The Performance of Multithreshold Decoders in Concatenated Schemes Over Erasure Channels

Multithreshold decoders (MTD) of self-orthogonal codes (SOC) for erasure channels implementing error correction methods based on searching global extremum of functions in discrete spaces are considered. To increase the efficiency of erasure recoveries the concatenated codes comprising inner SOC and outer codes being simple for decoding such as parity-check codes, Hamming codes or BCH codes are offered. The usage of the codes offered provides efficient erasure recovery when operating near channel capacity with linear decoder complexity. The questions of high-throughput software MTD implementation recovering erasures using GPU are considered. The MTD versions developed are shown to be able to perform data flow decoding with the rate of several hundred MB/s using GPU.

I. Introduction

Error-correcting coding is widely used in communication systems to correct the errors arisen during data transmission [1]. Over the past decades efficient methods of coding and simple decoding providing the operation near the capacity of typical communication channels including the model of channel with erasures have been developed [1]. Despite its simplicity this model can be used in modeling of computer systems, data storage systems and many other systems. Besides, the decoders for this model of erasure channel turn out to be computationally simpler than the decoders for the channels with errors. Therefore, in high-rate data transmission and data storage systems a receiver doesn't use a complex error-correcting algorithm, but with the help of check sums erases certain unreliable symbols or even the whole blocks of symbols for their further recovery using error-correction code decoder. Here we should mention that nowadays for such channel different codes and methods of their decoding achieving its maximum throughput are known [2]–[4], but in case of finite code length their efficiency is not always the best, the decoder complexity remaining residually high.