octonary (8-level) CPM scheme whose phase transitions are those of π/8-shift 8PSK. The same trellis code and receive filter optimization are also applied to this modulation which is shown to achieve better error rate performance than MSK, while saving some 60% of the transmitted signal bandwidth     

Concatenated codes for fading channels based on recursive space-time trellis codes

We propose a class of codes which combine the principles of turbo coding and space-time trellis codes. It is first shown that several classes of space-time codes have an equivalent recursive realization. This fact is then exploited to design serial concatenated coding schemes with an outer code, interleaver, and an inner recursive space-time encoder. Two solutions are proposed in this paper - the use of convolutional outer codes aimed mainly to improve the power efficiency and the use of very high-rate outer codes to obtain significant improvement in power efficiency with a marginal decrease in spectral efficiency. We show that single parity check based turbo product codes are a good candidate for very high-rate outer codes. Finally, we propose an automatic repeat request scheme based on recursive realizations of space-time codes and show that the proposed scheme provides significant reduction in frame error rate.     

A trellis code construction and coding theorem for stationary Gaussian sources (Corresp.)

For stationary discrete-time Gaussian sources and the squared-error distortion measure, a trellis source code is constructed. The encoder consists of a Karhunen-Loeve transform on the source output followed by a search on a trellis structured code, where the decoder is a time-variant nonlinear filter. The corresponding code theorem is proved using the random coding argument. The proof technique follows that of Viterbi and Omura, who proved the trellis coding theorem for memoryless sources. The resultant coding scheme is implementable and applicable at any nonzero rate to a stationary Gaussian source with a bounded and continuous power spectrum. Therefore. for stationary sources, it is more general than Berger's tree coding scheme, which is restricted to autoregressive Gaussian sources in a region of high rate (low distortion).     

Practical coding for QAM transmission of HDTV

It is demonstrated how modulation schemes based on QPSK can be directly incorporated into QAM-based systems. It is argued that this leads directly to an easily implementable structure that is both efficient in bandwidth and data reliability. It is contended that the correct solution to the concatenated coding problem for HDTV transmission is to simply extend the modulation codes developed for QPSK-to-QAM modulation. In nonconcatenated situations, a trellis code based on a binary code at rate 2/3 is usually best. However, this is not the case for higher error rates at the output of the trellis decoder (e.g., when a symbol error correcting decoder follows as a concatenated code). The reason for this follows from an analysis of the effect of the number of nearest neighbors on the error rate. A four-way partition of QAM is a natural extension of QPSK modulation; it is a simple matter to incorporate any good QPSK code into a trellis coding scheme for QAM modulation. A concatenated coding scheme based on QPSK trellis codes and symbol error correcting coding is proposed. An example is presented to show the advantages of this approach     

Efficient computation of trellis code generating functions

For trellis codes, generating function techniques provide the distance spectrum and a union bound on bit-error rate. The computation of the generating function of a trellis code may be separated into two stages. The first stage reduces the number of states as much as possible using low-complexity approaches. The second stage produces the generating function from the reduced-state diagram through some form of matrix inversion, which has a relatively high complexity. In this paper, we improve on the amount of state reduction possible during the low-complexity first stage. We also show that for a trellis code that is a linear convolutional code followed by a signal mapper, the number of states may always be reduced from N/sup 2/ to ((N/sup 2/-N)/2)+1 using low-complexity techniques. Finally, we analytically compare the complexity of various matrix inversion techniques and verify through simulation that the two-stage approach we propose has the lowest complexity. In an example, the new technique produced the union bound in about half the time required by the best algorithm already in the literature.     

A Combined Interleaving Technique for Trellis Coded MPSK Systems in Rayleigh Fading Channels

Freedom of mobility is the latesttrend in the evolution of digital communicationsystems. In these systems bandwidth and powerconstraints limit the mobility of the users. TCM(trellis coded modulation) is a combined coding andmodulation scheme which increases the productivity ofa digital communication system without increasing thetransmitted power or the required bandwidth. A mobilecommunication channel is affected from noise andfading because of the multipath propagation. On aRayleigh fading channel, coding should be used withtechniques which uncorrelate the received energy ofeach consecutive coded symbol. Interleaving is one ofthese techniques and used to make burst errors intorandom errors which can be corrected by errorcorrecting codes. In this paper, the trellis codingsystem which combines a regular convolutional encoder,bit interleaver, coordinate interleaver, and anappropriate decoder is considered. The analytical biterror probability upper bounds are derived for the8-PSK TCM system whose diversity is increased by usinga regular 2/3 rate convolutional code followed bythree bit interleavers and a 8-PSK signal mapperfollowed by two coordinate interleavers. Theanalytical and simulation results show that toincrease the diversity of the trellis coded M-PSKsystems in Rayleigh fading channels is the primary keyfor reliable transmission of high quality voice anddigital data.     

An extensive search for good punctured rate-k/(k+1) recursive convolutional codes for serially concatenated convolutional codes

In many practical applications requiring variable-rate coding and/or high-rate coding for spectral efficiency, there is a need to employ high-rate convolutional codes (CC), either by themselves or in a parallel or serially concatenated scheme. For such applications, in order to keep the trellis complexity of the code constant and to permit the use of a simplified decoder that can accommodate multiple rates, a mother CC is punctured to obtain codes with a variety of rates. This correspondence presents the results of extensive search for optimal puncturing patterns for recursive convolutional codes leading to codes of rate k/(k+1) (k an integer) to be used in serially concatenated convolutional codes (SCCC). The code optimization is in the sense of minimizing the required signal-to-noise ratio (SNR) for two target bit-error rate (BER) and two target frame-error rate (FER) values. We provide extensive sample simulation results for rate-k/(k+1) SCCC codes employing our optimized punctured CC.