The trellis complexity of convolutional codes

Convolutional codes have a natural, regular, trellis structure that facilitates the implementation of Viterbi's algorithm. Linear block codes also have a natural, though not in general a regular, “minimal” trellis structure, which allows them to be decoded with a Viterbi-like algorithm. In both cases, the complexity of an unenhanced Viterbi decoding algorithm can be accurately estimated by the number of trellis edge symbols per encoded bit. It would therefore appear that we are in a good position to make a fair comparison of the Viterbi decoding complexity of block and convolutional codes. Unfortunately, however, this comparison is somewhat muddled by the fact that some convolutional codes, the punctured convolutional codes, are known to have trellis representations which are significantly less complex than the conventional trellis. In other words, the conventional trellis representation for a convolutional code may not be the “minimal” trellis representation. Thus ironically, we seem to know more about the minimal trellis representation for block than for convolutional codes. We provide a remedy, by developing a theory of minimal trellises for convolutional codes. This allows us to make a direct performance-complexity comparison for block and convolutional codes. A by-product of our work is an algorithm for choosing, from among all generator matrices for a given convolutional code, what we call a trellis-canonical generator matrix, from which the minimal trellis for the code can be directly constructed. Another by-product is that in the new theory, punctured convolutional codes no longer appear as a special class, but simply as high-rate convolutional codes whose trellis complexity is unexpectedly small

Irregular Turbo Codes in Block-Fading Channels

We study irregular binary turbo codes over non-ergodic block-fading channels. We first propose an extension of channel multiplexers initially designed for regular turbo codes. We then show that, using these multiplexers, irregular turbo codes that exhibit a small decoding threshold over the ergodic Gaussian-noise channel perform very close to the outage probability on block-fading channels, from both density evolution and finite-length perspectives.Comment: to be presented at the IEEE International Symposium on Information Theory, 201

Capacity-achieving CPM schemes

The pragmatic approach to coded continuous-phase modulation (CPM) is proposed as a capacity-achieving low-complexity alternative to the serially-concatenated CPM (SC-CPM) coding scheme. In this paper, we first perform a selection of the best spectrally-efficient CPM modulations to be embedded into SC-CPM schemes. Then, we consider the pragmatic capacity (a.k.a. BICM capacity) of CPM modulations and optimize it through a careful design of the mapping between input bits and CPM waveforms. The so obtained schemes are cascaded with an outer serially-concatenated convolutional code to form a pragmatic coded-modulation system. The resulting schemes exhibit performance very close to the CPM capacity without requiring iterations between the outer decoder and the CPM demodulator. As a result, the receiver exhibits reduced complexity and increased flexibility due to the separation of the demodulation and decoding functions.Comment: Submitted to IEEE Transactions on Information Theor

Turbo space-time coded modulation : principle and performance analysis

A breakthrough in coding was achieved with the invention of turbo codes. Turbo codes approach Shannon capacity by displaying the properties of long random codes, yet allowing efficient decoding. Coding alone, however, cannot fully address the problem of multipath fading channel. Recent advances in information theory have revolutionized the traditional view of multipath channel as an impairment. New results show that high gains in capacity can be achieved through the use of multiple antennas at the transmitter and the receiver. To take advantage of these new results in information theory, it is necessary to devise methods that allow communication systems to operate close to the predicted capacity. One such method recently invented is space-time coding, which provides both coding gain and diversity advantage. In this dissertation, a new class of codes is proposed that extends the concept of turbo coding to include space-time encoders as constituent building blocks of turbo codes. The codes are referred to as turbo spacetime coded modulation (turbo-STCM). The motivation behind the turbo-STCM concept is to fuse the important properties of turbo and space-time codes into a unified design framework. A turbo-STCM encoder is proposed, which consists of two space-time codes in recursive systematic form concatenated in parallel. An iterative symbol-by-symbol maximum a posteriori algorithm operating in the log domain is developed for decoding turbo-STCM. The decoder employs two a posteriori probability (APP) computing modules concatenated in parallel; one module for each constituent code. The analysis of turbo-STCM is demonstrated through simulations and theoretical closed-form expressions. Simulation results are provided for 4-PSK and 8-PSK schemes over the Rayleigh block-fading channel. It is shown that the turbo-STCM scheme features full diversity and full coding rate. The significant gain can be obtained in performance over conventional space-time codes of similar complexity. The analytical union bound to the bit error probability is derived for turbo-STCM over the additive white Gaussian noise (AWGN) and the Rayleigh block-fading channels. The bound makes it possible to express the performance analysis of turbo-STCM in terms of the properties of the constituent space-time codes. The union bound is demonstrated for 4-PSK and 8-PSK turbo-STCM with two transmit antennas and one/two receive antennas. Information theoretic bounds such as Shannon capacity, cutoff rate, outage capacity and the Fano bound, are computed for multiantenna systems over the AWGN and fading channels. These bounds are subsequently used as benchmarks for demonstrating the performance of turbo-STCM

Τεχνικές Κωδικοποίησης Καναλιού με Έμφαση στους Συγκεραστικούς και στους Τούρμπο Κώδικες

