WO1997014223A1

WO1997014223A1 - Method for coding and decoding a digital message

Info

Publication number: WO1997014223A1
Application number: PCT/SE1996/001296
Authority: WO
Inventors: Jan Endresen
Original assignee: Adtranz Signal Ab
Priority date: 1995-10-13
Filing date: 1996-10-11
Publication date: 1997-04-17
Also published as: SE9503585D0; SE9503585L; AU7351596A

Abstract

The present invention relates to a method for coding and transmitting a digital message (c(x)) comprising a first number of information bits (a(x)) and a second number of control bits (b(x)), said message or code word normally transmitted continuously, as well as a method for receiving and decoding such a digital message. In order to allow for a reliable block synchronization and error detection, there is according to the invention suggested a code format by which there is allowed verification before synchronization. The invention has specifically the purpose of providing a method for preventing a possible repeated pattern comprised in the message to be recognized as a correct message.

Description

Method for coding and decoding a digital message

FIELD OF THE INVENTION

The present invention relates to a method for coding and transmitting a digital message comprising a first number of information bits and second a number of control bits, said message or code word being normally transmitted continuously.

Further, the invention relates to a method for receiving and decoding a transmitted digital message comprising a first number of information bits and a second number of control bits, said message or code word being received normally continuously .

In particular, the invention has the purpose of solving problems concerning the protection against error caused by repeated patterns.

BACKGROUND OF THE INVENTION The present invention has been developed in connection with automatic train control systems, but should not be limited to such systems. Further, the present invention has been developed in connection with intermittent communication, in which the communication can last only for a certain period of time due to physical constraints, but neither shall the invention be limited to this specific type of communication.

However, in the present specification the invention will be explained in connection with for example an automatic train system. PRIOR ART

In intermittent communication which due to physical

constraints can only last for a certain period, it is important to maximize the information transferred for a given reliability. An example is a train passing a radio beacon (sent from a transponder or balise) which transmits a message containing control information. The normal way to solve this problem is for the beacon to transmit a known synchronization bit pattern before the message. This way put a constraint on the information in the message to avoid false synchronization.

Another way of solving the synchronization problem is to slave the radio beacon to the train receiver, but this is more complex and requires a transmitter in the train. The message is repeatedly transmitted by the beacon to increase the probability of correct reception. Those aspects of the system that are relevant can be summarized as follows

The beacon transmits a binary message of the given length n. This message is repeated without gaps for as long as the beacon gets enough power. - The receiver must be able to determine the block boundaries in the received data stream.

The probability of undetected error (the reliability) of the transmission must be guaranteed.

Problems related to coding and decoding a digital message as described are solved and discussed in the patent document WO 93/06662. Said document discloses a method, in which there is avoided the need to wait for a start of a block or message, and in which there is allowed data verification before synchronization. Another objects of that prior art presentation is to provide a method, in which error control and synchronization are combined in the same parity bits. The above objects are achieved in that on the transmitter side there is selected a generator polynomial G(x) producing a cyclic code, that said information bits are divided by said generator polynomial for thereby generating a remainder polynomial which is included in the message to be

transmitted as said second number of control bits.

Thereby is achieved a valid code word provided the correct number of bits are received, but independent of the

synchronization shift or start bit thereof.

In order to facilitate the control of any synchronization shift in the message or code word it is required that on the transmitter side there are selected first, G(x), and second, F(x), polynomials both being generators for cyclic codes, which polynomials are multiplied with each other, and that said information bits are divided by said products for thereby generating a remainder polynomial which is included in the message to be transmitted as said second number of control bits, and more specifically in that the first, G(x), of the two cyclic code generator polynomials is used for controlling error detecting capability of the message in question, whereas the second, F(x), of the two cyclic code generator polynomials is used for acquiring synchronization. In a specific embodiment of said prior art invention the length of the digital message or code word comprises a specific number of n bits, and there is used first, G(x), and second, F(x), selected generator polynomials which both produce cyclic code words of length n, said second generator polynomial, F(x), being irreducible and not a factor in said first generator polynomial, G(x).

In a still more specific embodiment of said prior art invention an offset polynomial is added modulo 2 to the remainder of the code word in question, the offset

polynomial being divisable by the error control generator polynomial (G(x)) but not the synchronization generator polynomial (F(x)).

Consequently, at the receiver side the method according to said prior art disclosure is characterized in that the message or code word is registered as such independently of the sequential appearance of the start of the information bits as long as the correct number of bits (n) in one message block are received.

