Low complexity algorithm for the decoding of convolutional codes of any rate

Abstract

It is well known that convolutional codes can be optimally decoded by using the Viterbi Algorithm (VA). We propose a decoding technique where the VA is applied to identify the error vector rather than the information message. We previously focused on convolutional coders of rate ½ [4] [5]. Here we generalize the method to codes of any rate. We show that, with the proposed type of decoding, the exhaustive computation of a vast majority of state to state iterations is unnecessary. Hence, performance close to optimum is achievable with a significant reduction of complexity. The higher the SNR, the greater the improvement for reduction in complexity. For instance, for SNR greater than 3 dB, a five fold reduction in complexity for the computation of ACS (Add Compare Select) is achieved.

Low Complexity SST Viterbi Decoder

“…However, the SST scheme cannot reduce the ACS computation complexity, while the low complexity algorithm in [1] …”

“…Numerous methods have been proposed to reduce the computation complexity of the decoder. Recently, Dany et al [1], [2] and [3] has proposed a low complexity decoding algorithm to eliminate some of the ACS computation using the information of the syndrome. However, there are two important issues which render this algorithm impractical or too costly to be adopted for real implementation.…”

“…In this work, we propose a scheme that facilitates the implementation of the algorithm [1] by building it on the Scarce State Transition (SST) Viterbi decoding scheme. By using a SST Viterbi decoder, Dany's algorithm can be implemented naturally without the additional implementation overhead.…”

Complexity Reduction of Convolutional and Turbo Decoding Based on Reliability Thresholds

“…There are some papers that propose different methods to reduce the complexity of convolutional and turbo decoding, such as [3][4][5][6]. Regarding convolutional codes, [3] shows that it is possible to decrease complexity by approximately 1/3, but only for a specific type of encoder and [4] also achieves a good complexity reduction, but only for signal to noise ratios (SNR) greater than a specific value.…”

“…Regarding convolutional codes, [3] shows that it is possible to decrease complexity by approximately 1/3, but only for a specific type of encoder and [4] also achieves a good complexity reduction, but only for signal to noise ratios (SNR) greater than a specific value. Regarding turbo codes, [5] proposes a method in which the variance between the log likelihood ratio (LLRs) of the current iteration and the previous one is measured.…”