Implementation of the Berlekamp-Massey algorithm using a DSP

Abstract

Reed-Solomon (RS) codes are error-correcting codes used in many of today's communication systems. RS encoding and decoding are typically implemented using dedicated hardware elements used in ADSL modems and digital TV. In this paper we propose using software in lieu of a hardware-based RS de-coder. This is accomplished using the Berlekamp-Massey algorithm, implemented on a programmable DSP. This softwarebased RS decoder using Berlekamp-Massey is implemented on Motorola's MSC8101 StarCore DSP. In order to evaluate the algorithm we use the following criteria: computation cost, cycle count, critical paths in the decoding scheme, and error location in the codeword. Furthermore, we examine the effect of changing the RS code's k, t parameters and its primitive polynomial in real-time implementation. The Berlekamp-Massey algorithm operates over finite field arithmetic, whose steps, as applied on the StarCore DSP, are discussed in detail and specifically evaluated using the assembly code for the syndrome search. We conclude that the Berlekamp-Massey algorithm, used for RS decoding, should be implemented using long codewords.

A real-time, DSP-based JPWL implementation for wireless High Definition video transmission

“…table can decrease the complexity[7].In our solution, initially, codeword message and parity parts are swapped in order to be processed by the customized decoder: the decoding procedure is based on the well known PGZ (Peterson-Gorenstein-Zierler) algorithm. An optimized version for C64x+ DSP[8] was customized according to JPWL algorithm specifIcations.The codewords, after the reordering, are then processed by the following JPWL operations.The DSP dedicated instruction set has been used for decoder performance optimization, since this phase is more complex than its encoding counterpart.…”