A problem is that a telegram is handled by hardware and software. It is possible for both hardware and software to generate repeated patterns, which may exert an influence on a fail-safe communication when using the above described coding and decoding of a digital message. For hardware the most common repeated pattern periodz would be 1, 8 or 16 bits and for software it would be 8 or 16 bits, but both can generate any error pattern period. The object of this invention is to provide a method to prevent disturbance on communication with digital messages caused by repeated patterns.

DESCRIPTION OF THE INVENTION

According to the invention the problem with disturbances acting on a digital message caused by repeated patterns is solved by a method for coding and transmitting a digital message (c(x)) comprising a first number of information bits (a(x)) and a second number of control bits (b(x)), said message or code word normally being transmitted

continuously, where on the transmitter side there are selected first and second polynomialls (G(x)) and (F(x)) both being generators for cyclic codes, which polynomials are multiplied with each other, that said information bits (a(x)) are divided by the formed product (G(x)*F(x)) for thereby generating a remainder polynomial (c_r(x)) which is included in the message to be transmitted as said second number of control bits (a(x), Cr(x)) , that the possible error pattern is described in terms of the product of a random polynomial Rand(x) and a fixed polynomial Fix(x), whereby the second polynomial F(x) is chosen to be a factor of the fixed polynomial Fix(x).

An advantage with the disclosed method is that all repeated patterns are valid code words with respect to the

synchronisation polynomial F(x), i. e, the remainder is zero after a division of the repeated pattern with F(x), which is not allowed for correct messages, since the remainder of a correct message is non-zero after dividing it with the polynomial F(x). This property is guaranteed because the F(x) factor is present in all the fixed polynomials being a factor of the repeated pattern. The synchronisation

polynomial F(x) has therefore the added benefit of guarding against repeated pattern.

BRIEF DISCLOSURE OF THE DRAWINGS

Figure 1 illustrates the format of a code word block

according to the specified prior art technique.

Figure 2 illustrates the polynomial corresponding to the data seen through a window of length n.

DETAILED DESCRIPTION OF EMBODIMENTS

In the following an example telegram consisting of 255 bits is chosen, but the disclosed method can be generalised to any code length.

A telegram message consisting of 255 bits can be factored into 1, 3, 5 and 17. Error patterns with a period equal to any of the factors or any product of the factors less than 255 will repeat itself after 255 bits. Altogether, there are 7 valid period length for cyclic error patterns, namely 1, 3, 5, 15, 17, 51 and 85.

In the approach used in this invention, the possible repeated patterns are written in the form of a product of two polynomials, one random Rand(x) and one fixed, Fix(x).

For a cyclic repeated pattern possible in a 255 bits message said polynomials are listed in the table

where the a_i are random variables of value 0 or 1. To evaluate whether a repeated pattern is a valid code word the polonomials (Rand(x), Fix(x)) associated with the repeated pattern can be factorized to check if all the factors of G(x) are present. The fixed polynomials can be factorized and summarised as shown in the table below.

The numbering of the factors is following the numbering scheme of minimal polynomials according to appendix B of "Lin and Costello: Error control Coding", Prentice Hall, 1983. The names of the polynomials indicate the possible fixed polynomials. These fixed polynomials P₃ (x), ..., P₈₅ (x) as well as the polynomials G(x) and P₁ (x) are listed at the end of the description.

As can be seen from the table all the factors of G(x) are present in the fixed polynomials P₃ (x), P₅ (x) and P₁₅ (x).

This means that any random repeated polynomial of length 3, 5 or 15 bits will be valid code words with respect to G(x). For the fixed polynomials P17 (x), P₅₁(x) and P₈₅ (x) nearly all the factors of G(x) are present. The missing factors have to be found in the random polynomials for the repeated patterns to become valid code words. This can be satisfied for a large number of repeated patterns since the random polynomials have an order much larger than the missing factors. But, as is concluded above, by choosing the

synchronisation polynomial, F(x), as one being a common factor for all the fixed polynomials at the same time, it is guaranteed that the remainder of the repeated pattern after division by the chosen synchroniation polynomial F(x) is zero, which is not allowed for a correct balise telegram.

In a specific embodiment the synchronisation polynomial is chosen to be F(x) = (1 + x + x⁵ + x⁸) .

THE CODE FORMAT Binary vectors are denoted by polynomials, e.g. the vector v = [v_k-1, ..... ,v₁,v₀], is represented by the polynomial v(x)- = v_k-1x^k-1 + ... + v₁x + v₀.

The transmitted message (the code word) is denoted by c = [c_k-1, .....,c₁,c₀], corresponding to the polynomial c(x).

