Abstract:
An LDPC decoder having a determined number of processing units operating in parallel, storage circuitry capable of containing first words containing a juxtaposition of messages of a first type, and second words containing a juxtaposition of messages of a second type, a message provision unit capable of providing each processing unit with a message of the first type or a message of the second type, and a message write unit capable of writing, into the storage circuitry, first words or second words. The message provision unit is capable of providing a message at a position in a word which depends on the word or the message write unit is capable of writing each message at a position in the word which depends on the word.

Description:
BACKGROUND OF THE INVENTION 
   1. Field on the Invention 
   The present invention relates to an LDPC (Low Density Parity Check) decoder. 
   2. Discussion of the Related Art 
   LDPC decoding enables obtaining performance very close to the Shannon limit. LDPC decoders generally have better performance than turbo-code decoders and are currently used in broadcasting systems, for example, satellite digital television broadcasting systems. 
   LDPC decoding consists, for a given word s containing k bits, of transmitting a word u containing n bits, among which n-k additional bits called parity bits which fulfill n-k parity equations. The matrix H having n-k lines and n columns verifying the following relation is called the code control matrix:
 
 H*   t u=0  (1)
 
   The size of the matrices H generally used is significant since they may comprise more than 60,000 columns and 50,000 lines. Further, such matrices are practically empty and may comprise one “1” for approximately 10,000 “0 ”s. This is why they are called low-density matrices. 
   The number of “1”s in the line is called the check node degree of a line and the number of “1”s in the column is called the bit node degree. There are two types of LDPC codes: regular codes and irregular codes. Matrix H of a regular code has a constant number of “1”s per line and per column. The check node and bit node degrees are then constant. An irregular code has no constant check node degrees and/or bit node degrees and has a more random character. However, the best performances are obtained for irregular codes. The problem of an irregular matrix is that it is random. The decoding can then be difficult. European digital satellite television standard DVB-S2 advocates for the use of a matrix H which has a constant check node degree, between 4 and 30, and a bit node degree that can take three values, between 2 and 13. 
     FIG. 1  shows a graph corresponding to an equivalent representation of a matrix H of an LDPC code. Each circle  10  represents a bit node. As an example, six bit nodes BNi, With i ranging from 0 to 5, are shown. Each square  12  represents a check node. As an example, four check nodes CNj, with j ranging from 0 to 3, are shown. Branches  14  connect given bit nodes BNi to given check nodes CNj. The presence of a branch  14  between a bit node of index i and a check node of index j means that the equivalent matrix H has a “1” at line j and at column i. Note Ne the total number of branches  14  in the graph. Number Ne thus corresponds to the number of “1”s of matrix H. 
   The matrix H equivalent to the graph shown in  FIG. 1  is the following: 
   
     
       
         
           
             
               
                 H 
                 = 
                 
                   ( 
                   
                     
                       
                         
                           1 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           0 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           0 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           0 
                         
                       
                     
                     
                       
                         
                           1 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           0 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           0 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           0 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                       
                     
                     
                       
                         
                           0 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           0 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           0 
                         
                       
                     
                     
                       
                         
                           0 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           0 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           0 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                       
                     
                   
                   ) 
                 
               
             
             
               
                 ( 
                 2 
                 ) 
               
             
           
         
       
     
   
   Such a matrix H has a constant bit node degree equal to 2 and a constant check node degree equal to 3. 
   LDPC decoding uses log-likelihood ratios (LLR). For a transmitted information bit d to which corresponds a signal y received by the decoder after addition of the transmit channel noise, the LLR ratio of bit d with respect to signal y is defined as follows: 
   
     
       
         
           
             
               
                 
                   LLR 
                   ⁡ 
                   
                     ( 
                     y 
                     ) 
                   
                 
                 = 
                 
                   
                     LLR 
                     ⁡ 
                     
                       ( 
                       
                         d 
                         | 
                         y 
                       
                       ) 
                     
                   
                   = 
                   
                     ln 
                     ⁢ 
                     
                       
                         P 
                         ⁡ 
                         
                           ( 
                           
                             d 
                             = 
                             
                               0 
                               | 
                               y 
                             
                           
                           ) 
                         
                       
                       
                         P 
                         ⁡ 
                         
                           ( 
                           
                             d 
                             = 
                             
                               1 
                               | 
                               y 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
             
             
               
                 ( 
                 3 
                 ) 
               
             
           
         
       
     
       
       
         
           where P(d=0|y) is the probability for transmitted bit d to be equal to 0 according to the received value y and P(d=1|y) is the probability for transmitted bit d to be equal to 1 according to the received value y. Such probabilities especially depend on the features of the transmit channel. The larger LLR(y), the greater the probability for transmitted bit d to be equal to “0”. As an example, it may be decided, for a received signal y, that if LLR(y) is negative, then transmitted bit d is a “1” and that, otherwise, transmitted bit d is a “0 ”. 
         
       
     
  
   LDPC decoding is based on a so-called message passing algorithm. Such an algorithm consists of associating with each bit node a received signal to which corresponds an initial LLR ratio, and of iteratively exchanging messages between bit nodes  10  and check nodes  12 , along branches  14  of the graph corresponding to matrix H. The exchanged messages are log likelihood ratios and enable determining, after several iterations, for each received signal a corrected LLR ratio based on which the bit which has been transmitted is finally determined. 
   An iteration of such an algorithm mainly comprises two steps:
         a “bit node determination” step which consists, for each bit node, of gathering the messages transmitted to the bit node by the check nodes to which the bit node is connected and of sending a new message to each check node to which the bit node is connected; and   a “check node determination” step which is the symmetrical operation and which consists, for each check node, of gathering the messages transmitted to the check node by the bit nodes to which the check node is connected and of sending a new message to each bit node to which the check node is connected.       

   It can actually be considered that each branch  14  corresponds to a memory element from which a message is read before each bit or check node determination step and into which a message is written after each bit or check node determination step. 
   The LDPC decoding algorithm will now be more specifically described for a graph having dbn bit nodes BNi, i ranging from 0 to dbn-1, and dcn check nodes CNj, j ranging from 0 to dcn-1. For the first iteration, the bit node determination step is carried out by using, for each bit node BNi, value LLR(y i ) where y i  is the received signal associated with bit node BNi. Values LLR(y i ) are obtained from the characteristics of the transmit channel. Message v i→j , called a bit node message, transmitted by bit node BNi to check node CNj, is initialized as follows:
 
 v   i→j   =LLR ( y   i )  (4)
 
   The next check node determination step consists, for each check node CN j , of transmitting a message w j→i , called a check node message, to each bit node BNi connected to parity node CNj. Each message w j→i  is determined from the check equation associated with check node CNj. For this purpose, the bit node messages provided by the bit nodes BNk connected to check node CNj are simply used, except for bit node BNi to which message w j→i  is transmitted, and message w j→i  is obtained by verifying the parity equation. Let S 1   j  be the subset of [0,dbn-1] containing the indexes k such that bit nodes BNk are connected to check node CNj. The expression of w j→i  is given by the following relation: 
   
     
       
         
           
             
               
