FR2787263A1 - TRANSMISSION METHOD WITH EFFICIENT AND MODULAR INTERLACING CHANNEL CODING FOR TURBO CODES - Google Patents

Abstract

In order to be able to implement a turbo code without having to make a specific hardware circuit, provision is made to constitute a permutating interleaver in the form of a congruence algorithm (21). It is shown that such an algorithm can then be used for any lengths of bits to be processed, while imposing fewer constraints on the production of specific circuits. Turbo codes can then be more easily implemented in radio-type links with mobile telephones.

Description

Transmission method with efficient interleaving channel coding and

  The present invention relates to a transmission method with channel coding, that is to say with a preparation of bits to be transmitted which takes account of the transmission performance of a channel in such a way that the quality of transmission is as perfect as possible, despite the inevitable physical defects inherent in this channel. The object of the invention is to propose a method in which a practical implementation of a theoretical and proven solution is simple to carry out with signal processing equipment with limited power. This equipment is in particular mobile telephones. The main application of the invention is therefore that of mobile telephony. However, the invention could also be used in links with satellites. In general, the invention can be used whenever we want to implement a turbo code for which efficient and modular interleaving is sought. In terms of digital transmission of information (speech, image, data, etc.), a distinction is made between source coding and channel coding. The purpose of source coding is to compress the digital information to be transmitted, so that it occupies the least possible volume, so that the useful bit rate is maximum. In contrast, channel coding involves adding redundancy to the information to be transmitted so that

  the information received is more robust in the face of errors made by the channel.

  By acting in this way, a useless redundancy, that of the initial information, is transformed into a useful redundancy, that making it possible to resist transmission noise. Channel coding is therefore of paramount importance. A wide range of channel codings has been available since the 1960s. We thus know convolutional codings, BCH codings, Reed-Solomon codings, etc. The channel codings used differ according to the

targeted applications.

  In French patent application 91 05280 entitled "Error correcting coding method with at least two systematic convolutional codings in parallel, iterative decoding method, decoding module and corresponding decoder", as well as in the document "Near Shannon limit error -correcting coding and decoding: Turbo Codes "Proc.1993 International Conference on Communications, due to C. Berrou, A. Glavieux and P. Thitimajshima, we proposed a new coding scheme called turbo code whose performances approach the theoretical limit of the capacity of a channel as described by C. Shannon's theorem. In an example where the coding rate is 1/3, a stream X of data to be coded is transmitted with such coding in the form of three streams Y1, Y2, and Y3 of coded data. In an example, the flow Y1 is the same as the flow X. The flow Y2 results from the coding of the flow X by a first recursive convolutional coder. The flow Y3 results from the coding of a permutation, one improperly speaks of an interleaving, of the bits of the flow X by a second recursive convolutional coder. A turbo encoder thus uses at least two convolutional, preferably recursive, systematic encoders, the second being

  preceded by a time interleaver operating on blocks of fixed size.

  The permutator-interleaver is an essential component of turbo codes. A conceptual interpretation of their mode of operation is given in the article by G. Battail "A conceptual framework for understanding Turbo Codes" IEEE Journal on Selected Areas in Communications, Vol.16, No 2, February 1998. Very briefly, we can remember that interleaving allows, if done right, to imitate random coding. It should also be remembered that the role of random coding in the proof of C. Shannon's capacity theorem is central. It is generally agreed that there are two very important factors in the design of such an interleaver. The first factor is the depth of this interleaver. The depth is the size of the interleaver, in clear the number n of bits that it is likely to swap. The greater the depth, the better, that is to say the more the randomness will be effective. The second factor is the degree of randomness that the interleaver can introduce on a given block. An ideal interleaver is then a purely random interleaver,

  but this does not exist in practice.

  In fact, an interleaver aims to break the least significant code words that are transmitted. It is also possible to design non-random interleavers that effectively fight low-order code words. But unfortunately, these latter interleavers tend to amplify the effects of the most significant code words, which is not desirable either. The criterion for choosing an optimal interleaver must consider the codes of all the weights simultaneously, and obtain an overall optimum. The determination

  of this criterion is still an unsolved problem.

  The interlacing techniques used in real systems of the prior art use matrices. These matrices are implemented with hardware circuits. In such hardware circuits, the data, or bits, of a block are entered online, line of the matrix after line of the matrix. They are then read in column. Simulations show, however, that the performances obtained with such matrix interleavers are lower than those obtained with

  interleavers produced by computer programs imitating randomness.

