Joint source and channel coding using turbo codes over rings

Turbo codes are a practical solution for achieving large coding gains. We present a new turbo coding scheme where the component codes are convolutional codes (CCs) over the ring of integers modulo M, with M being the alphabet size of the source encoder. The a priori knowledge of the source statistics is used during the iterative decoding procedure for improved decoder performance. As an example of application, we examine differential pulse code modulation (DPCM) encoded image transmission     

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.     

Multilevel turbo coding with short interleavers

The impact of the interleaver, embedded in the encoder for a parallel concatenated code, called the turbo code, is studied. The known turbo codes consist of long random interleavers, whose purpose is to reduce the value of the error coefficients. It is shown that an increased minimum Hamming distance can be obtained by using a structured interleaver. For low bit-error rates (BERs), we show that the performance of turbo codes with a structured interleaver is better than that obtained with a random interleaver. Another important advantage of the structured interleaver is the short length required, which yields a short decoding delay and reduced decoding complexity (in terms of memory). We also consider the use of turbo codes as component codes in multilevel codes. Powerful coding structures that consist of two component codes are suggested. Computer simulations are performed in order to evaluate the reduction in coding gain due to suboptimal iterative decoding. From the results of these simulations we deduce that the degradation in the performance (due to suboptimal decoding) is very small     

Combined turbo coding and unitary space-time modulation

Space-time coding is well understood for high data rate communications over wireless channels with perfect channel state information. On the other hand, channel coding for multiple transmit antennas when channel state information is unknown has only received limited attention. A new signaling scheme, named unitary space-time modulation, has been proposed for the latter case. In this paper, we consider the use of turbo coding together with unitary space-time modulation. We demonstrate that turbo coded space-time modulation systems are well suited to wireless communication systems when there is no channel state information, in the sense that the turbo coding improves the bit error rate (BER) performance of the system considerably. In particular, we observe that the turbo-coded system provides 10-15 dB coding gain at a BER of 10/sup -5/ compared to the unitary space-time modulation for various transmit and receive antenna diversity cases.     

Joint source-channel turbo coding for binary Markov sources

We investigate the construction of joint source-channel (JSC) turbo codes for the reliable communication of binary Markov sources over additive white Gaussian noise and Rayleigh fading channels. To exploit the source Markovian redundancy, the first constituent turbo decoder is designed according to a modified version of Berrou's original decoding algorithm that employs the Gaussian assumption for the extrinsic information. Due to interleaving, the second constituent decoder is unable to adopt the same decoding method; so its extrinsic information is appropriately adjusted via a weighted correction term. The turbo encoder is also optimized according to the Markovian source statistics and by allowing different or asymmetric constituent encoders. Simulation results demonstrate substantial gains over the original (unoptimized) Turbo codes, hence significantly reducing the performance gap to the Shannon limit. Finally, we show that our JSC coding system considerably outperforms tandem coding schemes for bit error rates smaller than 10/sup -4/, while enjoying a lower system complexity.     

Improving turbo code error performance by multifold coding

This article presents a simple turbo coding technique to improve the error performance of a convolutional rate-1/3 turbo code by shaping its weight spectrum closer to the binomial weight distribution of a random code. This technique can be applied to both symmetric and asymmetric rate 1/3 turbo codes to achieve additional coding gain     

Lossy source coding

Lossy coding of speech, high-quality audio, still images, and video is commonplace today. However, in 1948, few lossy compression systems were in service. Shannon introduced and developed the theory of source coding with a fidelity criterion, also called rate-distortion theory. For the first 25 years of its existence, rate-distortion theory had relatively little impact on the methods and systems actually used to compress real sources. Today, however, rate-distortion theoretic concepts are an important component of many lossy compression techniques and standards. We chronicle the development of rate-distortion theory and provide an overview of its influence on the practice of lossy source coding     