                 
                   w 
                   
                     j 
                     → 
                     i 
                   
                 
                 = 
                 
                   ln 
                   ( 
                   
                     
                       1 
                       + 
                       
                         
                           ∏ 
                           
                             
                               k 
                               ∈ 
                               S1j 
                             
                             , 
                             
                               k 
                               ≠ 
                               i 
                             
                           
                         
                         ⁢ 
                         
                           tan 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             h 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   v 
                                   
                                     k 
                                     → 
                                     j 
                                   
                                 
                                 / 
                                 2 
                               
                               ) 
                             
                           
                         
                       
                     
                     
                       1 
                       - 
                       
                         
                           ∏ 
                           
                             
                               k 
                               ∈ 
                               S1j 
                             
                             , 
                             
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                               ≠ 
                               i 
                             
                           
                         
                         ⁢ 
                         
                           tan 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             h 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   v 
                                   
                                     k 
                                     → 
                                     j 
                                   
                                 
                                 / 
                                 2 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   ) 
                 
               
             
             
               
                 ( 
                 5 
                 ) 
               
             
           
         
       
     
   
   For the next iterations, the bit node determination step is carried out, for each bit node BNi, based on the check node messages provided by check nodes CNj connected to bit node BNi. For each check node CNj connected to bit node BNi, a message v i→j  corresponding to the sum of initial value LLR(y i ) and of all the messages received from the check nodes connected to bit node BNi, except for the message transmitted by node CNj is provided. Let S 2   i  be the subset of [0,dcn-1] containing indexes k such that check nodes CNk are connected to bit node BNi. The expression of v i→j  thus is the following: 
   
     
       
         
           
             
               
                 
                   v 
                   
                     i 
                     → 
                     j 
                   
                 
                 = 
                 
                   
                     LLR 
                     ⁡ 
                     
                       ( 
                       
                         y 
                         i 
                       
                       ) 
                     
                   
                   + 
                   
                     
                       ∑ 
                       
                         
                           k 
                           ∈ 
                           S2i 
                         
                         , 
                         
                           k 
                           ≠ 
                           j 
                         
                       
                     
                     ⁢ 
                     
                       w 
                       
                         k 
                         → 
                         i 
                       
                     
                   
                 
               
             
             
               
                 ( 
                 6 
                 ) 
               
             
           
         
       
     
   
   Once a determined number of iterations has been performed, a value Li corresponding to a corrected LLR ratio is determined for each bit node BNi. Li is determined by the following equation: 
   
     
       
         
           
             
               
                 
                   L 
                   i 
                 
                 = 
                 
                   
                     LLR 
                     ⁡ 
                     
                       ( 
                       
                         y 
                         i 
                       
                       ) 
                     
                   
                   + 
                   
                     
                       ∑ 
                       
                         k 
                         ∈ 
                         S2i 
                       
                     
                     ⁢ 
                     
                       w 
                       
                         k 
                         → 
                         i 
                       
                     
                   
                 
               
             
             
               
                 ( 
                 7 
                 ) 
               
             
           
         
       
     
   
