Symbol-level Decoding Research Articles

Symbol-level iterative information set decoding of RS codes

This paper presents the implementation of a low-complex iterative symbol-level decoding scheme for Reed-Solomon codes. Most soft-decision iterative decoders for Reed-Solomon codes work on a bit level due to the efficient passing of soft information due to the sparsity of the binary parity check matrix. These decoders yield a good error correction performance, but this comes at the cost of an increased computational complexity resulting from working at a bit-level. This study aims to lower the computational complexity of iterative decoding of Reed-Solomon codes by introducing a high-performance soft-decision iterative Reed-Solomon decoder that works on a symbol-level, in contrast to the bit-level implementation used in most iterative Reed-Solomon decoders. The proposed algorithm utilises soft information to decode while applying information set decoding techniques to an extended parity check matrix. The use of the extended parity check matrix provides additional parity check equations which assist the algorithm in determining the correct information set of symbols used in the decoding process. For a given (n,k) Reed-Solomon code, the algorithm converges to a valid codeword by correctly decoding a specified information set of k symbols from the received vector. Simulations run show the proposed algorithm performs favourably when compared to other symbol-level iterative decoders while working at a relatively lower complexity.

Marker Codes Using the Decoding Based on Weighted Levenshtein Distance in the Presence of Insertions/Deletions

A random marker code is inserted into the information sequences periodically, and a novel symbol-level decoding algorithm considering the weighted Levenshtein distance (WLD) is designed for correcting insertions, deletions, as well as substitutions in the received sequences. In this method, branch quantities in the decoding trellis are calculated by measuring the WLD, which is done using the dynamic programming. A simulation study is performed to demonstrate the effectiveness of the presented scheme in the practical system, especially for channels with weak synchronization problems.

SYMBOL LEVEL DECODING FOR DUO-BINARY TURBO CODES

This paper investigates the performance of three different symbol level decoding algorithms for Duo-Binary Turbo codes. Explicit details of the computations involved in the three decoding techniques, and a computational complexity analysis are given. Simulation results with different couple lengths, code-rates, and QPSK modulation reveal that the symbol level decoding with bit-level information outperforms the symbol level decoding by 0.1 dB on average in the error floor region. Moreover, a complexity analysis reveals that symbol level decoding with bit-level information reduces the decoding complexity by 19.6 % in terms of the total number of computations required for each half-iteration as compared to symbol level decoding.