Iterative Soft Input Soft Output Decoding of Reed-Solomon Codes by Adapting the Parity Check Matrix

An iterative algorithm is presented for soft-input-soft-output (SISO) decoding of Reed-Solomon (RS) codes. The proposed iterative algorithm uses the sum product algorithm (SPA) in conjunction with a binary parity check matrix of the RS code. The novelty is in reducing a submatrix of the binary parity check matrix that corresponds to less reliable bits to a sparse nature before the SPA is applied at each iteration. The proposed algorithm can be geometrically interpreted as a two-stage gradient descent with an adaptive potential function. This adaptive procedure is crucial to the convergence behavior of the gradient descent algorithm and, therefore, significantly improves the performance. Simulation results show that the proposed decoding algorithm and its variations provide significant gain over hard decision decoding (HDD) and compare favorably with other popular soft decision decoding methods.Comment: 10 pages, 10 figures, final version accepted by IEEE Trans. on Information Theor

Fast Convergence and Reduced Complexity Receiver Design for LDS-OFDM System

Low density signature for OFDM (LDS-OFDM) is able to achieve satisfactory performance in overloaded conditions, but the existing LDS-OFDM has the drawback of slow convergence rate for multiuser detection (MUD) and high receiver complexity. To tackle these problems, we propose a serial schedule for the iterative MUD. By doing so, the convergence rate of MUD is accelerated and the detection iterations can be decreased. Furthermore, in order to exploit the similar sparse structure of LDS-OFDM and LDPC code, we utilize LDPC codes for LDS-OFDM system. Simulations show that compared with existing LDS-OFDM, the LDPC code improves the system performance

Parallel vs. Sequential Belief Propagation Decoding of LDPC Codes over GF(q) and Markov Sources

A sequential updating scheme (SUS) for belief propagation (BP) decoding of LDPC codes over Galois fields, $GF(q)$, and correlated Markov sources is proposed, and compared with the standard parallel updating scheme (PUS). A thorough experimental study of various transmission settings indicates that the convergence rate, in iterations, of the BP algorithm (and subsequently its complexity) for the SUS is about one half of that for the PUS, independent of the finite field size $q$. Moreover, this 1/2 factor appears regardless of the correlations of the source and the channel's noise model, while the error correction performance remains unchanged. These results may imply on the 'universality' of the one half convergence speed-up of SUS decoding