   It is then decided, for each bit node BNi, based on value L i , which is the value of the bit associated with the received signal y i . For example, if Li is negative or zero, it may be decided that the bit is equal to 1 and if Li is strictly positive, it may be decided that the bit is equal to 0. 
     FIG. 2  schematically shows an example of the forming of an LDPC decoder  20  implementing the previously-described algorithm. 
   Decoder  20  comprises a processing unit  22  comprising NB separate elementary processing units  24  (Mod j , j ranging from 1 to NB) capable of performing in parallel calculation operations to provide the bit and check node messages. 
   Decoder  20  comprises a RAM  26  in which are stored the bit node messages provided by units  24  after a bit node determination step and check node messages provided by units  24  after a check node determination step. Memory  26  comprises Ne/NB lines. At each line of memory  26  is stored a word containing a number of bits equal to the product of number NB of units  24  by the number of bits that can be processed by a unit  24 . Each word corresponds to the juxtaposition of NB bit node messages or of NB check node messages. 
   Decoder  20  comprises an input memory  28  in which are stored initial values LLR(y i ), i ranging from 0 to dbn-1. Decoder  20  also comprises an output memory  30  in which are stored values Li, i ranging from 0 to dbn-1. 
   Processing unit  22  is connected to a multiplexer  32 , controlled by a control signal S 1  which, according to the value of control signal S 1 , provides processing unit  22  with a word from input memory  28 , a word directly read from memory  26 , or a word provided by a rearrangement unit  34  and which corresponds to a word of memory  26  in which the order of the messages forming the word has been modified. More specifically, when a word is transmitted to processing unit  22 , the message at the first position in the word is transmitted to the first elementary processing unit Mod 1 , etc., and the message at the NB th  position in the word is transmitted to the NB th  elementary processing unit Mod NB . 
   Processing unit  22  is capable of successively providing words corresponding to the juxtaposition of NB bit node messages or of NB check node messages. More specifically, when a word is transmitted to processing unit  22 , the message at the first position in the word is provided by first elementary processing unit Mod 1 , etc., and the message at the NB th  position in the word is provided by the NB th  elementary processing unit Mod NB . The words provided by processing unit  22  may be transmitted to output memory  30  or to a rearrangement unit  38  capable of providing a new word from a received word and corresponding to the received word in which the order of the NB bit node messages or of the NB check node messages is modified. 
   Rearrangement unit  38  drives a first input of a multiplexer  39 , controlled by a signal S 3 . Processing unit  22  drives a second input of multiplexer  39 . According to the value of S 3 , multiplexer  39  provides memory  26  with the word provided by rearrangement unit  38  or by processing unit  22 . 
   Decoder  20  comprises an address provision unit  40 , for example, comprising a ROM. At each line of address provision unit  40  are stored an address in memory  26  and rearrangement data. Rearrangement units  34  or  38  are capable of modifying the order of the messages in a word based on rearrangement data. The rearrangement data may correspond to a number of shift positions. By successively reading the lines of address provision unit  40 , a series of addresses of memory  26  is obtained in an order different from the regular order of the reading from the lines of memory  26 . 
   Upon operation of decoder  20 , for a bit node determination step or for a check node determination step, an elementary unit  24  is brought to use bit or check node messages which are located at different locations in memory  26 . 
   Generally, the messages are distributed in memory  26  so that, in a check node determination step, the words can be read successively according to the regular order of access to memory  26 , the bit node message placed at the first position of each word of memory  26  being used by first elementary unit MOD 1 , etc., and the bit node message placed at the NB th  position being used by the NB th  elementary unit MOD NB . After a check node determination step, each check node message is stored at the same position as the bit node message previously associated with the same branch. 
   In the next bit node determination step, rearrangement unit  34  reads the words from memory  26  according to the read order provided by address provision unit  40 . For each read word, rearrangement unit  34  provides a new word corresponding to the read word in which the message order is modified based on the rearrangement data of address provision unit  40 . The messages are, for example, shifted to the left by a number of positions equal to the number of shift positions stored in address provision unit  40  for the read address. The message at the first position in the new word is then provided to first elementary unit Mod 1 , etc. and the message at the NB th  position in the new word is provided to the NB th  elementary processing unit Mod NB . 
   From a word transmitted by processing unit  22 , rearrangement unit  38  provides a new word that it stores in memory  26  according to an order provided by address provision unit  40  so that each bit node message is stored at the same location as the previous check node message associated with the same branch. For example, each new word corresponds to the received word in which the bit node messages are shifted to the right by a number of shift positions stored in address provision unit  40 . 
   Memory  26  is generally a large size memory since Ne may be greater than 200,000. It generally is a dual port random access memory (DPRAM) which especially enables simultaneous reading of a first word and writing of a second word stored at different lines in the memory. Indeed, in a bit node determination step or in a check node determination step, the readings from memory  26  of words transmitted to processing unit  22  are performed simultaneously with the writings into memory  26  of words provided by processing unit  22 . This enables reducing to a minimum the duration of an iteration of the decoding algorithm. 
   However, dual access memories have disadvantages. The duration of a read or write operation may be a limiting factor for the total duration of an iteration of the decoding algorithm. Further, the average power consumed by such a memory amounts to a non-negligible part of the decoder power consumption. 
   SUMMARY OF THE INVENTION 
   The present invention aims at obtaining an LDPC decoder having improved characteristics of rapidity of completion of an iteration of the decoding algorithm. 
   The present invention also aims at obtaining an LDPC decoder having improved power consumption characteristics. 
   To achieve these and other objects, the present invention provides an LDPC decoder comprising a determined number of processing units operating in parallel, capable of receiving first messages and of providing second messages based on a processing of the first received messages; first and second single-port memories; and means capable of reading first words both from the first single-port memory and from the second single-port memory, each first word containing a juxtaposition of first messages in a number equal to said determined number; providing first messages to the processing units based on the first read words; forming second words, each second word containing a juxtaposition of second messages provided by the processing units in a number equal to said determined number; and writing the second words into the first and second single-port memories, said means being capable, for at least a first word and a second word, of reading the first word from the first single-port memory and of simultaneously writing the second word into the second single-port memory or of reading the first word from the second single-port memory and of simultaneously writing the second word into the first single-port memory. 
   According to an embodiment of the present invention, the processing units are capable of receiving second messages and of providing new first messages based on a processing of the second messages, the processing of the second messages being different from the processing of the first messages, said decoder further comprising means capable of reading second words both from the first single-port memory and from the second single-port memory; providing second messages to the processing units from the second read words; forming new first words from the new first messages provided by the processing units; and writing the new first words into the first and second single-port memories, said means being capable, for at least a second word and a new first word, of reading the second word from the first single-port memory and simultaneously writing the new first word into the second single-port memory or of reading the second word from the second single-port memory and simultaneously writing the new first word into the first single-port memory. 
   According to an embodiment of the present invention, the decoder comprises a first rearrangement unit capable of providing each processing unit, for each first read word, with a first message at a position in the first word which depends on the first read word and on the processing unit; and a second rearrangement unit for forming the second words, the position of a second message in the second word depending on the second word and on the processing unit having provided the second message. 
   According to an embodiment of the present invention, the decoder comprises a rearrangement unit capable of providing each processing unit, for each first read word, with a first message at a position in the first word which depends on the first read word and on the processing unit, and capable of providing each processing unit, for each second read word, with a second message at a position in the second read word which depends on the second read word and on the processing unit. 
   According to an embodiment of the present invention, the decoder comprises a rearrangement unit capable forming the second words, the position of a second message in a second word depending on the second word and on the processing unit having provided the second message, and capable of forming the new first words, the position of a new first message in a new first word depending on the new first word and on the processing unit having provided the new first message. 
   The present invention also provides an iterative LDPC decoding method, comprising a determined number of processing units operating in parallel, said method comprising the reading of first words both from a first single-port memory and from a second single-port memory, each first word containing a juxtaposition of first messages in a number equal to the determined number; the provision to each processing unit, for each first read word, of a first message of the first word; the provision, by each processing unit, of second messages based on a processing of the first messages; and the writing of the second words into the first and second single-port memories, each second word corresponding to a juxtaposition of second messages in a number equal to the determined number, for at least a first word and a second word, the reading of the first word from the first memory being performed simultaneously with the writing of the second word into the second memory or the reading of the first word from the second memory being performed simultaneously with the writing of the second word into the first memory. 
   According to an embodiment of the present invention, the method further comprises the steps of reading the second words both from the first single-port memory and from the second single-port memory; providing each processing unit, for each second read word, with a second message of the second word; having each processing unit provide new first messages based on a processing of the second messages, the processing of the second messages being different from the processing of the first messages; and writing into the first and second memories new first words obtained from the new first messages, for at least a second word and a new first word, the reading of the second word from the first memory being performed simultaneously with the writing of the new first word into the second memory or the reading of the second word from the second memory being performed simultaneously to the writing of the new first word into the first memory. 
   According to an embodiment of the present invention, the order of the reading of the first words from the first and second single-port memories is different from the order of the reading of the second words from the first and second single-port memories. 
   According to an embodiment of the present invention, at the step of providing each processing unit, for each first read word, with a first message of the first read word, the first message is at a position in the first read word which depends on the first read word and on the processing unit, and at the step of writing the second words into the first and second single-port memories, each second word contains a second message at a position in the second word which depends on the second word and on the processing unit having provided the second message. 
   According to an embodiment of the present invention, at the step of providing each processing unit, for each first read word, with a first message of the first read word, the first message is at a position in the first read word which depends on the first read word and on the processing unit, and at the step of providing each processing unit, for each second read word, with a second message of the second read word, the second message is at a position in the second read word which depends on the second read word and on the processing unit. 
   According to an embodiment of the present invention, at the step of writing the second words into the first and second single-port memories, each second word contains a second message at a position in the second word which depends on the second word and on the processing unit having provided the second message, and at the step of writing the new first words into the first and second single-port memories, each new first word contains a new first message at a position in the new first word which depends on the new first word and on the processing unit having provided the new first message. 
   The foregoing and other objects, features, and advantages of the present invention will be discussed in detail in the following non-limiting description of specific embodiments in connection with the accompanying drawings. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1 , previously described, shows a graph illustrating an example of an LDPC decoding; 
       FIG. 2 , previously described, schematically shows an example of the forming of a conventional LDPC decoder; 
       FIG. 3  shows a first example of embodiment of an LDPC decoder according to the present invention; 
       FIG. 4  shows a second example of embodiment of an LDPC decoder according to the present invention; 
       FIG. 5  shows a third example of embodiment of an LDPC decoder according to the present invention; 
       FIG. 6  shows in further detail elements of the decoder of  FIG. 4 ; and 
       FIG. 7  shows in further detail elements of the decoder of  FIG. 5 . 
   

