Interleaver Design for Turbo Codes - Assignment Example

Interleaver Design for Turbo s Interleaver Design for Turbo s Introduction Interleaver design plays a significantly critical role in the performance of turbo codes. Although there are a number of systematic methods of designing interleaver for turbo codes, most of the designs are based on two major criteria. There are currently two major criteria that are commonly employed in the design of interleaver. These criteria include the distance spectrum properties of the code as well as the correlation between soft output of each of the decoders and the information input data corresponding to the decoder’s parity bits. With regard to the use of distance spectrum as an important criterion, distance spectrum has a number of effects on the bit error probability of the target turbo codes (Sadjadpour et al. 2002, p.832). A crucial component in attaining good performance with iterative decoding associated with a turbo code is the interleaver. Inside the turbo codes, the interleaver has three roles: building very long codes whose weight distributions tend towards those of random codes, help during iterative decoding through decorrelation of the input LLRs to the SISO decoders in the best way possible, appropriate termination of the trellis in a defined state following the transmission of any short to medium length frames to evade the edge effects which increase the multiplicity of low weight paths inside the trellises that form part of the component codes. Generally, the excellent performance of turbo codes especially at low signal to noise ratios (SNR). For example, the excellent performance of the turbo codes at low SNRs is widely regarded as a manifestation of the sparse distance spectrum of the code as opposed to dense spectral convulutional codes. This is particularly explained by the fact that interleaver in the turbo encoders normally tend to reduce the number of low weight code words through spectral thinning process. According to Hanzo (2011, p.46), the thinned distance spectrum often results on free distance asymptote becoming the dominant performance parameter particularly for the low and moderate signal to noise ratios. This paper critically analyzes the main design aspects and criteria employed in the design of interleaver for turbo codes including the way in which block length and distance spectrum properties of the code affect performance. Distance Spectrum Properties of the Code A turbo code is normally said to be an optimal distance spectrum (ODS) when its main distance spectral lines are below those of any other code with a similar interleaver size, same sate and memory order. According to Perez (2009, p.1702), the error floor can be effectively lowered by simply increasing the size of the interleaver without necessarily changing the free distance of the code. Alternatively, the free distance of the code can increased through the use of primitive feedback polynomials. The interleaver design along with the generator polynomials used inside the component codes plus the puncturing used at the encoder can dramatically affect the free distance associated with resultant turbo code (Hanzo 2011, p. 131). Despite the proposed algorithms attempting to select good interleavers based on keeping the minimum free distance of the code at maximum, the process has remained complex and optimum performance has never been guaranteed in the resultant interleavers. Many researchers argue that the “error floor” that is normally observed in the performance of the turbo codes is usually attributed to their comparatively low free distance.In this regard, the inteleaver can be designed in such as way that it reduces the number of low weight code words by thinning the distance spectrum (Sadjadpour et al. 2001, p.835). For example, during the design of the interleaver for turbo codes, the sparse distance spectrum of the turbo codes is mainly due to the code words structure in a parallel concatenation as well the use of pseudorandom interleaving. For any given interleaver size, the distance spectrum of the candidate turbo code should be evaluated. Next, the turbo code with the smallest error coefficient for the low and medium hamming distances is chosen to help in the design of the interleaver. Iteractive Decoding Suitability The distance spectrum properties of the code as well as the correlation between soft output of each of the decoders and the information input data corresponding to the decoder’s parity bits which is also sometimes referred to as iteractive decoding suitability(IDS) criterion is generally a measure of the interactive decoding algorithm effectiveness. The interleaver design also affects the performance through reduction of the level of correlation between the soft output of every decoder and this becomes extrinsic information to the other decoder. The performance of the turbo decoder increases with a decrease in the level of correlation between the two soft-information decreases. This is particularly based on the fact that the less correlated the extrinsic information to the input information data sequence, the more likely the iteractive decoding algorithm BER performance will improve. Hanzo (2011, p.78) argues that the turbo codes performance at low BER is primarily dominated by the minimum free distance. As a result, the design of the interleaver for turbo codes should focus on increasing the minimum effective free distance. For example, the iteractive decoding algorithm is widely believed to perform better when the information sent to each decoder from the other decoders is less correlated to the data sequence of the input information. On the other hand, Kandani (1999, p.26) suggests that smaller values of the minimum effective free distance are not recommended for the design of the interleavers because they are more likely to degrade the overall performance of the turbo code. Turbo codes with well designed interleavers have increasingly demonstrated high levels of performance that is close to the capacity limit on the additive white Gaussian noise channel. Block Sizes For applications that require less delays and less complexity such as voice, large block size interleavers are usually recommended for use in the turbo codes. As a result, it is critically important to design interleavers for turbo codes in a way that affectively demonstrates sufficient bit error rate (BER) performance. Consequently, in order to take advantage of the numerous coding gains that turbo codes can potentially offer for such applications, an appropriate choice of the interleaver block size is critically important and should be taken into consideration. Effects of Block Length on Performance The block length has a significant effect on the performance of the turbo codes. For example, compared to the convolutional codes, turbo codes can only achieve optimal performance when the when the interleaver block lengths are longer and in the order of thousands of bits. On the other hand, shorter interleaver lengths should not be used during the design of the interleaver because they substantially degrade the performance of the turbo codes to the point that the bit error rate (BER) is significantly worse than the traditional convolution codes (Herzberg, 1998, p.304). Conclusion In conclusion, interleaver for turbo codes should be designed in a way that enhances the minimum effective free distance of the turbo code while at the same time reducing the correlation properties of the code between the information input data sequences. Turbo codes with well designed interleavers have shown a level of performance that is close to the capacity limit on the additive white Gaussian noise channel. Lastly, both the block size and block length have a significant effect on the performance of the turbo codes and should therefore also be taken into consideration during the design. References Hanzo, L. 2011. Turbo coding, turbo equalisation, and space-time coding: exit-chart aided near-capacity designs for wireless channels. Chichester, West Sussex, U.K., Wiley. Kandani, A.K. 1999. Optimization of the Interleaver Structure for Turbo-codes. In prog. Canadian workshop information theory, 25-28.  Perez, L. 2009. A Distance Spectrum Interpretation of Turbo Codes. IEEE Transactions on Information Theory 42(6), pp. 1698-1709. Sadjadpour, H.R. Sloane, N.J.A. Salehi, M. Nebe, G. 2001."Interleaver design for turbo codes. IEEE J. Selected Areas in Communications 19(5), pp. 831-837. Herzberg, H. 1998. Multilevel Turob Coding with Short Interleavers. IEEE Journal on selected areas in Communications16(2), pp. 303-309. Read More