Abstract- Iterative decoding of two-dimensional systematic convolutional codes has been termed “turbo ” (de)coding. Using log-likelihood algebra, we show that any decoder can he used which accepts soft inputs-including a priori values-and delivers soft outputs that can he split into three terms: the soft channel and a priori inputs, and the extrinsic value. The extrinsic value is used as an a priori value for the next iteration. Decoding algorithms in the log-likelihood domain are given not only for convolutional codes hut also for any linear binary systematic block code. The iteration is controlled by a stop criterion derived from cross entropy, which results in a minimal number of iterations. Optimal and suboptimal decoders with reduced complexity are presented. Simulation results show that very simple component codes are sufficient, block codes are appropriate for high rates and convolutional codes for lower rates less than 213. Any combination of block and convolutional component codes is possible. Several interleaving techniques are described. At a bit error rate (BER) of lo- * the performance is slightly above or around the bounds given by the cutoff rate for reasonably simple block/convolutional component codes, interleaver sizes less than 1000 and for three to six iterations. Index Terms- Concatenated codes, product codes, iterative decoding, “soft-inlsoft-out ” decoder, “turbo ” (de)coding.

Joint source-channel decoding is formulated as an estimation problem. The optimal solution is stated and it is shown that it is not feasible in many practical systems due to its complexity. Therefore, a novel iterative procedure for the approximation of the optimal solution is introduced, which is based on the principle of iterative decoding of turbo-codes. New analytical expressions for different types of information in the optimal algorithm are used to derive the iterative approximation.

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In this contribution, we provide an overview of the novel class of channel codes referred to as turbo codes, which have been shown to be capable of performing close to the Shannon Limit. We commence with a brief discussion on turbo encoding, and then move on to describing the form of the iterative decoder most commonly used to decode turbo codes. We then elaborate on various decoding algorithms that can be used in an iterative decoder, and give an example of the operation of such a decoder using the so-called Soft Output Viterbi Algorithm (SOVA). Lastly, the effect of a range of system parameters is investigated in a systematic fashion, in order to gauge their performance ramifications.

For practical communications which transmit finite blocks of source data over noisy channels, we question the common practice to compress (C) the source and then to add redundancy for error control. Rather we exploit the redundancy of the noncompressed source (NC) at the channel decoder by source-controlled channel decoding. For a simple binary Markov source and a Rayleigh fading channel we simulated in a fair comparison the 2 systems (C and NC) using an ARQ/FEC scheme with RCPC codes, LempelZiv compression and a modified Viterbi decoder. We indicate parameter regions where it is better not to compress. I. Introduction In today's digital storage and transmission systems for data, text, speech, audio, fax, image and video the source is compressed as much as possible and the resulting bits are transmitted. For noisy channels one has to add redundancy for error correction and detection. Supposedly this two step method is supported by Shannon's famous separation theorem [1], which states...

Abstract — We propose to use joint network-channel coding based on turbo codes for the multiple-access relay channel. Such a system can be used for the cooperative uplink for two mobile stations to a base station with the help of a relay. We compare the proposed system with a distributed turbo code for the relay channel and with a system which uses separate network-channel coding for the multiple-access relay channel. Simulation results confirm that the systems with network coding for the multipleaccess relay channel gain cooperative diversity compared to the system with the distributed turbo code for the relay channel. Moreover, the results show that joint network-channel coding outperforms separate network-channel coding. The reason for this is that the redundancy which is contained in the transmission of the relay can be exploited more efficiently with joint networkchannel coding. I.

We propose a macroscopic multistage compression system to provide progressive and robust transmission of images across noisy channels with varying statistics. Each stage encodes the residual image of the previous stage. The choice of source coder and transmission rate at each stage are design parameters. The multistage structure allows the use of efficient unequal error protection channel coding and introduces source redundancy to enable graceful degradation under severe channel conditions. Both bit errors and packet losses are considered. Specific examples are provided to demonstrate the performance of the proposed method. Keywords: robust image compression, packet erasure, multistage coding 1. INTRODUCTION Modern communication systems experience channel conditions that change over time due to such things as mobile receivers and transmitters or varying levels of multiuser interference. Handheld wireless devices, for example, must operate in severe channel conditions with limited ban...

In digital mobile communications efficient compression algorithms are needed to encode speech or audio signals. As the determined source parameters are highly sensitive to transmission errors, robust source and channel decoding schemes are required. This

This is a tutorial paper meant to introduce the reader to the new concept of turbo codes. This is a new and very powerful error correction technique which outperforms all previous known coding schemes. It can be used in any communication system where a significant power saving is required or the operating signal--to--noise ratio (SNR) is very low. Deep space communications, mobile satellite/cellular communications, microwave links, paging, etc., are some of the possible applications of this revolutionary coding technique. Part I of the paper discussed the history of turbo codes, why they are different from traditional convolutional/block codes, the turbo encoder structures and issues related to the interleaver design. Part II addresses the decoder architecture, the achievable performance for turbo codes for a wide range of coding rates and modulation techniques and discusses delay and implementation issues. 2 1 Introduction The optimum decoding of turbo codes is the maximum likeli...

Recent results indicate that the same turbo principle which delivers near to optimal strategies for channel coding, can be used to obtain very efficient source coding schemes. We investigate this issue applying ten Brink's EXIT chart analysis and show how this technique can be used to select the most efficient match of component codes and puncturing matrices to compress discrete memoryless sources. Aiming at perfect reconstruction at the decoder, i.e. lossless source coding, we present an encoding algorithm, which gradually removes the redundancy while checking the decodability of the compressed bit stream. This concept of decremental redundancy is dual to the principle of incremental redundancy that characterizes hybrid ARQ (Type II) communication protocols. Both principles can be combined when the channel is noisy.