   DETAILED DESCRIPTION 
   For clarity, the same elements have been designated with same reference numerals in the different drawings. 
   The present invention comprises replacing the dual-port memory with first and second single-port random access memories (SPRAMs). A first part (for example, half) of the data usually stored in the dual-port memory is stored in the first memory, and the rest (for example, the second half) of the data usually stored in the dual-port memory is stored in the second memory. 
   In a bit node or check node determination operation, words are read from the first memory and from the second memory. Each read word is transmitted (possibly in modified form) to processing unit  22 . Simultaneously, the words successively provided by processing unit  22  are written (possibly in modified form) into the first memory and into the second memory. In more detailed fashion, for reasons of rapidity of execution of the decoding iterations, the read and write operations may be simultaneous. When a word is read from the first memory, a word is then written into the second memory and conversely. The arrangement of the words in the first and second memories is such that, in a bit node or check node determination operation, a word is not written at the location of a word to be used subsequently in the same bit or check node determination step. This can be obtained by taking into account the waiting time necessary for the processing unit to provide new words from the words which are transmitted thereto. Indeed, when words are transmitted to the processing unit, said unit simultaneously provides new words obtained from words which have been previously transmitted thereto. 
   According to a first advantage of the present invention, the total surface area taken up by the first and second single-port memories is smaller, or even much smaller, than the surface area of dual-port memory  26 . Indeed, the first and second memories each comprise the same number of lines equal to half the number of lines of memory  26 , a word stored in the first or the second memory having the same number of bits as a word stored in memory  26 . For the same amount of stored data, a single-port memory has a surface area much smaller than the surface area of a dual-port memory. The sum of the surface areas of the first and second memories thus is substantially smaller than that of memory  26 . 
   According to a second advantage of the present invention, the duration of a decoding iteration of the decoder according to the present invention is decreased. Indeed, the duration of a write or read operation in a single-port memory containing a determined number of words is smaller than that of a dual-port memory containing twice as many words, by at least 15%. The time required to simultaneously perform a reading from one of the first or second single-port memories and a writing into the other one of the first or second memories is thus shorter than the time required to perform the same simultaneous read and write operations for a dual-port memory. 
   According to a third advantage of the present invention, the average power of the decoder according to the present invention is reduced. Indeed, with current technologies, the average power consumed by a single-port memory comprising half as many data as a dual-port memory is divided by a factor strictly greater than 2 with respect to the average power consumed by the dual-port memory. The total power consumed by the first and second memories used in the present invention is thus smaller than the power consumed by a dual-port memory. 
     FIG. 3  shows a first example of embodiment of an LDPC decoder  41  according to the present invention having a general operation similar to that of decoder  20  shown in  FIG. 2 . Memory  26  is replaced with a first single-port RAM  42 , which will be called hereafter the even RAM, and a second single-port RAM  44 , which will be called hereafter the odd RAM. Even RAM  42  and odd RAM  44  each contain half as many data as memory  26 . Even RAM  42  drives a first input of a multiplexer  45  and odd RAM  44  drives a second input of multiplexer  45 . The output of multiplexer  45  is connected to rearrangement unit  34  and to multiplexer  32 . A control unit  46  is capable of providing a read address add_r on a first input and a write address add_w on a second input corresponding to access addresses of first and second memories  42 ,  44 . Multiplexer  45  is controlled by a control signal SM 1  provided by control unit  46 . 
   Decoder  41  comprises two switches  48 ,  49  respectively controlled by control signals SC 1 , SC 2  provided by control unit  46  and each receiving, on a first input, read address signal add_r and on a second input, write address signal add_w. Each switch  48 ,  49  comprises two outputs and is capable of providing on an output one of the address signals and on the other output the other address signal according to the received control signal SC 1 , SC 2 . 
   An output of switch  49  drives a first input of a multiplexer  50 , controlled by a signal SM 2  provided by control unit  46 , and the other output of switch  49  drives a first input of a multiplexer  51 , controlled by a signal SM 3  provided by control unit  46 . An output of switch  48  drives a first memory  52 , which will be called hereafter the even ROM. The other output of switch  48  drives a second memory  54 , which is called hereafter the odd ROM. Even ROM  52  is capable, on reception of an address add_r or add_w, of providing a signal even_out corresponding to another read or write address in even RAM  42  or in odd RAM  44 . Odd ROM  54  is capable, on reception of an address add_r or add_w, of providing a signal odd_out corresponding to another read or write address in odd RAM  44  or in even RAM  42 . 
   Signal even_out drives a first input of a switch  56 . Signal odd_out drives a second input of switch  56 . Switch  56 , controlled by a signal SC 3  provided by control unit  46 , is capable of providing a first output with one of signals even_out or odd_out and a second output with the other signal even_out or odd_out. The first output of switch  56  drives a second input of multiplexer  50  and the second output of switch  56  drives a second input of multiplexer  51 . The output of multiplexer  50  drives odd RAM  44  and the output of multiplexer  51  drives even RAM  42 . Simultaneously to the provision of signal even_out, even ROM  52  provides a signal shift_value_even representative of a specific rearrangement operation to be performed at a first input of a switch  58 . Simultaneously to the provision of signal odd_out, ROM  54  provides a signal shift_value_odd representative of a specific rearrangement operation to be performed at a second input of switch  58 . Switch  58  is controlled by a signal SC 4  provided by control unit  46  and is capable of providing, according to control signal SC 4 , rearrangement unit  34  with one of signals shift_value_even or shift_value_odd and rearrangement unit  38  with the other one of signals shift_value_even or shift_value_odd. 
   The operation of decoder  41  according to the present invention is the following:
         as an example, it will be assumed that after a bit node determination step, bit node messages are distributed in even RAM  42  and odd RAM  44 . At the next check node determination step, the bit node messages are read from even RAM  42  and odd RAM  44  and for each memory, according to a first read order provided by control unit  46 . Control unit  46  provides, via switch  49 , the read addresses add_r of even RAM  42  and odd RAM  44 . As processing unit  22  receives the bit node messages, it provides check node messages which are written into even RAM  42  and odd RAM  44  according to a first read order provided by control unit  46  of access to these memories. Control unit  46  is capable of controlling switches  48 ,  49 ,  56 , and  58  and multiplexers  50 ,  51  so that, when the read and write operations are performed simultaneously, it either simultaneously generates a read address in even RAM  42  and a write address in odd RAM  44  or simultaneously a write address in even RAM  42  and a read address in odd RAM  44 .       

