Publications – Details
The Performance of Short Random Linear Fountain Codes under Maximum Likelihood Decoding
- Authors:
- Birgit Schotsch, Henning Frederik Schepker, and Peter Vary
- Book Title:
- Proceedings of IEEE International Conference on Communications (ICC)
- Venue:
- Kyoto, Japan
- Event Date:
- 5.-9.6.2011
- Organization:
- IEEE
- Date:
- June 2011
- Pages:
- 1–5
- ISSN:
- 1550-3607
- URL:
- 10.1109/icc.2011.5962476
- Language:
- English
Abstract
In this paper, two particular instances of LT codes with short message blocklength k and maximum likelihood (ML) decoding over the binary erasure channel (BEC) are investigated, i.e., random linear fountain (RLF) codes and (nearly) checkconcentrated LT codes. Both show an almost equally good performance. The focus of this paper will be on RLF codes, a type of LT codes whose generator matrices are constructed from independent Bernoulli trials and have a binomial check node degree distribution. A new simple expression for an upper bound on the bit erasure probability under ML decoding is derived for RLF codes with density Delta = 0.5, i.e., with check node degree distribution Omega(x) = 2^−k*(1+x)k. It is shown that RLF codes with a minimum density far less than 0.5 are equally well suited to achieve a certain bit erasure probability for a given reception overhead. Furthermore, a characteristic term from a general upper bound on the bit erasure probability under ML decoding is identified that can be used to optimise check node degree distributions. Its implications on the performance of LT codes are qualitatively analysed.
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