Improved spectral efficiency through iterative concatenated convolutional reed-solomon software decoding

Abstract

In this paper we describe on iterative algorithm for concatenated convolutional Reed-Solomon decoders that improve the spectral efficiency of the communication system by increasing the error correction capabilities and as a consequence lowering the retransmission rate. In our method, the decoding process starts assuming the received code word has at most t errors, where 2t+1 is the Reed-Solomon code's minimum distance. If, after the decoding process, all the syndromes are zero the decoding is successful; otherwise there were more than t errors encountered. At this point, the decoder assumes s erasure positions based on the erasure information coming from the convolutional decoder. If the error locator polynomial has degree equal to r = (2t-s)/2, then most likely the error positions are in the current Galois-field and a second decoding algorithm is performed. Otherwise, s = s+2 erasures are assumed and again the degree of the error locator polynomial is checked. This continues until the maximum number of erasures, 2t, is reached. The Reed-Solomon decoder is executed entirely in software on the Sandbridge processor, which features special instructions for single instruction multiple data (SIMD) Galois field (GF) multiplication and other SIMD operations. Multiple decoder algorithms with different degrees of complexity are stored in external memory, such that for a particular RS data packet the one with less computational complexity can be employed, depending on the error/erasure information. By using our method, the packet retransmission rate is decreased, resulting in improved spectral efficiency. The improved spectral efficiency is reflected by a total link budget improvement of up to one dB