Digital Signal Processing and System Theory

Talk Norbert Görtz

How significant are your bits?

Date: 16.05.2011, 17:15 h - 18:15 h,
Room: Aquarium

Univ. Prof. Dr.-Ing. Norbert Görtz
Vienna University of Technology, Vienna, Austria


It is well-known that there is no way to build error-correction channel coding at limited block size (i.e., any practical channel coding scheme) that will guarantee a data-bit error probability of "zero" after decoding. However, "symbol-by-symbol" decoders can be realised by "soft-output" algorithms leading to different reliabilities of the data bit decisions for any given input from the channel. Those soft-values have been very successfully used in iterative channel decoding, which started with the invention of Turbo codes in the 1990s and is now the basis for every practical (de)coding scheme that performs close to the theoretical limits of information theory - exactly the theory that itself does not know a quantitative concept of "reliability".

The "significance" of source data can be seen as a transmitter-based counterpart of "reliability". As yet, it has, however, only been exploited by rather simple and often heuristic system designs. A major example is unequal error protection, which is used, e.g., in mobile radio: the source coding scheme, which is necessarily non-ideal (again due to limited block size), is known to generate bits that have different significances for the quality at the decoder output. Hence, the data bits are grouped into classes that are protected by several channel-codes with different degrees of error protection. Such a fixed code design is, however, only possible with average bit-significances, although the bit-significances change very dynamically from one data block to another. Hence, one could try to systematically quantify the "significances" of source-coded data realisations and exploit the resulting real numbers in subsequent steps of a communication transmitter. While it has been shown that indeed large gains can be achieved by soft modulation at the transmitter, it is not so clear how to use soft significance values in combination with error-correction channel coding. What is essentially required is soft channel encoding, leading from soft input significances to soft output significances, which then can be used by the modulator.

A related problem has recently been of interest in another very active research area: relaying is a concept in which communication between a source and a destination is supported by a relay that will overhear the coded data communicated from the source. With the received soft data from the source, the relay can perform soft-output channel decoding and the resulting data-bit reliabilities can be interpreted as "significance" values that have to be re-encoded for the transmission from the relay to the destination. At the latter, a joint decoder operates on the data received from both the direct link and the link from the relay, and this option to use information received from more than one spatial direction allows to exploit a diversity effect, leading to potentially better overall performance, particularly when fading channels are involved. The key question is, however, the same as for soft re-encoding of source-significance data: how can soft values, describing properties of the data bits, be soft channel-encoded?

In the talk we review possible definitions of the "significance" of source coded data and we investigate performance benefits from exploiting significances in soft modulation. We then turn to the question, how channel encoders can be realised that can handle soft inputs (such as significance values) and we investigate the resulting performance. We use a soft encoding scheme known from the literature and we compare its performance with other soft-encoders we propose. As our simulations show, soft channel encoding as such does not lead to a performance improvement compared to hard channel encoding with maximum likelihood decoding. The performance improvements in soft-relaying reported in the literature are really due to the sub-optimal iterative decoder used at the destination to decode a distributed Turbo code. We take a closer look at the problem by quantifying and comparing the mutual information loss that occurs due to hard and soft channel encoding.