D.A. Tavalinsky1, N.V. Shishkin2, A.V. Yurlov3

1 Military Order of Zhukov University of Radio Electronics (Cherepovets, Russia)
2,3 Russian Federation Security Guard Service Federal Academy (Oryol, Russia)
 

Turbo product codes are a class of high-performance forward error correction codes developed in 1993.These are the first practical codes to closely approach the channel capacity. Today the steady tendency of growth of popularity of a block turbo codes was outlined in systems of satellite communication, it is caused first of all thanks to its good correcting opportunities.

The turbo product codes (TPC) are decoded using an iterative decoding algorithm based on soft decoding and a soft decision of the component codes. For decoding of this code broad application was received by algorithm of Chase-Pyndiah. Use of that algorithm allows to receive exact a posteriori estimates of probabilities of symbols of accepted code word.

In many applications, the detection of erroneous blocks after forward error correction is used to improve overall system performance. For instance, this information can be used by the source decoder to reduce performance degradation due to transmission errors.

The article studies the performance of block turbo codes through computer simulation. The idea we follow is simply to use the reliability information at the output of the turbo decoder. We are introducing a decoder for the concatenation of source and channel codes. The source and channel codes are jointly decoded at the receiver.

This method relies on residual redundancy in the source code; in particular, sometimes redundancy is retained in the Deflate coder. Deflate is based on a variation Lempel-Ziv (LZ77) dictionary compression combined with Huffman static coding. Deflate is a popular compression method that was originally used in the well-known Zip and Gzip software and has since been adopted by many applications, the most important of which are the HTTP protocol, the PPP compression control protocol, the many graphics file formats, Adobe's PDF and others.

The data at the output of the receiver corresponding to a transmitted code word of TPC is iteratively decoded row after row then column after column. After the iterative decoding process of TPC we must consider undesirable event is a code word contains residual errors and these errors are not detected by the error detection algorithm. The event corresponds to undetected errors of TPC. The undetected errors that cannot be fixed by a turbocode decoder negatively affects the decoding process in case of transmitting compressed data that demands to investigate the error configuration and it’s features for the purpose of the further possibility to modify the decoding algorithm.

In article the method, allowing to reduce negative influence of undetected errors is offered and to use statistics of decoding of symbols of the code word for additional updating of decisions for the purpose of reduction probability of an error of decoding in output sequence of bits in comparison with known decisions. To reveal the location of undetected errors in the source code on turbocode word length it is suggested to use the context modeling of the decoded messages. The location of error in the decoding message is determined by analyzing context match factor for the current and ideal messages.

The error detection performance of TPC has been evaluated by Monte-Carlo simulations on a Gaussian channel using QPSK signaling. The efficiency of the error detection scheme decreases with the signal-to-noise ratio. Additive White Gaussian channels are realized and information encoded using various turbo product codes are transmitted over the channels and retrieved at the receiver side using a modified Chase-Pyndiah decoder. The simulation show that our decoding method helps correct undetected errors and improve the achievable bit error rate (BER).

Tavalinsky D.A., Shishkin N.V., Yurlov A.V. Research of the block turbo code's error effect on the data decompression process. Dynamics of complex systems. 2022. V. 16. № 4. P. 26−38. DOI: 10.18127/j19997493-202204-03 (in Russian)

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