Abstract
A new non-binary decoding method, which is called Yaletharatalhussein decoding algorithm, is designed and implemented for decoding non-binary convolutional codes which is based on the trellis diagram representing the convolutional encoder. Yaletharatalhussein decoding algorithm outperforms the Viterbi algorithm and other algorithms in its simplicity, very small computational complexity, decoding reliability for high states TCM codes that suitable for Fourth-Generation (4G), decreasing errors with increasing word length, and easy to implement with real-time applications. The proposed Yaletharatalhussein decoding algorithm deals with non-binary error control coding of the convolutional and TCM codes. Convolutional codes differ from block codes in that a block code takes a fixed message length and encodes it, whereas a convolutional code can encode a continuous stream of data, and a hard-decision decoding can easily be realized using the Yaletharatalhussein algorithm. The idea of non-binary codes has been extended for symbols defined over rings of integers, which outperform binary codes with only a small increase in decoding complexity. The simulation results show that the performance of the nonbinary TCM-based Yaletharatalhussein algorithm outperforms the binary and non-binary decoding methods.
Highlights
When conventional coding techniques are introduced in a transmission system, the bandwidth of the coded signal after modulation is wider than that of the uncoded signal for the same information rate and the same modulation scheme
As a total of m + 1 modulo-M coded symbols xk are transmitted per single trellis branch, ring-Trellis Code Modulation (TCM) codes can be considered as 2(m +1) -dimensional TCM codes
The performances of the 4 -Ring-TCM-PAM schemebased Yaletharatalhussein decoding algorithm and the schemes of work [16] can be summarized in Table 3, where the coding gains are defined as the ( Eb N0 )
Summary
When conventional coding techniques are introduced in a transmission system, the bandwidth of the coded signal after modulation is wider than that of the uncoded signal for the same information rate and the same modulation scheme. Digital data can be encoded in such a way as to introduce dependency among a large number of symbols, enabling a receiver to make a more accurate detection of the symbols The design of signal processing algorithms for digital data seems much easier than designing analog signal processing algorithms The abundance of such digital algorithms, including error control and correction techniques, combined with their ease of implementation in very large-scale integrated (VLSI) circuits, has led to many successful applications of error control coding in practice. Iteratively decoded BICM [13] using set partitioning was proposed
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