RU2321170C2 - Method for receiving signals with turbo-encoding on basis of convolution codes with element-wise decision-making according to algorithm of maximum a posteriori probability - Google Patents

Abstract

FIELD: communication systems which use signals with turbo-encoding on basis of convolution codes, namely, methods for iterative receipt of signals with turbo-encoding.

SUBSTANCE: in accordance to the method, received series is decoded according to algorithm of maximum a posteriori probability, soft solutions of informational and check bits are normalized, solved code words are generated at given length of decision-making, scalar result of multiplication of normalized series and generated code words is computed, most probable code word is selected on basis of maximum scalar result of multiplication, scalar result of multiplication is compared to boundary of existence of single code word, informational bits are extracted and rigid decision is made.

EFFECT: reduced probability of errors per block of turbo-code, resulting in increased trustworthiness of receipt of turbo-encoded signals.

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Description

The present invention relates to communication systems using signals with turbo coding (TC) based on convolutional codes, and in particular to methods for iteratively receiving signals from TC.

There is an iterative method of receiving signals from the TC based on the Viterbi algorithm with soft solutions [1]. The method involves updating the metrics of the surviving path along the grate due to the passage of the grating in the opposite direction. The disadvantage of this method is the greater probability of error per bit compared with the algorithm for maximum posterior probability (MAP) due to the consideration of only surviving paths.

A known iterative method for receiving signals with turbo coding based on the MAP window algorithm [2]. The method has high speed, but as a result of dividing the whole block into a number of independent sections, it is inferior to the complete MAP algorithm in probability of error per bit.

As a prototype, the authors adopted a method of receiving signals with turbo coding (TC) with iterative decoding to the maximum a posteriori probability [3]. At each iteration, the decoders exchange soft decisions obtained at previous iterations.

The disadvantage of the method selected as a prototype is the relatively high probability of errors per block at the end of the iterative decoding process due to the influence of residual errors.

The aim of the claimed invention is to reduce the likelihood of errors per block when receiving signals with turbo coding.

This goal is achieved through the use of the reception algorithm as a whole with element-wise decision making on the maximum of posterior probability. For this, a block for generating permitted code words is used, not a separate component code, but the turbo code as a whole. The block of calculations based on the estimates obtained by the MAP algorithm finds the scalar product of the received turbocode code vector and each allowed code word. The allocation unit determines the most probable turbocode codeword from the maximum of the scalar product, and the decision unit performs hard decoding of the systematic bits of the selected word.

Thanks to this, a technical result is obtained, namely, the probability of error per turbocode block is reduced, which generally increases the reliability of receiving signals from the TCS.

The inventive method of receiving signals from TCS is illustrated by drawings, where

figure 1 schematically shows the main blocks of an iterative process for decoding turbo codes;

figure 2 shows the block diagram of the decision-making as a whole, taking into account the element-wise assessment.

Figure 1 shows an iterative decoder turbo code based on two component decoders. According to FIG. 1, the first component decoder 2 receives systematic convolutional code signals Xk, the check bits Y1k of the first component code from the output of demultiplexer 1, and a priori information Lu from the output of the second component decoder 4 at the previous iteration through deinterleaver 5. At the first iteration, there is no a priori information and Lu = 0. Next, the first component decoder 2 decodes the received sequence according to the maximum posterior information algorithm (MAP) and the a priori information Lu is input to the second decoder 4 through the interleaver 3. The second component decoder 4 also decodes the received sequence consisting of information bits Xk, check bits Y2k and Lu a priori information, thus completing one complete iteration. The iterative decoding process continues either to a given number of iterations, or until the criterion for stopping the iterative process by the correlation of the outputs of the component decoders is triggered.

The output of the MAP algorithm is written as

where L (x _k | y) is the output logarithmic likelihood ratio,

x _k is the kth information bit,

y is the accepted sequence,

- прямая метрика состояния,

- direct metric of state,

β _k (s) is the inverse metric of the state,

- метрика ветви,

- branch metric,

- предыдущее состояние кодера,

- previous state of the encoder,

s is the next state of the encoder.