  On the other hand, third generation cellular radio mobile communications, in particular within the framework of the IMT 2000 recommendation, require the use of a wide variety of services associated with different bit rates and time constraints. Given the performance of turbo codes, it is likely to be used for services that require strong protection against errors but which bear a certain delay (that of the interleaver). The problem not solved by the matrix systems is then the fixed character of the dimension of the blocks of data likely to be treated. These frozen dimensions result

  the size of the chosen matrices and their writing-reading system.

  Thus, if we suppose to have k different services, each supporting the time delays of rl, r2, ..., rk bits, the goal is to seek, for each service, to make an interleaver of maximum depth, knowing that

  interleaving performance is based on the size of the interleaver.

  A difficulty in the conventional matrix implementation is to have to rigidly specify the different interleavers for the

different block sizes.

  The object of the present invention is to remedy these problems. It proposes to design an interleaver produced in software, which also requires very few parameters in memory. In the invention, for a block of n bits to be interleaved, with rows k numbered from 1 to n in the chain of bits to be transmitted, another block of n bits of an interlaced chain is created by permutation. The ranks of the bits in the interlaced string are then ranks h, such that h = f (k). The function f must be

  a permutation of {1, ..., n} that is to say a bijective application of {1, ..

  n} in itself. In the invention to perform the function f, an equation of linear congruence is applied. It can then be shown that the choice of such a solution has the effect of dispensing with specific circuits, and furthermore requiring only low resources in terms of software. The randomness is thus not theoretically perfect but its approximation by a simple algorithm, of congruence, is quite effective with regard to the problem of improving the performance of coding.

of channel sought.

  The subject of the invention is therefore a method of transmission with channel coding, between a transmitter and a receiver, in which - a binary chain of n bits to be transmitted is coded with a first coder to obtain a first coded chain, - one permutes bits of the binary chain to be transmitted to obtain another so-called interlaced binary chain, - the interleaved chain is coded with a second coder to obtain a second coded chain, - the binary chain to be transmitted is transmitted from the transmitter to the receiver and or the first and or the second coded strings, - and the corresponding strings transmitted on the receiver side are received and decoded in correspondence to reconstruct the binary string to be transmitted, characterized in that - to permute the bits of the binary string of n bits to be transmitted, a bit of rank k of the binary chain to be transmitted is assigned a rank hk in

  the interlaced string, which depends on a rank hk-, assigned to a bit of rank k -

  1 of the binary chain to be transmitted, so that the rank hk assigned is of the type: hk = a.hk 1 + b modulo m, a, b and m being integers

  The invention will be better understood on reading the description which follows

  and examining the accompanying figures. These are presented for information only and in no way limit the invention. The figures show: - Figure 1: the functional representation of a coding device which can be used to implement the method of the invention; Figure 2: a flow diagram of steps of the interleaving method of the invention

  - Table 1, which is an explicit part of the description, includes

  preferred values of parameters subscribing to preferred variants

  of implementation of the algorithm of the invention.

  FIG. 1 shows a functional representation of means for implementing a transmission method according to the invention. This process

  is intended to be implemented between a transmitter 1 and a receiver 2.

  The transmitter 1 and the receiver 2 are symbolically shown and are linked together by a channel 3. The transmission method with channel coding of the invention is of the type transforming a data stream X produced by the transmitter 1 into several data streams Y1, Y2, Y3, Yi transmitted by the channel 3. The channel 3 will mostly be a radio channel, a coding circuit 4 implementing the method of the invention, and interposed between the transmitter 1 and the receiver 2, further comprising an associated radio transmission circuit not shown. In reception, circuits are adapted to decode and receive in correspondence the chains Y1, Y2, Y3, Yi

  and to reconstitute the transmitted X chain.

  The channel coding circuit 4 comprises a first convolutional coder which produces a bit chain Y2 from a chain to be coded X. In one example, this convolutional coder is a recursive convolutional coder. In principle, it comprises a certain number of delay circuits 6 to 9, in cascade from one another, and the outputs of which are connected to adders or more generally to operators 10 to 13. The aim of operators 10 to 13 to combine together bits of the chain X available at a given date with bits of this same chain, or a transformation of this chain, available at a later date. The convolutional coder 5 shown is said to be recursive because the convolution products, in particular those from the operator 12 are combined at the input of the system, in an operator 13, with bits not yet processed of the chain X of the bits to be coded. As indicated above, the realization of a recursive convolutional coder is preferred because at equal coding complexity (and at equal protection efficiency) such a recursive coder requires fewer operators and delay circuits than a non-coder recursive which would perform the same transformation. That said, in the invention it is therefore not a priori necessary for the coder 5 to be a recursive convolutional coder. It could be a simple convolutional coder, or even another coding system of the BCH type.

  or Reed SOLOMON, or whatever, but the performance would be different.

