Protograph-Based Raptor-Like Codes
- Created: Wednesday, 01 January 2014
- NASA’s Jet Propulsion Laboratory, Pasadena, California
The proposed codes have the advantage of low-complexity encoder and decoder implementation.
Theoretical analysis has long indicated that feedback improves the error exponent but not the capacity of point-to-point memoryless channels. The analytic and empirical results indicate that at short blocklength regime, practical rate-compatible punctured convolutional (RCPC) codes achieve low latency with the use of noiseless feedback. In 3GPP, standard rate-compatible turbo codes (RCPT) did not outperform the convolutional codes in the short blocklength regime. The reason is the convolutional codes for low number of states can be decoded optimally using Viterbi decoder. Despite excellent performance of convolutional codes at very short blocklengths, the strength of convolutional codes does not scale with the blocklength for a fixed number of states in its trellis.
Protograph-based (PB) Raptor-like codes can provide good performance in an incremental redundancy scheme with noiseless feedback over an additive white Gaussian noise channel. Additionally, these codes are also desirable for other applications were there is a need for simple generation of various code rates.
The proposed codes are based on protograph construction and they represent a novel contribution. In the original Raptor code, the redundant bit generation is based on a random selection of precoded bits that are produced from an unstructured LDPC (Low Density Parity Check) code. These redundant bits are selected based on some optimized distribution. Due to the nature of random selection, the original Raptor code required some additional information to be transmitted to the receiver in order to enable the decoding process. In the proposed codes, the redundant bits are generated based to optimized protograph structure with degree-1 nodes. Thus they do not need any additional information to be transmitted to the receiver. The proposed codes with protograph-based structure have the advantage of low-complexity encoder and decoder implementation. The proposed codes were designed for short block sizes, but a similar construction method can be applied to longer block lengths for other applications.
Hybrid ARQ (hybrid automatic repeat request — HARQ) is an error control method. In standard ARQ error detection, symbols such as cyclic redundancy check (CRC) are added to the information data. In HARQ, forward error correction code such as LDPC code symbols are also added to the existing error detection symbols, such that small random errors are corrected without retransmission, and major errors are corrected via a request for retransmission. The hybrid scheme performs better than standard ARQ in poor signal conditions. The proposed protograph-based Raptor-like codes can be used with HARQ.