Using the likelihood logarithm algebra [4], expression (1) is written as

where L (x _k | y) is the output logarithmic likelihood ratio,

L _c y _k - channel measurements of the received sequence,

Lu - a priori information.

After the end of the iterative decoding process, soft decisions of both information bits and updated test ones are fed from the output of the last iteration decoder to the value normalization unit 7. Normalization of the values of the soft decisions of the decoder is carried out according to expression 3:

where c is the scale factor

d is the shear coefficient,

[min] is the minimum value

[max] - the maximum value.

In block 8, allowed codewords are generated at a given decision length K. Block 9 calculates the scalar product of the accepted normalized sequence and codewords. Block 10, by the maximum of the scalar product, selects the most probable codeword, and in block 11 the scalar product is compared with the boundary of the existence of a single codeword [5]:

Where

- нормированная последовательность мягких решений декодера,

- normalized sequence of soft decisions of the decoder,

- разрешенное кодовое слово,

- allowed codeword,

n is the length of the decision block,

d is the minimum distance of the turbo code,

α - coefficient taking into account the soft decisions of the decoder.

, поскольку декодирование турбокодов происходит поблочно.In [5], an expression for block codes is presented. For component convolutional codes, instead of the minimum code distance d, it is necessary to use a segment distance

, since the decoding of turbo codes occurs block by block.

The minimum segment distance [6] of the turbo code is calculated according to expression 5:

- минимальное сегментное расстояние,Where

- minimum segment distance

j is the number of steps on the code lattice,

σ ₁ , σ ' ₁ , σ ₂ , σ' ₂ are the states of component encoders,

- расстояние Хэмминга.

- Hamming distance.

If inequality (4) holds, then the accepted word is marked as correct. The marking of the correct code words is carried out to reduce search options with additional procedures for analyzing the accepted sequence. For example, if there is an external CRC code, it is advisable to sort out the least reliable positions in the accepted sequence, while marked code words are assumed to be received with high reliability.

In block 12, the allocation of information bits and the adoption of a tough decision.

Thus, the application of the technique as a whole with the element-wise MAP decision-making allows correcting residual single errors, which reduces the probability of an error per block.

Bibliography

1. US patent No. 6487694, IPC H03M 13/29, 2002.

2. US patent No. 6980605, IPC H03D 1/00, 2005.

3. US patent No. 5446747, IPC G06F 11/10, 1992.

4. B. Sklyar. Digital communication. Theoretical Foundations and Practical Applications, 2nd Edition - M.: Williams Publishing House, 2003

5. R. Bleikhut. Theory and practice of error control codes - M .: Mir, 1986

6. M. Handler, R. Johannesson, V.V. Zyablov. Decoding in a window from the point of view of distances // Problems of information transfer 2002. V.38, No.3.

Claims (5)

1. A method of receiving signals in general with turbo coding based on convolutional codes, which includes the steps of decoding the received sequence using the algorithm of maximum posterior probability, normalizing soft decisions of information and test bits, generating allowed code words for a given decision length, calculating the scalar product of the normalized sequence and generated code words, choosing the most likely code word for the maximum of the scalar product, comparing the scalar product with the boundary of the existence of a single codeword, the allocation of information bits and making a tough decision. 2. The reception method according to claim 1, characterized in that the most probable codeword of the turbo encoder is selected based on the element-wise estimates of the decoder to the maximum posterior probability. 3. The reception method according to claim 1, characterized in that the formation of the permitted code words is carried out for the entire turbo code, not only component codes. 4. The reception method according to claim 1, characterized in that the most probable codeword is selected according to the maximum scalar product of the normalized received sequence and generated codewords. 5. The method of reception according to claim 1, characterized in that the scalar product is compared with the boundary of the existence of a single code word to determine the correct code words.

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