KR100205610B1 - Product code and decode method in raily phading channel - Google Patents

Abstract

Here, a decoding method using a new interleaving technique and a decoding algorithm of a component code is disclosed. The performance of the decoding method according to the present invention is verified in a Rayleigh fading channel. According to the decoding method of the present invention, component codes are independently decoded. Prior to this, a new interleaving is used to give an effect of interleaving to both the row component code and the column component code. The order of decoding the component codes is determined from the probability that the component codes are correctly decoded. The probability of correct decoding of each component code is obtained from the channel state information of the symbol. According to this decoding method, there is an advantage that decoding can be performed only by the decoding algorithm and the calculation of the component code.

Description

METHOD FOR DECODING A PRODUCT CODE WITH DIAGONAL INTERLEAVING IN A RAYLEIGH FADING CHANNEL IN RAILLE FADING CHANNEL

The present invention relates to a method for decoding a product code in a Rayleigh fading channel.

In a mobile communication environment, the signal undergoes Rayleigh fading due to multi-path propagation as well as noise effects [Johon G. Proakis, "DIGITAL COMMUNICATIONS", 3rd ed., Pp 758-762, McGraw-Hill, New York, 1995.]

In such a fading environment, a burst error occurs in transmission data. An error correcting code is used to improve performance in communication. The error correction code corrects the random error. The burst error generates a decoding error in the decoding of the error correction code. Therefore, the use of efficient error correction codes in fading channels requires the use of interleaving, which converts burst errors into sporadic errors. The performance of the error correction code in the fading channel is improved by using channel state information in the decoding algorithm. [J. Hagenauer and E. Lutz, "Forward error correction coding for fading compensation in mobile satellite channels," IEEE Journal in Selected Areas in Communications, vol. 5, no. 2, pp. 215-225, Fab. 1987.]

The product code is made by using a simple component code. The product code is long and has a large error correction capability. Generally, the larger the error correction capability of a code, the more complicated the decoding algorithm becomes. [R. E. Blahut, Theory and Practice of Error Control Codes. Addison-Wesley, 1983.]

However, the product code can be decoded using a simple component code decoding algorithm. [S. M. Reddy and J. P. Robinson, "Random error and burst error correction by iterated codes," IEEE Transactions on Information Theory, vol. 18, no. 1, pp. 182-185, Jan. 1972.]

Among conventional techniques for using channel state information for a long code in a decoding algorithm, a concatenated convolutional code, which is known as a turbo code, includes a decoding algorithm using a channel state, And uses a feedback decoding technique based on the reliability of the symbol. [C. Berrou, A. Glavieux, and P. Thitimajshima, "Near Shannon limit error-correcting coding and decoding: Turbo codes (1)," in Proceedings of IEEE International Conference on Communications pp. 1064-1070.]

The concept of this feedback decoding technique is applied to the decoding algorithm of the product code. [R. Pyndiah, A. Glavieux, A. Picart, and S. Jacq, "Near optimal decoding of product codes," in Proceedings of the IEEE GlobeCom, pp. 339-343.]

The sequential decoding method, which starts with the symbol with the highest reliability and decodes with the order of the symbol with low reliability, is used in the 'maximum likelihood sequence estimation'. [R. Walton and M. Wallace, "Near Maximum Likelihood Demodulation for M-Ray Orthogonal Signalling, in Proceedings of IEEE Vehicular Technology Conference, pp. 5-8." In these algorithms, the channel state information of a channel symbol and the decoded symbol According to this method, new decoding algorithms that use channel state information are needed. In this method, channel state information of each symbol is repeatedly generated.

An object of the present invention is to provide a decoding method capable of improving error correction performance in a fading channel.

1 is a block diagram schematically showing a configuration of a system to which the present invention is applied;

2 is a diagram illustrating a structure of a product code according to the present invention;

3 is a diagram illustrating diagonal interleaving in accordance with the present invention;

FIG. 4 shows the probability of decoding failure when decoding is performed according to known algorithms in a Rayleigh fading channel; FIG.

Calculating a symbol error rate of each of the row-component code symbols and the column-component code symbols of each product codeword from the lowest symbol rate to the highest symbol rate among the code symbols; A method for decoding a product code in a Rayleigh fading channel, which includes performing interleaving in a diagonal space, is provided.

Example

Here, a novel decoding method using a new interleaving technique and a decoding algorithm of a component code is disclosed. The performance of the novel decoding method according to the present invention is verified in a Rayleigh fading channel. According to the decoding method of the present invention, component codes are independently decoded. Prior to this, a new interleaving is used which gives an effect of interleaving (an effect of converting a burst error to a scatter error) in both a row component code and a column component code. The order of decoding the component codes is determined from the probability of decoding correctly of the component codes (including row codes and column codes). The probability of correctly decoding each component code is obtained from the channel state information of a symbol.

1 is a block diagram showing a configuration of a communication system according to the present invention. The encoder uses the product code ) In other words, ( ) And the row component code of ( ) Is used. Here, n ₁ and n ₂ represent the size of the product code.