Capacity-approaching turbo coding and iterative decoding for relay channels

In this paper, we design turbo-based coding schemes for relay systems together with iterative decoding algorithms. In the proposed schemes, the source node sends coded information bits to both the relay and the destination nodes, while the relay simultaneously forwards its estimate for the previous coded block to the destination after decoding and re-encoding. The destination observes a superposition of the codewords and uses an iterative decoding algorithm to estimate the transmitted messages. Different from the block-by-block decoding techniques used in the literature, this decoding scheme operates over all the transmitted blocks jointly. Various encoding and decoding approaches are proposed for both single-input single-output and multi-input multi-output systems over several different channel models. Capacity bounds and information-rate bounds with binary inputs are also provided, and it is shown that the performance of the proposed practical scheme is typically about 1.0-1.5 dB away from the theoretical limits, and a remarkable advantage can be achieved over the direct and multihop transmission alternatives.     

A novel ARQ technique using the turbo coding principle

A novel automatic repeat request (ARQ) technique based on the turbo coding principle is presented. The technique uses the log-likelihood ratios generated by the decoder during a previous transmission as a priori information when decoding retransmissions. Simulation results show a significant decrease in frame error rate, especially at low-to-moderate E_b/N₀     

Parallel turbo coding interleavers: avoiding collisions in accessesto storage elements

High-speed, low latency convolutional turbo codes require a parallel decoder architecture. To maximise the gain in speed, the interleaver also should have a parallel structure. Here, a class of optimum parallel interleavers regarding the access to storage elements is presented. They combine regularity (easy implementation) with no latency in data transfer between the decoder module and intrinsic/extrinsic values memories, and show excellent BER performance     

Partial turbo detection with reduced complexity

In this article, we propose a novel method for reducing the complexity of the turbo detector MAP (maximum a posteriori). The basic idea consists in turbo detecting a part of intersymbol interference (ISI) after decomposing the channel in two parts. We show that we can reduce the trellis complexity in the turbo process at a certain cost, i.e. performance loss.     

Bandwidth‐efficient turbo coding over Rayleigh fading channels

Introduced in 1993, turbo codes can achieve high coding gains close to the Shannon limit. In order to design power and bandwidth‐efficient coding schemes, several approaches have been introduced to combine high coding rate turbo codes with multilevel modulations. The coding systems thus obtained have been shown to display near‐capacity performance over additive white Gaussian noise (AWGN) channels. For communications over fading channels requiring large coding gain and high bandwidth efficiency, it is also interesting to study bit error rate (BER) performance of turbo codes combined with high order rectangular QAM modulations. To this end, we investigate, in this paper, error performance of several bandwidth‐efficient schemes designed using the bit‐interleaved coded modulation approach that has proven potentially very attractive when powerful codes, such as turbo codes, are employed. The structure of these coding schemes, termed ‘bit‐interleaved turbo‐coded modulations’ (BITCMs), is presented in a detailed manner and their BER performance is investigated for spectral efficiencies ranging from 2 to 7 bit/s/Hz. Computer simulation results indicate that BITCMs can achieve near‐capacity performance over Rayleigh fading channels, for all spectral efficiencies considered throughout the paper. It is also shown that the combination of turbo coding and rectangular QAM modulation with Gray mapping constitutes inherently a very powerful association, since coding and modulation functions are both optimized for operation in the same signal‐to‐noise ratio region. This means that no BER improvement is obtainable by employing any other signal constellation in place of the rectangular ones. Finally, the actual influence of the interleaving and mapping functions on error performance of BITCM schemes is discussed. Copyright © 2002 John Wiley & Sons, Ltd.     

Unit-rate complex orthogonal space-time block code concatenated with turbo coding

Space-Time Block （STB） code has been an effective transmit diversity technique for combating fading due to its orthogonal design, simple decoding and high diversity gains. In this paper, a unit-rate complex orthogonal STB code for multiple antennas in Time Division Duplex （TDD） mode is proposed. Meanwhile, Turbo Coding （TC） is employed to improve the performance of proposed STB code further by utilizing its good ability to combat the burst error of fading channel. Compared with full-diversity multiple antennas STB codes, the proposed code can implement unit rate and partial diversity; and it has much smaller computational complexity under the same system throughput. Moreover, the application of TC can effectively make up for the performance loss due to partial diversity. Simulation results show that on the condition of same system throughput and concatenation of TC, the proposed code has lower Bit Error Rate （BER） than those full-diversity codes.     

