Abstract
The main challenge for hardware implementation of non-binary LDPC decoding is the high computational complexity and large memory requirement. To address this challenge, five new low complexity LDPC decoding algorithms are proposed in this paper. The proposed algorithms are developed specifically towards the low complexity, yet effective, decoding of the NB LDPC codes. The proposed decoding algorithms update, iteratively, the hard decision received vector to search for the valid codeword in the vector space of Galois field ${(GF)}$ . The selection criterion for least reliable symbol positions is based on the information from the failed checks and the reliability information from the Galois field structure as well as from the received channel soft information. To choose the correct value for the candidate symbol, two methods are used. The first method is based on the prediction of the error symbol from the set of Galois field symbols which maximize an objective function. In the second method, individual bits are flipped based on the reliability information obtained from the channel. Algorithms 1 and 2 flip a single symbol per iteration whilst the other three algorithms 3 , 4 and 5 flip multiple symbols in each iteration. The proposed voting based Algorithms 1 , 2 and 5 first short list the unreliable positions using a majority voting scheme and then choose the candidate symbol value from the set of the symbols in ${GF(q)}$ while not violating the field order ${q}$ . These methods simplify the decoding complexity in terms of computation and memory. Results and analysis of these algorithms show an appealing tradeoff between computational complexity and bit error rate performance for NB LDPC codes.
Highlights
Reliable and efficient communication depends on the performance of forward error correction (FEC) codes
The objective of this paper is to propose algorithms with good performance and low complexity to fulfill the requirement of low power and efficient memory usage
COMPLEXITY ANALYSIS we evaluate the decoding computational complexity and memory requirement of the proposed algorithms in comparison with various existing NB LDPC decoding algorithms
Summary
Reliable and efficient communication depends on the performance of forward error correction (FEC) codes. The performance of LDPC codes depend on the type of decoders used. One of the good decoders is the q−ary sum-product algorithm (QSPA) decoder which passes a vector of q probability messages over. The high check node computational complexity of the QSPA decoder is a major obstacle to their finding a place in practical applications. After the invention of the NB LDPC codes [1], most of the research has focused on how to reduce the computational complexity of the check node processing. To lower the complexity of QSPA, a Fast Fourier transform based SPA (FFT-SPA) algorithm was proposed in [5] to reduce the check node computational complexity from order of O(q2) to O(q log q) for each check node update. Other low complexity algorithms called extended min-sum (EMS) [6], [7], trellis based EMS [8], bubble check EMS [9] and min-max algorithms [10] were proposed but they have a performance
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