  In addition to being transmitted as is in the chain Y1, or in a convoluted form in the chain Y2, in the invention the bit chain to be processed X is transmitted in the form of a third chain coded Y3 by another coder 14 which also receives the string X of bits to be coded. The particularity of the chain Y3 is that it is produced from a permutation of the chain X of the bits to be coded. This permutation is carried out by a permutation circuit, also called interleaver 15, interposed between

  the input of the encoder 14 and the input of the coding circuit 4.

  The left of FIG. 1 shows in an example in a 12-bit chain X, the processing carried out bit by bit by the interleaver 15 to transform the chain X into a permuted chain X '. The interleaver 15 is preferably a software interleaver and its transformation algorithm is shown in FIG. 2. In accordance with what was mentioned previously, to permute the bits of the binary chain of n bits to be transmitted, here twelve bits in l 'example, a bit of rank k of the binary chain X is assigned to transmit a rank hk in the interlaced chain X'. The particularity of the invention is that the rank hk in the chain X 'depends on the rank hk.l assigned to a bit of rank k-1 of the binary chain X of bits to be transmitted. The dependence is such that hk = a.hk- 1 + b modulo m In this formula a, b and m are integers, parameters of the transformation. To be complete, an additional parameter, essential to the invention, is the number n of bits of the chain X to be coded. In fact, as indicated in the preamble, the invention makes it possible to adapt the coding to the length of the words to be transmitted. For example, in the context of GSM, we know that out of a useful window of 156 bits, only 142 have an informative meaning. Among these 142 bits, three groupings are formed. A first and a third grouping represents information to be transmitted. A second grouping, intermediate between the other two, includes coherence information enabling a channel decoding circuit, on reception, to find the two expected groupings of bits, and to improve the transmission performance of the channel. Other standards are possible. Even in GSM it is possible to adapt high speed transmission protocols. In these cases, the key length of the words to be transmitted is no longer 142 bits but

  may be much larger. For example it can be 1024 bits or more.

  Also, during a step 16, the values of the parameters n, a, b and m are defined in the program implemented by the interleaver 15. We will see below what are the constraints weighing on judicious choices of these parameters, the non-compliance with these constraints leading to degraded operation, although possibly acceptable of the coding algorithm of the invention. After step 16, during a step 17, one begins to scan the chain X of bits to be transmitted. This is done in the form of two instructions 18 and 19, respectively an instruction 18 k = 1 and hk = 1 followed by an instruction 19 k = k + 1. Instruction 18 actually means that we will assign to the bit of rank 1 in the chain X to transmit a rank hk = 1 in the chain X ', before its coding by the coder 14. This is not an obligation. In particular, it would be possible for k = 1 to choose a starting hk other than 1. It would simply suffice that hk is less than n. Choosing hk other than 1 can lead, as mentioned above, to neither penalize nor unduly advantage the least significant or most significant bits. If necessary, provision can be made for hk to change value for each new chain X undergoing a permutation. Step 17 is followed by a test 20 during which it is checked whether the bit of rank k to be processed belongs to the chain X of n bits or whether it belongs to another chain, consecutive to the chain X, it also of n bits. If it is not the case, and at the beginning it is not the case, it is then possible to find the rank hk by applying the instruction 21

knowing that we know a, b and m.

  If they are produced in this way, the hk are not necessarily distributed in a well random manner over the entire chain of bits. Furthermore, it is even possible in certain cases that the transformation 21 is not a permutation of {1, 2, ..., n}. For these latter criteria to be obtained, certain constraints must be imposed on the parameters a, b and m. Indeed the (infinite) sequence defined by the linear congruence of step 21 has for period m if, and only if, b and m are prime between them; if for any prime number p dividing m, a - 1 is a multiple of p; and if a - 1 is a multiple of 4 when m is a multiple of 4. A justification for these constraints is found

  in the article by HULL and DOBELL, SIAM Review, 4 (1962), pages 230-254.

  In practice, it suffices to take m = n + 1 to produce a permutation.