   At the next bit node determination step, the check node messages written into even RAM  42  and odd RAM  44  are successively read via rearrangement unit  34  according to a second read order provided by even ROM  52  and odd ROM  54 . For this purpose, control unit  46  successively provides read addresses of even RAM  42  and odd RAM  44  according to the regular order of access to the lines of even memory  42  and odd memory  44  to even ROM  52  and odd ROM  54 . Even ROM  52  and odd ROM  54  then successively provide new read addresses to even RAM  42  and odd RAM  44  and simultaneously provide shift values shift_value_even and shift_value_odd to rearrangement unit  34  via switch  58 . As processing unit  22  receives the check node messages, it provides bit node messages which are successively written into even RAM  42  and odd RAM  44  according to a write order provided by even ROM  52  and odd ROM  54 . For this purpose, control unit  46  successively provides write addresses of even RAM  42  and odd RAM  44  according to the regular order of access to the lines of even RAM  42  and odd RAM  44 , via switch  48 , which drives even ROM  52  and odd ROM  54 . Even ROM  52  and odd ROM  54  then successively provide new addresses for the writing into even RAM  42  and odd RAM  44  and simultaneously provide, successively, shift values shift_value_even and shift_value_odd to rearrangement unit  38  via switch  58 . 
   The next successive bit node and check node determination steps develop identically to what has been described here above. 
   For such a decoder  41 , according to the previously-described example, a check node message “exchanged” between check node CNj and bit node BNi, obtained at a check node determination step, is written at the same “location” in one or the other of RAMs  42 ,  44 , as the bit node message “exchanged” between the same bit node BNi and the same check node CNj obtained at a bit node determination step. A rearrangement of the messages of each read and written word should then be performed at a bit node determination step only. 
   With a different control system, the rearrangement of the messages of each read and written word may be performed only in a check node determination step. Similarly, and independently from the preceding established fact, even ROM  52  and odd ROM  54  may be used to provide the address of even RAM  42  and odd RAM  44  in the check node determination step only. 
   A more detailed example of the operation of decoder  41  according to the first example of embodiment of the present invention will now be described for the following matrix H: 
   
     
       
         
           
             
               
                 H 
                 = 
                 
                   ( 
                   
                     
                       
                         1 
                       
                       
                         0 
                       
                       
                         1 
                       
                       
                         0 
                       
                       
                         1 
                       
                       
                         0 
                       
                       
                         0 
                       
                       
                         0 
                       
                       
                         1 
                       
                       
                         1 
                       
                       
                         1 
                       
                       
                         0 
                       
                     
                     
                       
                         0 
                       
                       
                         0 
                       
                       
                         1 
                       
                       
                         1 
                       
                       
                         1 
                       
                       
                         0 
                       
                       
                         1 
                       
                       
                         1 
                       
                       
                         0 
                       
                       
                         0 
                       
                       
                         0 
                       
                       
                         1 
                       
                     
                     
                       
                         1 
                       
                       
                         1 
                       
                       
                         0 
                       
                       
                         0 
                       
                       
                         0 
                       
                       
                         1 
                       
                       
                         1 
                       
                       
                         0 
                       
                       
                         0 
                       
                       
                         0 
                       
                       
                         1 
                       
                       
                         1 
                       
                     
                     
                       
                         1 
                       
                       
                         0 
                       
                       
                         0 
                       
                       
                         0 
                       
                       
                         1 
                       
                       
                         1 
                       
                       
                         0 
                       
                       
                         1 
                       
                       
                         1 
                       
                       
                         1 
                       
                       
                         0 
                       
                       
                         0 
                       
                     
                     
                       
                         0 
                       
                       
                         1 
                       
                       
                         1 
                       
                       
                         1 
                       
                       
                         0 
                       
                       
                         0 
                       
                       
                         0 
                       
                       
                         1 
                       
                       
                         0 
                       
                       
                         1 
                       
                       
                         0 
                       
                       
                         1 
                       
                     
                     
                       
                         0 
                       
                       
                         1 
                       
                       
                         0 
                       
                       
                         1 
                       
                       
                         0 
                       
                       
                         1 
                       
                       
                         1 
                       
                       
                         0 
                       
                       
                         1 
                       
                       
                         0 
                       
                       
                         1 
                       
                       
                         0 
                       
                     
                   
                   ) 
                 
               
             
             
               
                 ( 
                 8 
                 ) 
               
             
           
         
       
     
   
   Number Ne of “1”s of matrix H is equal to 36. Matrix H is associated with a graph with 12 bit nodes and with 6 check bit nodes. A (bit or check node) message exchanged between a bit node and a check node is called ek, with k varying from 0 to 35. The numbering of messages ek is performed according to the order of the lines of matrix H and is illustrated by the following matrix H′: 
   
     
       
         
           
             
               
                 
                   H 
                   ′ 
                 
                 = 
                 
                   ( 
                   
                     
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           0 
                         
                       
                       
                         0 
                       
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                       
                       
                         0 
                       
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                         
                       
                       
                         0 
                       
                       
                         0 
                       
                       
                         0 
                       
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           3 
                         
                       
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           4 
                         
                       
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           5 
                         
                       
                       
                         0 
                       
                     
                     
                       
                         0 
                       
                       
                         0 
                       
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           6 
                         
                       
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           7 
                         
                       
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           8 
                         
                       
                       
                         0 
                       
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           9 
                         
                       
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           10 
                         
                       
                       
                         0 
                       
                       
                         0 
                       
                       
                         0 
                       
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           11 
                         
                       
                     
                     
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           12 
                         
                       
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           13 
                         
                       
                       
                         0 
                       
                       
                         0 
                       
                       
                         0 
                       
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           14 
                         
                       
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           15 
                         
                       
                       
                         0 
                       
                       
                         0 
                       
                       
                         0 
                       
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           16 
                         
                       
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           17 
                         
                       
                     
                     
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           18 
                         
                       
                       
                         0 
                       
                       
                         0 
                       
                       
                         0 
                       
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           19 
                         
                       
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           20 
                         
                       
                       
                         0 
                       
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           21 
                         
                       
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           22 
                         
                       
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           23 
                         
                       
                       
                         0 
                       
                       
                         0 
                       
                     
                     
                       
                         0 
                       
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           24 
                         
                       
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           25 
                         
                       
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           26 
                         
                       
                       
                         0 
                       
                       
                         0 
                       
                       
                         0 
                       
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           27 
                         
                       
                       
                         0 
                       
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           28 
                         
                       
                       
                         0 
                       
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           29 
                         
                       
                     
                     
                       
                         0 
                       
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           30 
                         
                       
                       
                         0 
                       
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           31 
                         
                       
                       
                         0 
                       
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           32 
                         
                       
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           33 
                         
                       
                       
                         0 
                       
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           34 
                         
                       
                       
                         0 
                       
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           35 
                         
                       
                       
                         0 
                       
                     
                   
                   ) 
                 
               
             
             
               
                 ( 
                 9 
                 ) 
               
             
           
         
       
     
   
   In the present example, it is considered that number NB of elementary processing units  24  is equal to 3. For decoder  20  shown in  FIG. 2 , messages ek, k ranging from 0 to 35, may be stored in memory  26  according to an arrangement corresponding to the following memory MEM: 
   
     
       
         
           
             
               
                 MEM 
                 = 
                 
                   
                     [ 
                     
                       
                         
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             0 
                           
                         
                         
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             13 
                           
                         
                         
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             25 
                           
                         
                       
                       
                         
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                         
                         
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             12 
                           
                         
                         
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             24 
                           
                         
                       
                       
                         
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                         
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             14 
                           
                         
                         
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             26 
                           
                         
                       
                       
                         
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             3 
                           
                         
                         
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             15 
                           
                         
                         
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             27 
                           
                         
                       
                       
                         
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             4 
                           
                         
                         
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             16 
                           
                         
                         
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             29 
                           
                         
                       
                       
                         
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             5 
                           
                         
                         
