Performance Analysis of Joint Degree Distribution (JDD) in Luby Transform Codes

Abstract

Luby Transform (LT) codes, the first realization of rateless codes are widely used in wireless communication mainly for its adaptability to varying channel conditions and its capacity approaching performance. In spite of the above advantages and its simplicity in implementation, LT codes suffer from a bottle neck of premature termination due to the poor design of degree distribution. In this study, a novel degree distribution called Joint Degree Distribution (JDD) is proposed for the successful completion of LT encoder/decoder processes. The efficient utilization of the bandwidth is tried to be achieved by using only 'k' encoded symbols for 'k' source symbols, unlike in traditional systems. JDD is carefully designed to ensure that the encoding/decoding delay does not exceed that which is existent in the traditional systems. The performance of JDD for throughput and bit error rate, experimented over Additive White Gaussian Noise (AWGN) channel compared to conventional degree distribution was observed to be much better.

Enhanced Distributed Storage System Using Lower Triangular Matrix-Luby Transform Codes

“…The probability distribution of these degrees over the whole encoded blocks is called as degree distribution where the degree of the coded symbol is chosen at random according to that probability distribution [14,15]. Decoder failure occurs, if the decoder is unable to recover all the original source blocks [16,17].…”

“…Neighbor Array (NA) consists of the details of the source blocks present in the Recovered Source Block by using Eqs. ( 14)- (17). So, the NA of RSB1 is [1].…”