Reliability Analysis of the Sum-Product Decoding Algorithm for the PSK Modulation Scheme

Hadi Khodaei Jooshin,Mahdi Nangir

doi:10.29252/jist.8.31.167

Abstract

Iteratively decoding and reconstruction of encoded data has been considered in recent decades. Most of these iterative schemes are based on graphical codes. Messages are passed through space graphs to reach a reliable belief of the original data. This paper presents a performance analysis of the Low-Density Parity-Check (LDPC) code design method which approach the capacity of the Additive White Gaussian Noise (AWGN) model for communication channels. We investigate the reliability of the system under Phase Shift Keying (PSK) modulation. We study the effects and advantages of variation in the codeword length, the rate of parity-check matrix of the LDPC codes, and the number of iterations in the Sum-Product Algorithm (SPA). By employing an LDPC encoder prior to the PSK modulation block and the SPA in the decoding part, the Bit Error Rate (BER) performance of the PSK modulation system can improve significantly. The BER performance improvement of a point-to-point communication system is measured in different cases. Our analysis is capable for applying any other iterative message-passing algorithm. The code design process of the communication systems and parameter selection of the encoding and decoding algorithms are accomplished by considering hardware limitations in a communication system. Our results help to design and select paramours efficiently.

Highlights

Berrou et al introduced Turbo Codes in 1993 and made it possible that by utilizing these error correction codes, one can approach the Shannon limit of the channel capacity [12]
We investigate the Bit Error Rate (BER) performance of LowDensity Parity-Check (LDPC) codes over Additive White Gaussian Noise (AWGN) channels from different points of view caused by the parameter variation
The BER performance of a Phase Shift Keying (PSK) modulated communication is presented with respect to the number of iterations, the code length, and coding rate

Summary

Introduction

Berrou et al introduced Turbo Codes in 1993 and made it possible that by utilizing these error correction codes, one can approach the Shannon limit of the channel capacity [12]. The LDPC code is one of the hot research topics in the coding and information theory due to its high speed encoding and decoding algorithms, it’s capability to achieve the channel capacity providing a reliable communication for an arbitrary transmission rate. We investigate SPA, which is one of the fast, implementable, and simple iterative message-passing algorithms that have been utilized for decoding of the LDPC codes [14,15,16].

Results

Conclusion