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             17 
                           
                         
                         
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             28 
                           
                         
                       
                       
                         
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             6 
                           
                         
                         
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             18 
                           
                         
                         
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             30 
                           
                         
                       
                       
                         
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             7 
                           
                         
                         
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             19 
                           
                         
                         
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             32 
                           
                         
                       
                       
                         
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             8 
                           
                         
                         
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             20 
                           
                         
                         
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             31 
                           
                         
                       
                       
                         
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             9 
                           
                         
                         
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             21 
                           
                         
                         
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             34 
                           
                         
                       
                       
                         
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             10 
                           
                         
                         
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             22 
                           
                         
                         
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             33 
                           
                         
                       
                       
                         
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             11 
                           
                         
                         
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             23 
                           
                         
                         
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             35 
                           
                         
                       
                     
                     ] 
                   
                   ⁢ 
                   
                     
                       
                         0 
                       
                     
                     
                       
                         1 
                       
                     
                     
                       
                         2 
                       
                     
                     
                       
                         3 
                       
                     
                     
                       
                         4 
                       
                     
                     
                       
                         5 
                       
                     
                     
                       
                         6 
                       
                     
                     
                       
                         7 
                       
                     
                     
                       
                         8 
                       
                     
                     
                       
                         9 
                       
                     
                     
                       
                         10 
                       
                     
                     
                       
                         11 
                       
                     
                   
                 
               
             
             
               
                 ( 
                 10 
                 ) 
               
             
           
         
       
     
       
       
         
           where the last column corresponds to the lines of memory  26 . 
         
       
     
  
   Inversions should be noted between messages e 12  and e 13 , e 24  and e 25 , e 28  and e 29 , e 31  and e 32 , and e 33  and e 34 . Such inversions enable avoiding that messages intended to be used by the same elementary processing unit  24  are in the same word. For example, messages e 0  and e 12  used in first elementary processing unit Mod 1  in a bit node determination step are contained in two different words. 
   For decoder  41  shown in  FIG. 3 , messages ek, k ranging from 0 to 35 are, as an example, stored in even RAM  42  and odd RAM  44  according to an arrangement respectively corresponding to the following matrices MEM_EVEN and MEM_ODD: 
   
     
       
         
           
             
               
                 
                   
                     
                       MEM_EVEN 
                       = 
                       
                         
                           ( 
                           
                             
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   13 
                                 
                               
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   25 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                 
                               
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   14 
                                 
                               
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   26 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   4 
                                 
                               
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   16 
                                 
                               
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   29 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   6 
                                 
                               
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   18 
                                 
                               
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   30 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   8 
                                 
                               
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   20 
                                 
                               
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   31 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   10 
                                 
                               
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   22 
                                 
                               
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   33 
                                 
                               
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           
                             
                               0 
                             
                           
                           
                             
                               1 
                             
                           
                           
                             
                               2 
                             
                           
                           
                             
                               3 
                             
                           
                           
                             
                               4 
                             
                           
                           
                             
                               5 
                             
                           
                         
                       
                     
                   
                 
                 
                   
                     
                       MEM_ODD 
                       = 
                       
                         
                           ( 
                           
                             
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   12 
                                 
                               
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   24 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   3 
                                 
                               
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   15 
                                 
                               
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   27 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   5 
                                 
                               
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   17 
                                 
                               
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   28 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   7 
                                 
                               
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   19 
                                 
                               
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   32 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   9 
                                 
                               
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   21 
                                 
                               
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   34 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   11 
                                 
                               
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   23 
                                 
                               
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   35 
                                 
                               
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           
                             
                               0 
                             
                           
                           
                             
                               1 
                             
                           
                           
                             
                               2 
                             
                           
                           
                             
                               3 
                             
                           
                           
                             
                               4 
                             
                           
                           
                             
                               5 
                             
                           
                         
                       
                     
                   
                 
               
             
             
               
                 ( 
                 11 
                 ) 
               
             
           
         
       
     
       
       
         
           the last columns representing the line numbers of even RAM  42  and odd RAM  44 . It should be noted that the lines of odd RAM  42  correspond to the even lines of memory  26  and that the lines of odd RAM  44  correspond to the odd lines of memory  26 . 
         
       
     
  
   As an example, for decoder  20  shown in  FIG. 2 , address provision unit  40  comprises, at each line, a line number of memory  26  and a number of shift positions. Address provision unit  40  comprises, for example, a memory having a composition corresponding to the following matrix ROM: 
   
     
       
         
           
             
               
                 ROM 
                 = 
                 
                   
                     [ 
                     
                       
                         
                           0 
                         
                         
                           0 
                         
                       
                       
                         
                           1 
                         
                         
                           1 
                         
                       
                       
                         
                           6 
                         
                         
                           1 
                         
                       
                       
                         
                           7 
                         
                         
                           0 
                         
                       
                       
                         
                           2 
                         
                         
                           2 
                         
                       
                       
                         
                           8 
                         
                         
                           2 
                         
                       
                       
                         
                           10 
                         
                         
                           2 
                         
                       
                       
                         
                           9 
                         
                         
                           0 
                         
                       
                       
                         
                           3 
                         
                         
                           1 
                         
                       
                       
                         
                           5 
                         
                         
                           2 
                         
                       
                       
                         
                           4 
                         
                         
                           0 
                         
                       
                       
                         
                           11 
                         
                         
                           1 
                         
                       
                     
                     ] 
                   
                   ⁢ 
                   
                     
                       
                         0 
                       
                     
                     
                       
                         1 
                       
                     
                     
                       
                         2 
                       
                     
                     
                       
                         3 
                       
                     
                     
                       
                         4 
                       
                     
                     
                       
                         5 
                       
                     
                     
                       
                         6 
                       
                     
                     
                       
                         7 
                       
                     
                     
                       
                         8 
                       
                     
                     
                       
                         9 
                       
                     
                     
                       
                         10 
                       
                     
                     
                       
                         11 
                       
                     
                   
                 
               
             
             
               
                 ( 
                 12 
                 ) 
               
             
           
         
       
     
       
       
         
           where the first column corresponds to line numbers of memory  26  and the second column corresponds to a number of shift positions, the last column representing the line numbers of the memory. 
         