FIG. 2 shows a structure of a product code according to the present invention. In this product code, Let the elements of the i-th row and j-th column be c _{i, j} . The error correcting capability of the row component code as the component code is t ₁ , and the error correction capability of the column component code is t ₂ . The following interleaving technique is used to reduce the effect of miscellaneous errors on both the row component code and the column component code. The interleaver Codeword symbols are output in the codeword of the product code. first Let's say. The interleaver first outputs the symbol c _1,1 , and sequentially outputs the symbols corresponding to the index i, j obtained by the following algorithm.

k = 0;

m = 0;

for v = 1 to n ₁ * n ₂

{

i = (v-1 + k * m) mod n 2 + 1

j = (v-1) mod n ₁ + 1

_{if (i * j = n 1} * n 2), k = 1

if ( k = 1 j = n ₁ v mod n ₂ = 0), m = m + 1

}

There are no restrictions on the sizes of the product codes n ₁ and n ₂ . As shown in FIG. 3, since the code symbols are sequentially output in a diagonal direction, the interleaver proposed here will be referred to as a diagonal interleaver. By the action of the diagonal interleaver, the codewords in any row component code are separated by n ₂ -1 symbols or more from the channel, and the codewords in any column component code are separated by n ₂ symbols or more from the channel have.

Consider algorithms A, B, and C as decryption algorithms. Here, Algorithm A is an algorithm for performing component-by-component decoding without order of component codewords. In algorithm A, each component codeword is independently decoded, and the decoding order of component codewords is predetermined. According to S. M. Reddy and J. P. Robinson, previously described, this algorithm is known to average on the order of half of the number of errors guaranteed by the minimum distance of the product code.

In addition, in the above document, it is known that applying Forney's generalized minimum distance decoding to Algorithm A can correct errors as many as the number of errors guaranteed by the minimum distance of codes. Algorithm B is an algorithm that uses Honey's generalized minimum distance decoding algorithm to algorithm A. In this algorithm B, the component codes are related without being decoded independently.

In the decoding algorithm C according to the present invention, the respective component codes are independently decoded and the decoding order of the component codes is determined according to the probability of correctly decoding the component code. Hereinafter, this algorithm C will be referred to as ordered decoding.

In order decoding according to the present invention, the most reliable component codes (row codes or column codes) are first decoded. Then the second most reliable component code is decoded. To do this, we obtain the reliablity of each component code. As the reliability, we use the probability that the component code is correctly decoded. The decoder receives the estimated code symbol c ' _{i, j} and the channel state information y _{i, j} of the symbol. Where the channel state information y _{i, j} is the signal-to-noise ratio of the channel during which the corresponding code symbol is transmitted. From this value _, the symbol error probability P ^s _{i, j} of the code symbol c _{i, j} can be obtained.

Let N ^R _i be the number of errors in the ith row. The probability of occurrence of e errors in the ith row is given by:

The probability that the ith row from Equation (1) is decoded correctly is given by the following equation.

Let N ^C _j be the number of errors in the jth column. The probability of occurrence of e errors in the jth column is given by

The probability that the jth column is decoded correctly from Equation (3) is given by the following equation.

In the sequential decoding technique according to the present invention, the decoder decodes the component code having the largest P ^R _i (C) or P ^C _j (C) first, then the second largest P ^R _i (C ) Or P ^C _j (C) is decoded second, and all the component codes are decoded in this way. When a decoding result of a specific row component code or a column component code is a decoding failure, the symbols belonging to the component code are not corrected but left as they are. If decoding the decoded symbol in the course of decoding a specific component code, decoding of the component code is regarded as decoding failure.

In the sequential decoding method of the present invention, a component code decoding algorithm is required and calculation is required to determine the decoding order of component codes. There are many calculations that need to be done, but only once for each product codeword.

(example)

The decoding failure probability is taken into consideration as a performance measure in the component code unit decoding algorithm of the product code. The decoding failure is declared as a decoding failure if the code symbol in which both the row component code including the code symbol and the code of the column component are declared to be decoded is present.

Line code as Loa field to take out of the error correction capability t ₁ of a product code (Galois field) GF (q) RS using (Reed-Solomon) codes, and, as the heat code, an error correction capability t ₂ in GF (q on the ) Is used as the Reed-Solomon code. M-ary orthogonal signal is used as the modulation scheme. [Johon G. Proakis, "DIGITAL COMMUNICATIONS ", 3rd ed., McGraw-Hill, New York, 1995.] Consider the case where the size q and the signal set size M of the modulated signal are the same value.

In the Rayleigh fading channel, the symbol error rate when the M-ary orthogonality signal is used is given by the following equation.

Consider a case where the Doppler frequency fd of the channel is 30 Hz, the transmission rate R is 16 kbps, the RS of each row and column code is (7,3), and M = 8. In this way, when RSs 7 and 3 on GF (8) are used as the row and column codes, the decoding failure probability of each algorithm according to the use of the three algorithms A, B, and C 4. Referring to FIG. 4, in order to achieve a decoding failure probability of 10 ^-2 , the sequential decoding algorithm (algorithm C) according to the present invention has a gain of 5.5 dB for algorithm A and a gain of 1.0 dB for algorithm B .

The decoding method according to the present invention has an advantage of being able to decode only by decode algorithm of the component code and computation, since the probability of correct decoding of the component code is calculated from the channel state information of the channel symbol and the decoded method is applied to the component codes.

Claims (6)

A method for decoding product codewords received via a Rayleigh fading channel, the method comprising: Obtaining channel state information of each of the row component code symbols and the column component code symbols of each product codeword; And performing interleaving in diagonal directions of each product codeword according to the channel state information. The method according to claim 1, And the channel state information is a symbol error rate of each code symbol. 3. The method of claim 2, Wherein the interleaving is performed from symbols having the lowest symbol error rate to symbols having a higher symbol rate among code symbols. The method according to claim 1, Wherein the channel state information is a probability that the code symbols are correctly decoded. The method according to claim 1, Wherein the interleaving is performed from symbols having the highest probability of being correctly decoded to symbols having low symbols among code symbols. 6. The method according to any one of claims 2 to 5, Wherein the channel state information is obtained from a signal-to-noise ratio of the channel during which code symbols are transmitted through the channel.