The order of transmission is from left to right, i.e. c_n-1 is the bit transmitted first, then c_n-2, etc, and C_o is transmitted last. The same message is repeated continually. The transmitted messages are code words in a cyclic code of length n, the generator polynomial of which will be called G(x); i.e. c(x) is divisible by G(x). A cyclic code is such that every valid code word can be divided into two parts and the parts interchanged, and the new code word will still be valid. The error detecting and error correcting capability of the proposed scheme comes from G(x). The degree of G(x) will be denoted by m. A second polynomial, which will be denoted by F(x), will be used for synchronization. The polynomial F(x) - is irreducible

- divides xⁿ-1 but does not divide x^m-1 for O<m<n

- is not a factor of G(x).

The degree of F(x) is denoted by 1. The above constraints ensure that any cyclic shift of the code word has a unique syndrome with respect to F(x).

For any two polynomials h(x) and p(x) non zero, let

R_p(x)[h(x)] denote the unique polynomial r(x) of degree less than deg[p(x)] that satisfies h(x) = q(x)p(x) + r(x), i.e. it is the remainder that results from dividing h(x) by p(x).

Let a(x) be the information polynomial, i.e. the polynomial corresponding to the binary vector [a_k-1, ..... ,a₁,c₀] of information bits. The number k of information bits equals n-1-m. Note that there is no constraint on the information bits, i.e. all 2^k possibilities are allowed.

The encoding rule is: c(x) = x^{m+ l} a(x) + R_F(x)G(x) [x^m+l a(x)] + o(x)

The multiplication of a(x) with the factor x^m+l has the effect of shifting the information m+1 to the left, leaving m+l bits free for the parity and offset bits. The remainder is calculated with respect to the product of F(x) and G(x). The binary polynomial o (x) ("offset") is used for synchronization. It is divisable by G(x) but not F(x), and its degree is smaller than m+l. Any binary polynomial satisfying these constraints can be used; and as for F(x) above, there is no reason to choose a particular o(x). The resulting code format is shown in Fig. 1.

Since o(x) is divisible by G(x), c(x) is always divisible by G(x) and is therefore a code word in the cyclic code generated by G(x). Note also that c(x)-o(x) is divisible by F(x), but c(x) is not.

The central idea of this code format is that in the absence of errors, any block of length n that is cut out of the transmitted data stream is a code word in the cyclic code generated by G(x) . Any such block is thus protected by the full error-detecting capability provided by G(x) . The code format of this section may be used with a varity of codes .

DECODING

The basic operation to be performed by the receiver is thus as follows:

1. Receive a block of n bits .

2. Look at a given window of length n. Verify this code word with respect to G(x). If this is possible, go to step 3; otherwise shift the window and do step 2 again.

3. Recover data from window based on parity check with respect to F(x). As an alternative, the shifting of the windows in the case of an unsuccessful decoding attempt can be left out.

Now, consider point 3 of this procedure, i.e. the recovery of the information from the window. Let w(x) be the polynomial that corresponds to the data block as seen through a window of length n that is shifted by s positions with respect to the block boundaries of the transmitted data, see Fig 2.

If s is the shift between the block boundaries of the data stream and the window, then the received code word is w(x) = R_xn_-1 [x^s·c(x)]. It can be shown that all shift s in the range 0, ..... ,n-1 have unique syndrome R_F(x)[w(x)]. The information a(x) can thus easily be recovered from w(x); i.e. shifting w(x) cyclically s times to the right yields c(x). In the listing below of the polynomial factors the symbol denote the "power of" sign.

Claims

1. Method for coding and transmitting a digital message (c(x)) comprising a first number of information bits (a(x)) and a second number of control bits (b(x)), said message or code word normally being transmitted continuously, where on the transmitter side there are selected first and second polynomials (G(x)) and (F(x)) both being generators for cyclic codes, which polynomials are multiplied with each other, that said information bits (a(x)) are divided by the formed product (G(x)*F(x)) for thereby generating a

remainder polynomial (c_r(x)) which is included in the message to be transmitted as said second number of control bits (a(x), c_r(x)), characterized in that a possible repeated pattern comprised in the message is described in terms of the product of a random polynomial (Rand(x)) and a fixed polynomial (Fix(x)), whereby the second polynomial (F(x)) is chosen to be a factor of all the fixed polynomials (Fix(x)).

2. Method according to claim 1, characterized in that the second polynomial (F(x)) for a message consisting of 255 bits is chosen as a factor common to any of the polynomials P₁, P₃, P₅, P₁₅, P₁₇, P₅₁ and P₈₅, said polynomials being

3. Method according to claim 2, characterized in that the second polynomial (F(x)) for a message consisting of 255 bits is chosen as the factor (1 + x + x⁵ + x⁸) common to the polynomials P₁, P₃, P₅, P₁₅, P₁₇, P₅₁ and P₈₅.