       
     
  
   For the first example of decoder  41  according to the present invention, even ROM  52  and odd ROM  54  have a composition respectively corresponding to the following matrices ROM_EVEN and ROM_ODD: 
   
     
       
         
           
             
               
                 ROM_EVEN 
                 = 
                 
                   
                     
                       ( 
                       
                         
                           
                             0 
                           
                           
                             0 
                           
                         
                         
                           
                             6 
                           
                           
                             1 
                           
                         
                         
                           
                             2 
                           
                           
                             2 
                           
                         
                         
                           
                             10 
                           
                           
                             2 
                           
                         
                         
                           
                             3 
                           
                           
                             1 
                           
                         
                         
                           
                             4 
                           
                           
                             0 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       
                         
                           0 
                         
                       
                       
                         
                           1 
                         
                       
                       
                         
                           2 
                         
                       
                       
                         
                           3 
                         
                       
                       
                         
                           4 
                         
                       
                       
                         
                           5 
                         
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     ROM_ODD 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             1 
                           
                           
                             1 
                           
                         
                         
                           
                             7 
                           
                           
                             0 
                           
                         
                         
                           
                             8 
                           
                           
                             2 
                           
                         
                         
                           
                             9 
                           
                           
                             0 
                           
                         
                         
                           
                             5 
                           
                           
                             2 
                           
                         
                         
                           
                             11 
                           
                           
                             1 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       
                         
                           0 
                         
                       
                       
                         
                           1 
                         
                       
                       
                         
                           2 
                         
                       
                       
                         
                           3 
                         
                       
                       
                         
                           4 
                         
                       
                       
                         
                           5 
                         
                       
                     
                   
                 
               
             
             
               
                 ( 
                 13 
                 ) 
               
             
           
         
       
     
       
       
         
           where the last column represents the line numbers of even ROM  52  and odd ROM  54 . It should be noted that the lines of even ROM  52  correspond to the even lines of the memory represented by the ROM defined at relation (12) and that the lines of odd ROM  54  correspond to the odd lines of the memory represented by the ROM defined at relation (12). 
         
       
     
  
   An example of the progress of a check node determination step is illustrated in the following table I: 
   
     
       
             
             
             
             
             
             
             
           
             
             
             
             
             
             
             
           
         
             
               TABLE I 
             
             
                 
             
             
                 
                 
                 
                 
               Even 
                 
                 
             
             
                 
                 
                 
                 
               RAM 
               Odd RAM 
             
             
               Cycle 
               add_r 
               add_w 
               SC2 
               address 
               address 
               SM1 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
               0 
               0 
                 
               1 
               0R 
                 
                 
             
             
               1 
               1 
                 
               0 
                 
               0R 
               0 
             
             
               2 
               2 
                 
               1 
               1R 
                 
               1 
             
             
               3 
               3 
                 
               0 
                 
               1R 
               0 
             
             
               4 
               4 
                 
               1 
               2R 
                 
               1 
             
             
               5 
               5 
                 
               0 
                 
               2R 
               0 
             
             
               6 
             
             
               7 
                 
               5 
               1 
                 
               2W 
             
             
               8 
                 
               4 
               0 
               2W 
             
             
               9 
               6 
               3 
               1 
               3R 
               1W 
               1 
             
             
               10 
               7 
               2 
               0 
               1W 
               3R 
               0 
             
             
               11 
               8 
               1 
               1 
               4R 
               0W 
               1 
             
             
               12 
               9 
               0 
               0 
               0W 
               4R 
               0 
             
             
               13 
               10 
                 
               1 
               5R 
                 
               1 
             
             
               14 
               11 
                 
               0 
                 
               5R 
               0 
             
             
               15 
             
             
               16 
                 
               11 
               1 
                 
               5W 
             
             
               17 
                 
               10 
               0 
               5W 
             
             
               18 
                 
               9 
               1 
                 
               4W 
             
             
               19 
                 
               8 
               0 
               4W 
             
             
               20 
                 
               7 
               1 
                 
               3W 
             
             
               21 
                 
               6 
               0 
               3W 
             
             
                 
             
           
        
       
     
   
   In table I, the first column represents successive cycles of the clock synchronizing the components of decoder  41 . Table I does not take into account the delays in terms of clock cycles of the implementation of the different decoder components. Signals SC 2  and SM 1  are obtained from signals add_r and add_w. More specifically, signal SC 2  is equal to the least significant bit of signal add_w or to the inverse of the least significant bit of signal add_r and signal SM 1  is equal to the inverse of the least significant bit of signal add_r. To obtain the line number of even RAM  42  or of odd RAM  44  associated with a signal add_r or a signal add_w, it is enough to remove the least significant bit of signal add_r or of signal add_w. At the fifth and sixth columns of table I, letter “R” means that a read operation is performed in the considered RAM and letter “W” means that a write operation is performed in the considered memory. Switch  49  provides signal add_r to multiplexer  51  and signal add_w to multiplexer  50  when control signal SC 2  is at “1”, and provides signal add_r to multiplexer  50  and signal add_w to multiplexer  51  when control signal SC 2  is at “0”. All along the check node determination step, control signals SM 2  and SM 3  are constant and selected so that multiplexers  50 ,  51  respectively provide even RAM  42  and odd RAM  44  with signals add_r or add_w from switch  49 . The value of signal SC 4  here has no object since rearrangement units  34 ,  38  are not used in the check node determination step. 
   In the check node determination step, for each word read from even RAM  42  or from odd RAM  44 , the message at the first position is used by first elementary unit Mod 1 , the message at the second position is used by second elementary unit Mod 2 , and the message at the third position is used by third elementary unit Mod 3 . As an example, at cycles  0  to  5 , first elementary unit Mod 1  successively receives bit node messages e 0  to e 5  from which it determines check node messages e 0  to e 5  respectively stored at the same location as the preceding messages e 0  and e 5  in even RAM  42  or odd RAM  44 . It should be noted, in the present example, that if bit node messages e 0  to e 5  are successively read, elementary processing unit Mod 1  provides the check node messages in the inverse order, that is, e 5 , e 4 , e 3 , e 2 , e 1 , then e 0  are successively written. The distribution of messages ei, i ranging from 0 to 35, in even RAM  42  or odd RAM  44  thus respectively corresponds again to matrices MEM_EVEN and MEM_ODD defined at relation (11). 
   In a bit node determination step, rearrangement units  34 ,  38  use the information provided by even ROM  52  and odd ROM  54  to read and write the right messages at the right locations. 
   An example of the progress of a bit node determination step is illustrated in the following table II: 
   
     
       
             
             
             
             
             
             
             
             
             
             
             
             
             
             
             
           
             
             
             
             
             
             
             
             
             
             
             
             
             
             
             
           
         
             
               TABLE II 
             
             
                 
             
             
                 
                 
                 
                 
                 
               odd 
                 
                 
                 
               even 
               odd 
                 
                 
                 
                 
             
             
                 
                 
                 
                 
                 
               ROM 
                 
                 
                 
               RAM 
               RAM 
                 
                 
               Shift_value 
               Shift_value 
             
             
               Cycle 
               add_r 
               add_w 
               SC1 
               even ROM line 
               line 
               even_out 
               odd_out 
               SC3 
               address 
               address 
               SM1 
               SC4 
               (read) 
               (write) 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
               0 
               0 
                 
               1 
               0 
                 
               0 
                 
               0 
               0R 
                 
               1 
               0 
               0 
                 
             
             
               1 
               1 
                 
               0 
                 
               0 
                 
               1 
               0 
                 
               0R 
               0 
               1 
               1 
             
             
               2 
               2 
                 
               1 
               1 
                 
               6 
                 
               0 
               3R 
                 
               1 
               0 
               1 
             
             
               3 
             
             
               4 
                 
               2 
               0 
               1 
                 
               6 
                 
               0 
               3W 
                 
                 
               1 
                 
               1 
             
             
               5 
               4 
               1 
               1 
               2 
               0 
               2 
               1 
               0 
               1R 
               0W 
               1 
               0 
               2 
               1 
             