  --r1 In the example shown in Figure 1, we want to swap twelve bits. We can then take m = 13. It is indeed important that m is greater than n. We will see later how to take m much larger than n to solve certain difficulties of the algorithm. It remains to choose a and b. Choosing b different from zero means choosing hk different from 1 for k = 1. Most of the time we will choose b = 0. However, to go from one permutation to another, with a single algorithm implemented according to l step 21, it will suffice to add b (modulo m) to the rank of each bit produced by the interleaver 15 in which b will have value zero. Thus, in FIG. 1, the coding circuit 4 can include other coders to produce other chains Yi of coded bits. Rather than starting each time from chain X and providing for another complex interleaver 15, it may in this case be more useful to start from chain X ', to change the value of b, and thus to constitute an additional interleaver. inexpensively, by adding b modulo m,

to attack another encoder.

  It therefore remains to choose a. In an example, we can arbitrarily choose a order of half of n, or half of n - 1. For example here we will choose a = 6. The implementation of step 21, with a = 6 and b = 0 for m = 13 then gives the following results, the first line giving the rank k of the bits of the chain X, the second line giving the ranks assigned hk in the chain X:

1 2 3 4 5 6 7 8 9 10 11 12

1 6 10 8 9 2 12 7 3 5 4 11

  This example is moreover represented in the margin on the left of FIG. 1. The first line represents the rows k of the bits of the chain X of bits to be processed, the second chain representing the rows hk which have been allocated in application of the step 21 to these bits of rank k of the chain X. As mentioned in step 18, the bit of rank k = I is found ranked at rank hk = 1 in the chain X 'of coding bits. For the bit of rank k = 2, we apply the formula 21. This gives a rank h2 = 6 x 1 + 0 modulo 13 taking b = 0. The operation 6 x 1 + 0 gives 6, modulo 13 does not change the result. This leads to assign to the bit of rank k = 2 a rank hk = 6 in the chain X '. For the bit of rank k = 3, the application of the formula gives h3 = 6x6 + 0 modulo 13. This gives 36 modulo 13, that is 10. Thus, all the ranks hk are assigned. Knowing that bits of the chain X can be produced by the generator I progressively, the interleaver 15 then comprises a register 22 in which, according to a step 23, we rank, as and when they are produced by the generator 1, the bits of the chain X 'as a function of the place which will have been allocated to them by step 21. The arrows shown on the register 22 relate to this ranking 23. If one wants to permute a fixed number n of bits and that m = n + 1 cannot verify the constraints (which is rarely the case), we can find a m 'greater than m, make the permutation using a linear congruence in m', and then cross out the number greater than m. For example, if we want to swap ten bits, we can take as above m = 13, a = 6, b = 0 and hl = 1. We then obtain

1 2 3 4 5 6 7 8 9 10 11 12

I 6 10 8 9 2 4-2 7 3 5 4 14

  We then strike out 12 and 11 and obtain a randomly organized sequence.

1 2 3 4 5 6 7 8 9 10

1 6 10 8 9 2 7 3 5 4

  By doing so, for m strictly greater than n + 1, we assign a rank hk + î in the interlaced chain to a bit of rank k in the binary chain to be transmitted, when the rank hk normally attributable in the interlaced chain is greater to n, and this for all the bits of rank greater than k of the binary chain to be transmitted. Indeed, a rank 7 was assigned in the interleaved chain to the bit of rank 7 in the binary chain to be transmitted while the rank 12 normally attributable in the interlaced chain was greater than 10. Such a shift was carried out for all the bits of rank greater than 7, that is to say the bits of rank 8, 9 and 10, of the binary chain to be transmitted. In the example shown, of course the deletion of rank 11 has no influence since this rank was the last assigned. Nevertheless the principle of shift thus evoked can be applied

several times.

  Step 23 is followed by an iteration by branching between instructions 18 and 19. When in test 20 the rank of the bit produced by generator 1 becomes greater than k, then in step 24 the word contained in the register is read 22, it is coded by the coder 14. The chain Y3 of bits processed is then transmitted in a step 25 by the transmission circuit and is sent to the channel 3. To make the processing by the coder 14 more fluid, it it is possible to provide a second register 26. The second register 26 also belongs to the interleaver 15. In this case, during the reading of the chain X ′, the coding and the transmission of the bits contained in the register 22 , the interleaver 15 is responsible for constituting another chain X ′ of permuted bits. In this case, simultaneously with step 24, the algorithm of FIG. 2 comprises a connection 27 to a word of next n bits, to a

next X string to process.

