Title :
Area efficient evaluation based coding of shortened Reed-Solomon codes for memory constrained applications
Author :
Srivastava, Sanjeev ; McSweeney, Richard ; Popovici, Emanuel
Author_Institution :
Dept. of Electr. & Electron. Eng., Univ. Coll. Cork, Cork, Ireland
Abstract :
This paper presents an efficient algorithm for encoding and decoding Shortened Reed-Solomon (SRS) codes based on evaluation. The encoding and syndrome computations are performed using polynomial evaluation and the decoding is performed using a recursive extension of the original algorithm. The proposed decoding algorithm initially calculates the error locator polynomial by using the Berlekamp Massey (BM) algorithm and with the recursive computation of discrepancies, it decodes directly the message polynomial. Compared to the traditional decoding algorithm using BM algorithm, Chien search and Forney formula, the proposed algorithm results in area savings for hardware implementations due to hardware re-use and the reduced number of stages. Also, the savings in memory for the software implementation makes it suitable for memory constrained applications such as Wireless Sensor Networks (WSN) applications. For the hardware implementations, the number of clock cycles required are lower for the proposed scheme, which results in time savings. Also, software implementation results of RS (32, 24) for resource constrained WSN application on ATMEL Atmega 128 microcontroller show that the proposed encoder and decoder is only about 52% and 72% of the memory footprint of a traditional encoder and decoder respectively.
Keywords :
Reed-Solomon codes; decoding; encoding; polynomials; ATMEL Atmega 128 microcontroller; BM algorithm; Berlekamp Massey algorithm; Chien search; Forney formula; SRS code; WSN; area efficient evaluation based coding; clock cycle; decoding; encoding; error locator polynomial; memory constrained application; polynomial evaluation; shortened Reed-Solomon code; wireless sensor network; Berlekamp-Massey algorithm; Evaluation based Shortened Reed-Solomon codes; Recursive extension;
Conference_Titel :
Signals and Systems Conference (ISSC 2012), IET Irish
Conference_Location :
Maynooth
Electronic_ISBN :
978-1-84919-613-0
DOI :
10.1049/ic.2012.0174