Chair of Information and Coding Theory

Turbo Processing


In digital communication systems, frequently different processing stages are concatenated. For example, (i) a source encoder is followed by a channel encoder, (ii) a channel encoder is followed by a modulator, (iii) or two channel encoders are concatenated, among many other scenarios. This motivation has served as a starting point towards the invention of the soft-output Viterbi algorithm (SOVA) [1]. The SOVA is a maximum-likelihood sequence estimator, which supplements each binary decision by a reliability value. In other words, the SOVA accepts soft inputs from the previous processing stage and delivers soft outputs to the next processing stage - like a digital filter [1]. The latter insight has triggered the development of the famous Turbo codes by Claude Berrou and Alain Glavieux [2], and independently and in parallel the development of iterative decoding of block product codes [3,4]. An alternative of the SOVA is the Bahl-Cocke-Jelinek-Raviv algorithm, for which we proposed a low-cost implementation [5]. This solution became a benchmark for the next decade.

In the mean time, exchange of reliability values in the form of log-likelihood values between concatenated decoders/detectors and even inside decoders/detectors is common. Message passing is, for example, applied in any low-density parity-check (LDPC) decoder as well as in the decoding process of polar codes. Currently, these are the most popular channel code families worldwide.

Soft information, however, is not just useful for decoding/detection purposes. In [6], we proposed using log-likelihood values in Monte Carlo bit error rate simulations. Rather than counting bit errors as usual, one may use log-likelihood values to reduce the simulation time and/or to obtain more reliable decisions.Afterwards, we applied soft information for the purpose of information combining [7,8], for the purpose of enhancing EXIT-chart-based analyses [9], and as a stopping criterion in iterative processing.

Soft Monte Carlo bit error rate simulations have an interesting property: the estimates are based on the magnitude of the log-likelihood value [6]. In other words, the decoded/detected bits are not compared with the transmitted bits. This side-effect can be employed for online processing in an elegant way, because the receiver is able to calculate the reliability of each individual bit decision without knowledge of the transmitted data stream. In [10,11,12], the concept has been used in order to avoid an additional cyclic redundancy check in an automatic repeat request (ARQ) scenario.

This summary of three decades of own research indicates that soft information is a central theme throughout many contributions developed at the chair and even before at the German Aerospace Research Establishment (DLR) in Oberpfaffenhofen. Several other own contributions are based on soft information and iterative processing, including interleave-division multiple access and superposition modulation.


Selected References:

[1] J. Hagenauer and P. Hoeher, "A Viterbi algorithm with soft-decision outputs and its applications," in Proc. IEEE GLOBECOM '89, Dallas, Texas, pp. 1680-1686, Nov. 1989.

[2] C. Berrou, A. Glavieu, Reflections on the Prize Paper: "Near optimum error-correcting coding and decoding: turbo codes," IEEE Information Theory Society Newsletter, vol. 48, no. 2, June 1998.

[3] J.H. Lodge, P. Hoeher, and J. Hagenauer, "The decoding of multidimensional codes using separable MAP `filters'," in Proc. 16th Biennial Symposium on Communication, Kingston, Canada, pp. 343-346, May 1992.

[4] J.H. Lodge, R. Young, P. Hoeher, and J. Hagenauer, "Separable MAP 'filters' for the decoding of product and concatenated codes," in Proc. IEEE ICC '93, Geneva, Switzerland, pp. 1740-1745, May 1993.

[5] P. Robertson, E. Villebrun, and P. Hoeher, "A comparison of optimal and sub-optimal MAP decoding algorithms operating in the log-domain," in Proc. IEEE Int. Conference on Communications (ICC '95)}, Seattle, Washington, pp. 1009-1013, June 1995.

[6] P. A. Hoeher, U. Sorger, and I. Land, "Log-likelihood values and Monte Carlo simulation - Some fundamental results," in Proc. Int. Symp. on Turbo Codes & Related Topics, Brest, France, pp. 43-46, Sep. 2000.

[7] I. Land, S. Huettinger, P. A. Hoeher, and J. Huber, "Bounds on information combining," IEEE Trans. Inform. Theory, vol.51, no. 2, pp. 612-619, Feb. 2005.

[8] I. Land, Reliability Information in Channel Decoding: Practical Aspects and Information Theoretical Bounds. Dissertation, Faculty of Engineering, University of Kiel, 2005.

[9] I. Land, P. A. Hoeher, and S. Gligorevic, "Computation of symbol-wise mutual information in transmission systems with LogAPP decoders and application to EXIT charts," in Proc. Int. ITG Conference on Source and Channel Coding (SCC '04), Erlangen, Germany, pp. 195-202, Jan. 2004.

[10] J. Ch. Fricke, M. M. Butt, and P. A. Hoeher, "Quality-oriented adaptive forwarding for wireless relaying," IEEE Communications Letters, vol. 12, pp. 200-202, Mar. 2008.

[11] J. Ch. Fricke and P. A. Hoeher "Reliability-based retransmission criteria for hybrid ARQ," IEEE Trans. Commun., vol. 57, no. 8, pp. 2181-2184, Aug. 2009.

[12] J. Ch. Fricke, Reliability-Based Cross-Layer Design of Digital Transmission Systems. Dissertation, Faculty of Engineering, University of Kiel, 2009.


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