Gaussian multiterminal source coding

In this paper, we consider the problem of separate coding for two correlated memoryless Gaussian sources. We determine the rate-distortion region in the special case when one source provides partial side information to the other source. We also show that the previously obtained inner region of the rate-distortion region is partially tight. A rigorous proof of the direct coding theorem is also given     

Weak variable-length source coding

Given a general source X={Xⁿ}_n=1^∞ , source coding is characterized by a pair (φ_n, ψ_n) of encoder φ_n, and decoder ψ_n , together with the probability of error ε_n≡Pr{ψ_n(φ_n(Xⁿ ))≠Xⁿ}. If the length of the encoder output φ _n(Xⁿ) is fixed, then it is called fixed-length source coding, while if the length of the encoder output φ_n (Xⁿ) is variable, then it is called variable-length source coding. Usually, in the context of fixed-length source coding the probability of error ε_n is required to asymptotically vanish (i.e., lim_n→∞ε_n=0), whereas in the context of variable-length source coding the probability of error ε_n is required to be exactly zero (i.e., ε_n =0∀n=1, 2, ...). In contrast to these, we consider the problem of variable-length source coding with asymptotically vanishing probability of error (i.e., lim_n→∞ε_n =0), and establish several fundamental theorems on this new subject     

The source coding game

The encoding of a source whose probability distribution varies arbitrarily from letter to letter is considered. The problem is formulated as a two-person statistical game. The exponential rate of growth with block length of the minimum number of codewords needed to achieve a specified fidelity with respect to a single-letter distortion measure is determined. The rate distortion function of a source whose statistics are entirely unknown is obtained as a special case. The dependence of the results on the rules under which the game is played also is studied. The analysis is based on a refinement of the usual random coding argument for sources which sheds new light on the significance of the term that decays at a doubly exponential rate with block length.     

Adaptive distributed source coding

We consider distributed source coding in the presence of hidden variables that parameterize the statistical dependence among sources. We derive the Slepian-Wolf bound and devise coding algorithms for a block-candidate model of this problem. The encoder sends, in addition to syndrome bits, a portion of the source to the decoder uncoded as doping bits. The decoder uses the sum-product algorithm to simultaneously recover the source symbols and the hidden statistical dependence variables. We also develop novel techniques based on density evolution (DE) to analyze the coding algorithms. We experimentally confirm that our DE analysis closely approximates practical performance. This result allows us to efficiently optimize parameters of the algorithms. In particular, we show that the system performs close to the Slepian-Wolf bound when an appropriate doping rate is selected. We then apply our coding and analysis techniques to a reduced-reference video quality monitoring system and show a bit rate saving of about 75% compared with fixed-length coding.     

Bit rates in audio source coding

The goal is to introduce and solve the audio coding optimization problem. Psychoacoustic results such as masking and excitation pattern models are combined with results from rate distortion theory to formulate the audio coding optimization problem. The solution of the audio optimization problem is a masked error spectrum, prescribing how quantization noise must be distributed over the audio spectrum to obtain a minimal bit rate and an inaudible coding errors. This result cannot only be used to estimate performance bounds, but can also be directly applied in audio coding systems. Subband coding applications to magnetic recording and transmission are discussed in some detail. Performance bounds for this type of subband coding system are derived     

Sample converses in source coding theory

The rate and distortion performance of a sequence of codes along a sample sequence of symbols generated by a stationary ergodic information source are studied. Two results are obtained: (1) the source sample sequence is encoded by an arbitrary sequence of block codes which operate at a fixed rate level R, and a sample converse is obtained which states that, with probability one, the lower limit of the code sample distortions is lower bounded by D(R), the value of the distortion rate function at R; (2) the source sample sequence is encoded by an arbitrary sequence of variable-rate codes which operate at a fixed distortion level D, and a sample converse is obtained which states that, with probability one, the lower limit of the code sample rates is lower bounded by R(D), the value of the rate distortion function at D. A novel ergodic theorem is used to obtain both sample converses