### Unequal Error Protection Turbo Codes – (Master Thesis – Diploma)

Student:

Neele von Deetzen (diploma student of the University of Bremen and now PhD student at Jacobs University)

**Advisor:
**Prof. Dr.-Ing. Werner Henkel, Prof. Dr.-Ing. Karl Dirk Kammeyer

**Time frame:**

August 31, 2004, February 28, 2005

** **

**Description:**

In this work, we discussed possible solutions for achieving unequal error protection based on Turbo Codes. There exist several reasons that motivate the application of unequal error protection, for example if some kind of media should be handled by different terminal equipment, or if the bit-error rates have to be adapted to channel conditions.

One possibility of applying unequal error protection to Turbo Codes is puncturing, which means not transmitting all of the generated bits of a code sequence but puncturing a certain amount of them. This method enlarges the code rate $R_c = k/n$ by reducing the denominator, i.e., the number of output bits of the code. The increase of the code rate leads to a performance degradation, i.e., to a less powerful code. Thus, we can construct a family of unequally protecting codes by applying different puncturing patterns. As another option, we studied path-pruning. In this case, the code rate $R_c = k/n$ of a mother code is modified by varying the numerator, i.e., the number of input bits. We presented a procedure for constructing a more powerful code from a mother code, where the sub-code has a smaller number of information bits and the set of transitions in a trellis segment of the sub-code is a subset of the transitions of the mother code. If we follow a condition for “single-trellis decoding”, we only have to modify the state transitions of the trellis and are able to use the decoder of the mother code for decoding the sub-codes. For punctured and pruned Turbo Codes, we defined a rate-compatibility and a path-compatibility criterion, respectively, which guarantee that in transition regions between different sub-codes no distance losses or path discontinuities can occur.

When comparing the properties and results of punctured and pruned Turbo Codes, we should, first of all, note that both methods achieve unequal error protection without additional complexity. In both cases, we are able to decode all sub-codes by the decoders of their mother codes and therefore, do not have to implement additional decoders. One advantage of puncturing compared to pruning is that we can achieve a large number, i.e., a high resolution of different code rates just by enhancing the length of the puncturing period. When applying pruning to a mother code of rate $R_c = k/n$, we are able to construct only $k-1$ sub-codes, which is usually restricted to a small number, since we assume small component codes for Turbo Codes. Regarding the performance of punctured and pruned Turbo Codes, the obtained results were expected. For a family of $N$ codes with code rates $R_{c,1}$, $R_{c,2}$, …, and $R_{c,N}$ with $R_{c,1} > R_{c,2} > \ldots > R_{c,N}$, we obtain staggered bit-error rate curves, which are related according to $P_{b,1} > P_{b,2} > \ldots > P_{b,N}$. The exact gain is, of course, dependent on the properties of the used codes and on the system components, e.g., on the interleaver size. We do not list the gains again, but would like to mention that further optimization of the constituent codes needs to be done. However, the principal behavior shows up as expected and desired.

As future tasks, we may especially investigate pruned Turbo Codes in more detail. The optimization of possible component codes has not yet been done. One can, for example, apply differently pruned codes as component codes. Furthermore, the evaluation of source significance information and appropriate assignment to certain codes has to be investigated.

**+Documents**[Thesis] Unequal Error Protection Turbo Codes

**Status:**Completed