Belief propagation (BP) is a soft‐decision (SD) decoder that is commonly used to obtain near‐optimal decoding performance for linear codes defined over sparse parity‐check matrix. Nevertheless, the BP yields poor performance when used in the decoding of algebraic block codes, usually described by a dense parity‐check matrix. Hence, enhanced BP decoders transform the parity check matrix of such codes at each iteration for efficient decoding. In this article, the performance of the transformed parity‐check matrix of the iterative SD decoder is analysed for the class of binary cyclic codes using a perfect knowledge model (PKM). The PKM computes a list of candidate matrices and selects a baseline parity‐check matrix according to a distance metric. The selected matrix is optimal since it minimizes the probability of error over various choices in the list. Results show that, for a given channel condition, the conventional transformed matrix obtained by Gaussian elimination is sub‐optimal and does not necessarily contain unitary weighted columns at corresponding columns of the unreliable bits. Moreover, PKM can be used to verify the performances of newly developed iterative SD decoders for binary cyclic codes based on parity‐check equations instead of maximum‐likelihood decoding.

Iterative channel estimation and decoding over flat Rayleigh fading channels have been shown in literature to improve the performance of receivers in wireless communication systems. Turbo and low density parity check codes have mostly been used as the forward error correction (FEC) scheme in the iterative receiver structures. This study proposes a decision directed iterative channel estimation and decoding receiver using Reed–Solomon codes. In particular, the Koetter and Vardy, Reed–Solomon (KV–RS) soft decision decoder is adopted in the receiver structure as the FEC scheme. Two methods of deriving a priori information in joint iterative channel estimation and decoding receiver structures are also analysed in this study. The first method derives the a priori information employing the log likelihood ratio (LLR) method. A priori information derived using the LLR method is mostly used in iterative receiver structures in the literature. The second method derives the a priori information employing the distance metric (DM) method. The DM method is proposed in this study as an alternative approach to the LLR method of deriving a priori information in the iterative receivers. Hard and soft feedback information from the KV–RS decoder is considered to verify the performance of these methods. The performance of the two a priori information methods is documented through computer simulation assuming an M ‐ary quadrature amplitude modulation system. Simulation results verify the improvement in symbol error rate (SER) performance in the KV–RS iterative receiver structure in comparison with the KV–RS receiver without feedback. Also, the proposed DM method exhibits the same SER performance in comparison with the LLR method which is mostly used in the literature. More importantly, the proposed DM method has the advantage of less computational delay and time complexity compared with the LLR method.

We derive a simple formula to generate a wide-sense systematic generator matrixBfor a Reed-Solomon code. Specifically, we generate the generator matrixBsuch that the columns with indices ¿1, ¿2,..., ¿kare the columns of the identity matrixIk. One possible application of these wide-sense matrices is erasures-only decoding.

Narrowband interference can cause undetected errors when M-FSK data is encoded with an algebraic code containing the all-ecodewords. This is due to the fact that the narrowband interferer will cause the output of the M-FSK demodulator to correspond to one of the all-ecodewords. One possible solution is to use a coset code of a code containing the repetition code. The choice of the coset leader should be such that the resulting coset code has minimum same-symbol weight. We give a general construction for generating coset codes with minimum same-symbol weight and present results where an optimal coset code for an (n, k) Reed-Solomon code is applied in an M-FSK environment with narrowband interference. From the results it is evident that the optimal coset codes outperform linear codes when narrowband interference is present.

We consider the erasures-only decoding of Reed-Solomon codes. One class of erasure decoders of algebraic codes can be viewed as a transformation of the systematic generator matrix, as first noticed by Berlekamp. We extend Berlekamppsilas method to Reed-Solomon codes and compare the performance of the decoder with various other Reed-Solomon erasure decoders. The developed decoder reduces the decoding time of packet erasures significantly when used in conjunction with a modified interleaver found in the literature.

In some networks, data packets either arrive without any bit errors, or one or more packets are lost, with packet switched networks as one of the most evident examples. With real-time data, the delay introduced while recovering from these losses can have a great influence on the quality of service of the application. The paper introduces a decoding algorithm that can recover from bursts of erasures by utilizing cyclic Reed-Solomon codes.