FPGA Implementation Framework for LT CODEC

Binary Erasure Channels (BEC) can be used to model transmission erasures, for example, symbol erasures in TCP’s link layer and network layer. In order to tackle the erasures incurred, the transceiver system relies on retransmission of the lost packets using acknowledgment and repeat request based schemes. This missing packet information or acknowledgments can be conveyed by the receiver to the transmitter via a feedback channel. However, it might become very cumbersome to continue this feedback information approach for various scenarios like broadcasting, where one receiver with low attainable data-rate (due to severe fading channel characteristics or limiting receiver resources) can dominate the whole transmission, thereby under-utilizing the channel due to wasteful retransmissions and delays. It is also possible that the requests or acknowledgments from the receiver to transmitter are erased because they pass through the same channel. Hence, forward erasure corrections are important to insure that feedback from receivers is minimal. Coding methods like Reed-Solomon (RS) and Low Density Parity Check (LDPC) etc exist for this purpose; however, they have their limitations. For example, RS codes are efficient only for small length of encoding symbols and LDPC based transmission scheme can only generate a predetermined output from a given set of input symbols to the encoder. Recently, Digital Fountain codes have been introduced where a receiver collects packets from one or more servers and once a sufficient number of encoded packets are received, irrespective of the category and order of the packets, the decoder can reconstruct the original source. Examples of Digital Fountain codes are Tornado codes, Luby Transform (LT) codes and Raptor codes. LT codes are a realization of Digital Fountain codes. They are rateless, erasure correcting codes where an encoder can in principle generate an infinite stream of encoded outputs from a finite set of inputs owing to the demand of decoder. The decoder can regenerate the encoder’s input by gathering any subset of the encoded symbols. Moreover, LT codes lend itself to be efficiently employed specially, if the packet length grows, the encoding efficiency increases. Advantages of LT codes are imminent in data storage, wireless transmission, multicasting, video streaming and parallel downloading. LT encoder is simple and efficient; however, it’s the decoder that introduces the complexity in the CODEC. The LT encoder generator matrix is not fixed and is randomly created, on the fly, using a degree and random neighbor generator. Decoder has to regenerate the generator matrix before starting actual decoding, thus, increasing the latency of operations. Gaussian elimination at decoder becomes quite inefficient for large stream sizes and Belief Propagation (BP) algorithm is utilized. But the Tanner graph structure cannot be hard-coded (due to randomly generated generator matrix),