Improved Spectral Efficiency through Iterative Concatenated Convolutional Reed-Solomon Software Decoding

摘要

In this paper we describe an 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 [1]. 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.