The performance of serial turbo codes does not concentrate
(2012) In IEEE Transactions on Information Theory 58(5). p.25702588 Abstract (Swedish)
 Abstract in Undetermined
Minimum distances and maximum likelihood error probabilities of serial turbo codes with uniform interleaver are analyzed. It is shown that, for a fraction of interleavers approaching one as the blocklength grows large, the minimum distance of serial turbo codes grows as a positive power of their blocklength, while their error probability decreases exponentially fast in some positive power of their blocklength, on sufficiently good memoryless channels. Such a typical code behavior contrasts the performance of the average serial turbo code, whose error probability is dominated by an asymptotically negligible fraction of poorly performing interleavers, and decays only as a negative power of the... (More)  Abstract in Undetermined
Minimum distances and maximum likelihood error probabilities of serial turbo codes with uniform interleaver are analyzed. It is shown that, for a fraction of interleavers approaching one as the blocklength grows large, the minimum distance of serial turbo codes grows as a positive power of their blocklength, while their error probability decreases exponentially fast in some positive power of their blocklength, on sufficiently good memoryless channels. Such a typical code behavior contrasts the performance of the average serial turbo code, whose error probability is dominated by an asymptotically negligible fraction of poorly performing interleavers, and decays only as a negative power of the blocklength. The analysis proposed in this paper relies on precise bounds of the minimum distance of the typical serial turbo code, whose scaling law is shown to depend both on the free distance of its outer constituent encoder, which determines the exponent of its sublinear growth in the blocklength, and on the effective free distance of its inner constituent encoder. The latter is defined as the smallest weight of codewords obtained when the input word of the inner encoder has weight two, and appears as a linear scaling factor for the minimum distance of the typical serial turbo code. Hence, despite the lack of concentration of the maximum likelihood error probability around its expected value, the main design parameters suggested by the averagecode analysis turn out to characterize also the performance of the typical serial turbo code. By showing for the first time that the typical serial turbo code's minimum distance scales linearly in the effective free distance of the inner constituent encoder, the presented results generalize, and improve upon, the probabilistic bounds of Kahale and Urbanke, as well as the deterministic upper bound of Bazzi, Mahdian, and Spielman, where only the dependence on the outer encoder's free distance was proved. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/2294019
 author
 Garin, Federica; Como, Giacomo ^{LU} and Fagnani, Fabio
 organization
 publishing date
 2012
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 Error probability, minimum distance, serially concatenated codes, turbo codes, typical code analysis
 in
 IEEE Transactions on Information Theory
 volume
 58
 issue
 5
 pages
 2570  2588
 publisher
 IEEEInstitute of Electrical and Electronics Engineers Inc.
 external identifiers

 wos:000303204900003
 scopus:84860245324
 ISSN
 00189448
 DOI
 10.1109/TIT.2012.2184673
 language
 English
 LU publication?
 yes
 id
 f7d96e7d8ef2432a8a3d5fd268f2d61d (old id 2294019)
 date added to LUP
 20120113 09:57:09
 date last changed
 20170101 06:03:07
@article{f7d96e7d8ef2432a8a3d5fd268f2d61d, abstract = {<b>Abstract in Undetermined</b><br/><br> Minimum distances and maximum likelihood error probabilities of serial turbo codes with uniform interleaver are analyzed. It is shown that, for a fraction of interleavers approaching one as the blocklength grows large, the minimum distance of serial turbo codes grows as a positive power of their blocklength, while their error probability decreases exponentially fast in some positive power of their blocklength, on sufficiently good memoryless channels. Such a typical code behavior contrasts the performance of the average serial turbo code, whose error probability is dominated by an asymptotically negligible fraction of poorly performing interleavers, and decays only as a negative power of the blocklength. The analysis proposed in this paper relies on precise bounds of the minimum distance of the typical serial turbo code, whose scaling law is shown to depend both on the free distance of its outer constituent encoder, which determines the exponent of its sublinear growth in the blocklength, and on the effective free distance of its inner constituent encoder. The latter is defined as the smallest weight of codewords obtained when the input word of the inner encoder has weight two, and appears as a linear scaling factor for the minimum distance of the typical serial turbo code. Hence, despite the lack of concentration of the maximum likelihood error probability around its expected value, the main design parameters suggested by the averagecode analysis turn out to characterize also the performance of the typical serial turbo code. By showing for the first time that the typical serial turbo code's minimum distance scales linearly in the effective free distance of the inner constituent encoder, the presented results generalize, and improve upon, the probabilistic bounds of Kahale and Urbanke, as well as the deterministic upper bound of Bazzi, Mahdian, and Spielman, where only the dependence on the outer encoder's free distance was proved.}, author = {Garin, Federica and Como, Giacomo and Fagnani, Fabio}, issn = {00189448}, keyword = {Error probability,minimum distance,serially concatenated codes,turbo codes,typical code analysis}, language = {eng}, number = {5}, pages = {25702588}, publisher = {IEEEInstitute of Electrical and Electronics Engineers Inc.}, series = {IEEE Transactions on Information Theory}, title = {The performance of serial turbo codes does not concentrate}, url = {http://dx.doi.org/10.1109/TIT.2012.2184673}, volume = {58}, year = {2012}, }