Simplified decoding techniques for linear block codes


Autoria(s): Srivastava, Shraddha
Contribuinte(s)

Popovici, Emanuel M.

Science Foundation Ireland

CSI, Dublin

Data(s)

10/03/2014

2013

2013

Resumo

Error correcting codes are combinatorial objects, designed to enable reliable transmission of digital data over noisy channels. They are ubiquitously used in communication, data storage etc. Error correction allows reconstruction of the original data from received word. The classical decoding algorithms are constrained to output just one codeword. However, in the late 50’s researchers proposed a relaxed error correction model for potentially large error rates known as list decoding. The research presented in this thesis focuses on reducing the computational effort and enhancing the efficiency of decoding algorithms for several codes from algorithmic as well as architectural standpoint. The codes in consideration are linear block codes closely related to Reed Solomon (RS) codes. A high speed low complexity algorithm and architecture are presented for encoding and decoding RS codes based on evaluation. The implementation results show that the hardware resources and the total execution time are significantly reduced as compared to the classical decoder. The evaluation based encoding and decoding schemes are modified and extended for shortened RS codes and software implementation shows substantial reduction in memory footprint at the expense of latency. Hermitian codes can be seen as concatenated RS codes and are much longer than RS codes over the same aphabet. A fast, novel and efficient VLSI architecture for Hermitian codes is proposed based on interpolation decoding. The proposed architecture is proven to have better than Kötter’s decoder for high rate codes. The thesis work also explores a method of constructing optimal codes by computing the subfield subcodes of Generalized Toric (GT) codes that is a natural extension of RS codes over several dimensions. The polynomial generators or evaluation polynomials for subfield-subcodes of GT codes are identified based on which dimension and bound for the minimum distance are computed. The algebraic structure for the polynomials evaluating to subfield is used to simplify the list decoding algorithm for BCH codes. Finally, an efficient and novel approach is proposed for exploiting powerful codes having complex decoding but simple encoding scheme (comparable to RS codes) for multihop wireless sensor network (WSN) applications.

Science Foundation Ireland (06/MI/006)

Accepted Version

Not peer reviewed

Formato

application/pdf

Identificador

Srivastava, S. 2013. Simplified decoding techniques for linear block codes. PhD Thesis, University College Cork.

136

http://hdl.handle.net/10468/1436

Idioma(s)

en

en

Publicador

University College Cork

Direitos

© 2013, Shraddha Srivastava.

http://creativecommons.org/licenses/by-nc-nd/3.0/

Palavras-Chave #Error correction codes #Reed-Solomon codes #Hermitian codes #BCH codes #Toric codes #Subfield subcodes #Coding theory #Wireless sensor networks #Error-correcting codes (Information theory)
Tipo

Doctoral thesis

Doctoral

PHD (Engineering)