Στην παρούσα διατριβή προτείνεται η σχεδίαση συγκεκριμένης κατηγορίας κωδίκων χαμηλής πολυπλοκότητας με κατάλληλη προσαρμογή του διαγράμματος trellis των διάτρητων συγκεραστικών κωδίκων. Στόχος είναι η βελτίωση της απόδοσης, με λογική αύξηση της πολυπλοκότητας του διαγράμματος trellis. Στα πλαίσια της έρευνας παρέχεται ένας ικανοποιητικός αριθμός νέων κωδίκων διαφόρων ρυθμών και τιμών πολυπλοκότητας. Σε πολλές περιπτώσεις διαπιστώνεται πως ελάχιστη αύξηση της πολυπλοκότητας μπορεί να οδηγήσει σε μεγάλη βελτίωση της απόδοσης, συγκριτικά με τους διάτρητους συγκεραστικούς κώδικες. Παρουσιάζεται επίσης μια μέθοδος σχεδίασης νέων ευέλικτων συγκεραστικών κωδίκων, συνδυάζοντας τις τεχνικές της απαλοιφής μονοπατιών του διαγράμματος trellis και της απαλοιφής κωδικών bit. Οι νέοι κώδικες μπορούν να μεταβάλλουν το ρυθμό τους και την πολυπλοκότητα του διαγράμματος trellis, και κατ' επέκτασιν την υπολογιστική πολυπλοκότητα της διαδικασίας αποκωδικοποίησης, οδηγώντας σε σχήματα κωδικοποίησης που κάνουν αποδοτικότερη διαχείριση των πόρων του συστήματος, εν συγκρίσει με τους κλασικούς συγκεραστικούς κώδικες μεταβλητού ρυθμού. Τέλος, εξετάζεται η δυνατότητα εφαρμογής των προαναφερθέντων αποτελεσμάτων χρησιμοποιώντας αναδρομικούς συγκεραστικούς κωδικοποιητές, οι οποίοι είναι κατάλληλοι ως περιεχόμενοι κωδικοποιητές των τούρμπο κωδίκων. Στόχος είναι η σχεδίαση αποδοτικών ευέλικτων τούρμπο σχημάτων κωδικοποίησης. Προσομοιώσεις δείχνουν ότι σε συγκεκριμένες περιοχές τιμών του σηματοθορυβικού λόγου, μια σημαντική μείωση της υπολογιστικής πολυπλοκότητας της αποκωδικοποίησης μπορεί ακόμα και να μειώσει το ρυθμό εσφαλμένων bit.In this thesis, a family of low complexity convolutional codes is constructed, by modifying appropriately the trellis diagram of punctured convolutional codes. The goal is to improve performance at the expense of a reasonable low increase of the trellis complexity. Many new convolutional codes of various code rates and values of complexity are provided. In many cases, a small increase in complexity can lead to a great improvement of performance, compared to punctured convolutional codes. Furthermore, a method is presented for designing new flexible convolutional codes, by combining the techniques of path pruning and puncturing. The new codes can vary their rate, as well as the complexity of their trellis diagram, and hence the computational complexity of the decoding algorithm, leading to coding schemes that manage more efficiently the system resources, compared to variable rate convolutional codes. Finally, the possibility of applying the aforementioned results using recursive convolutional encoders, which are used as constituent encoders in turbo codes, is investigated. The goal is to construct flexible turbo coding schemes. Simulation results indicate that in specific ranges of the SNR, a decrease in the computational complexity of the decoding procedure can even result to a decrease in the bit error rate

A survey of digital television broadcast transmission techniques

This paper is a survey of the transmission techniques used in digital television (TV) standards worldwide. With the increase in the demand for High-Definition (HD) TV, video-on-demand and mobile TV services, there was a real need for more bandwidth-efficient, flawless and crisp video quality, which motivated the migration from analogue to digital broadcasting. In this paper we present a brief history of the development of TV and then we survey the transmission technology used in different digital terrestrial, satellite, cable and mobile TV standards in different parts of the world. First, we present the Digital Video Broadcasting standards developed in Europe for terrestrial (DVB-T/T2), for satellite (DVB-S/S2), for cable (DVB-C) and for hand-held transmission (DVB-H). We then describe the Advanced Television System Committee standards developed in the USA both for terrestrial (ATSC) and for hand-held transmission (ATSC-M/H). We continue by describing the Integrated Services Digital Broadcasting standards developed in Japan for Terrestrial (ISDB-T) and Satellite (ISDB-S) transmission and then present the International System for Digital Television (ISDTV), which was developed in Brazil by adopteding the ISDB-T physical layer architecture. Following the ISDTV, we describe the Digital Terrestrial television Multimedia Broadcast (DTMB) standard developed in China. Finally, as a design example, we highlight the physical layer implementation of the DVB-T2 standar

Large constraint length high speed viterbi decoder based on a modular hierarchial decomposition of the deBruijn graph

A method of formulating and packaging decision-making elements into a long constraint length Viterbi decoder which involves formulating the decision-making processors as individual Viterbi butterfly processors that are interconnected in a deBruijn graph configuration. A fully distributed architecture, which achieves high decoding speeds, is made feasible by novel wiring and partitioning of the state diagram. This partitioning defines universal modules, which can be used to build any size decoder, such that a large number of wires is contained inside each module, and a small number of wires is needed to connect modules. The total system is modular and hierarchical, and it implements a large proportion of the required wiring internally within modules and may include some external wiring to fully complete the deBruijn graph. pg,14