  We give below in table TABLE 1 according to examples

  of values of parameters a, b and m.

TABLE 1

a b m

6 0 13

0 17

7 0 257

206 7 1025

  In practice, the choice of parameters a, b and m is made, using a pragmatic approach, by comparing the overall performance of coding with different permutations. It would however be possible to provide an automatic algorithm which would calculate these parameters from a number n

given.

  In this calculation, in a first step, we choose m = n + 1. Then we choose a on the order of half of m or n. The condition of b and m

  prime among them is then naturally obtained by choosing b = 0.

  Then, we look for all the prime numbers p dividing m. And we seek a so that a - 1 is a multiple of p, whatever p. For example on a chain X of n = 1024 bits, we try m = 1025 which is not prime. We

  then reduce m to prime factor. We can thus write 1025 = 5 x 5 x 41.

  This leads to choosing, for a, the value 5 x 41 + 1. Let a = 206. We then verify that m - a is a multiple of 5 and 41. We can then define b according to the rank of the interleaver 15 in the set of interleavers used in the coding circuit 4. If there is only one b will be worth 0. If there are two, for the first b will be worth 0 for the second b will have a other value, by

example a / 2.

  The implementation of the algorithm of the invention requires the multiplication of the ranks hk-1 by a. This does not present any difficulties taking into account the speed of the operators currently available in the processing circuits. The addition of b is an operation which generally uses only one cycle time. The congruence, modulo m, can be achieved with a simple shift of the reading of the result produced by the adder which adds b or the multiplier by a. Choosing b = 0 obviously has the advantage of eliminating an operation, the shift being made in this case on the result

of multiplication.

  The advantages of the solution of the invention compared to the state of the art are: - great simplicity of production of the interleaver 15 (design, cost, etc.); - better performance in cases where flow rates and specific time constraints are to be respected; - a purely software management and requiring very little memory, only that of register 22 very rarely greater than 10 Kbits; - adaptability to the different services existing during an initial implementation as well as adaptability to possible subsequent modifications. It suffices to modify the program represented by FIG. 2. If the randomness must be modified, as explained above, we can add b to the calculated rows hk. Alternatively, it is possible to iterate the process on the hk found. In this iteration a, b and m can be the same or be changed. We then assign

  new hl rows to previous hk rows.

Claims (7)

  1 - Transmission method with channel coding (4), between a transmitter (1) and a receiver (2), in which - we code (5) a binary chain (X) of n bits to be transmitted with a first coder for get a first coded string (Y2), - we swap (15) bits of the binary string to be transmitted to obtain another binary string (X ') called interlaced, we code (14) the interlaced string with a second coder to obtain a second coded channel (Y3), - we transmit (3) from the transmitter to the receiver the binary channel to be transmitted and or the first and or the second coded channels, - and we receive and decode in correspondence the channels transmitted on the receiver side to reconstitute the binary chain to be transmitted, characterized in that - to swap the bits of the binary chain of n bits to be transmitted, one assigns (21) to a bit of rank k of the binary chain to be transmitted a rank hk in the chain interleaved, which depends on a rank hk-1 assigned to a bit of rank k- 1 of the binary chain to be transmitted, so that the rank hk assigned is of the type: hk = a.hk- 1 + b modulo m, a, b and m being integers   2 - Method according to claim 1, characterized in that m = n + 1.   3 - Method according to claim 1, modified in that m is greater than n + 1 and in that one assigns a rank hk + 1 in the interlaced chain to a bit of rank k of the binary chain to be transmitted when the rank hk normally attributable in the interleaved chain is greater than n, and this for all the bits of rank greater than k of the binary chain to be transmitted.   4 - Method according to one of claims 1 to 3, characterized in that   that b and m are prime to each other, in that, for any prime p which divides m, m - a is a multiple of p, and in that a - 1 is a multiple of 4 if m is a multiple of 4.   - Method according to one of claims 1 to 4, characterized in that that b is 0.   6 - Method according to one of claims 1 to 5, characterized in that   that the coding is a recursive convolutional coding.   7 - Method according to one of claims 1 to 5, characterized in that the parameters a b and m are given values corresponding to one of lines of the following table: 5 a b m 6 0 13 O0T 17 7 0 257 206 7 1025   8 - Method according to one of claims 1 to 7 characterized in that it reiterates the allocation of ranks by assigning new ranks (hi) to ranks (hk) already assigned.