             
               6 
               3 
               0 
               0 
               0 
               1 
               0 
               7 
               0 
               0W 
               3R 
               0 
               1 
               0 
               0 
             
             
               7 
               5 
                 
               0 
                 
               2 
                 
               8 
               1 
               4R 
                 
               1 
               1 
               2 
             
             
               8 
             
             
               9 
                 
               5 
               1 
                 
               2 
                 
               8 
               1 
               4W 
                 
                 
               0 
                 
               2 
             
             
               10 
               6 
               3 
               1 
               3 
               1 
               10 
               7 
               0 
               5R 
               3W 
               1 
               0 
               2 
               0 
             
             
               11 
               7 
               4 
               0 
               2 
               3 
               2 
               9 
               0 
               1W 
               4R 
               0 
               1 
               0 
               2 
             
             
               12 
               8 
                 
               1 
               4 
                 
               3 
                 
               1 
                 
               1R 
               0 
               0 
               1 
             
             
               13 
             
             
               14 
                 
               8 
               0 
               4 
                 
               3 
                 
               1 
                 
               1W 
                 
               1 
                 
               1 
             
             
               15 
               10 
               7 
               1 
               5 
               3 
               4 
               9 
               0 
               2R 
               4W 
               1 
               0 
               0 
               0 
             
             
               16 
               9 
               6 
               0 
               3 
               4 
               10 
               5 
               0 
               5W 
               2R 
               0 
               1 
               2 
               2 
             
             
               17 
               11 
                 
               0 
                 
               5 
                 
               11 
               0 
                 
               5R 
               0 
               1 
               1 
             
             
               18 
             
             
               19 
                 
               11 
               1 
                 
               5 
                 
               11 
               0 
                 
               5W 
                 
               0 
                 
               1 
             
             
               20 
                 
               9 
               1 
                 
               4 
                 
               5 
               0 
                 
               2W 
                 
               0 
                 
               2 
             
             
               21 
                 
               10 
               0 
               5 
                 
               4 
                 
               0 
               2W 
                 
                 
               1 
                 
               0 
             
             
                 
             
           
        
       
     
   
   In table II, the same conventions as those used for table I are used, except that signal SM 1  is equal to the inverse of the least significant bit of signal even_out or odd_out when said bit is associated with a read operation. Further, signal SC 1  is equal to the least significant bit of signal add_w or to the inverse of the least significant bit of signal add_r, signal SC 3  is equal to the least significant bit of signal even_out or to the inverse of the least significant bit of signal odd_out, and signal SC 4  is equal to the least significant bit of signal add_r or to the inverse of the least significant bit of signal add_w. To obtain the line number of even or odd ROM  52 ,  54  corresponding to a signal add_r or a signal add_w, it is enough to remove the least significant bit of signal add_r or of signal add_w. Similarly, to obtain the line number of even RAM  42  or odd RAM  44  corresponding to a signal odd_out or to a signal even_out, it is enough to remove the least significant bit of signal odd_out or of signal even_out. 
   Switch  48  provides signal add_r to even ROM  52  and signal add_w to odd ROM  54  when control signal SC 1  is at “1” and provides signal add_r to odd ROM  54  and signal add_w to odd ROM  52  when control signal SC 1  is at “0”. Switch  56  provides signal even_out to multiplexer  51  and signal odd_out to multiplexer  50  when control signal SC 3  is at “0” and provides signal even_out to multiplexer  50  and signal odd_out to multiplexer  51  when control signal SC 3  is at “1”. Switch  58  provides signal shift_value_even to rearrangement unit  38  and signal shift_value_odd to rearrangement unit  34  when control signal SC 4  is at “1” and provides shift_value_even to rearrangement unit  34  and signal shift_value_odd to rearrangement unit  38  when control signal SC 4  is at “0”. 
   In the bit node determination step, the words are read from even RAM  42  or from odd RAM  44  in the order indicated by even ROM  52  and odd ROM  54 . As an example, the determination of the bit nodes of index 0, 1, and 2 is obtained from line no° 0  of even ROM  52  which returns line number  0  used to read from even memory  42 , of line no° 0  of odd ROM  54  which returns line number  1  used to read from odd memory  44 , and of line no° 1  of even ROM  52  which returns line number  6  used to read from even memory  42 . 
   Rearrangement unit  34  thus receives the word stored at line no° 0  of even RAM  42  and performs a leftward shift of the messages of the read word by a number  0  of shift positions and provides message e 0 , at the first position of the modified word, to first elementary processing unit Mod 1 , message e 13 , at the second position, to second elementary processing unit Mod 2 , and message e 25 , at the third position, to third elementary processing unit Mod 3 . Rearrangement unit  34  then receives the word stored at line no° 0  of odd RAM  44 , performs a leftward shift of the messages of the read word by 1 shift position and thus provides message e 12 , at the first position of the modified word, to first elementary processing unit Mod 1 , message e 24 , at the second position, to second elementary processing unit Mod 2  and message e 1 , at the third position, to third elementary processing unit Mod 3 . Finally, rearrangement unit  34  then receives the word stored at line no° 3  of even RAM  42  and performs a leftward shift of the messages of the read word by 1 shift position and thus provides message e 18 , at the first position of the modified word, to first elementary processing unit Mod 1 , message e 30 , at the second position, to second elementary processing unit Mod 2 , and message e 6 , at the third position, to third elementary processing unit Mod 3 . 
   At the end of the determination of bit nodes no° 0 ,  1 , and  2 , rearrangement unit  38  successively receives the next three words (e 18 , e 30 , e 6 ), (e 12 , e 24 , e 1 ) and (e 0 , e 13 , e 25 ). To properly write the word (e 18 , e 30 , e 6 ), rearrangement unit  38  uses, at cycle  4 , the rearrangement data stored at line no° 1  of even ROM  52  which indicates a number  1  of shift positions. Rearrangement unit  38  then provides a new word (e 6 , e 18 , e 30 ) corresponding to the initial word circularly shifted to the right by one shift position. Line no° 1  of even ROM  52  sends back to line number no° 6 . Rearrangement unit  38  thus writes the new word (e 6 , e 18 , e 30 ) at line no° 3  of even RAM  42 . The distribution of messages ei, i ranging from 0 to 35, into RAMs  42 ,  44  thus corresponds, at the end of the bit node determination step, again to matrices MEM_EVEN and MEM_ODD defined at relation (11). 
     FIG. 4  shows a second example of embodiment of a decoder  60  according to the present invention. Conversely to decoder  41  shown in  FIG. 3 , decoder  60  comprises a single rearrangement unit  62  capable of reading words from even RAM  42  or odd RAM  44 , possibly according to an order different from the regular order of access to the lines of even RAM  42  or odd RAM  44 , and of performing a rearrangement of the messages forming the read word. Signal shift_value_even, provided by even ROM  52 , arrives onto a first input of a multiplexer  63 , controlled by a control signal SM 4  provided by control unit  46 , and signal shift_value_odd, provided by odd ROM  54 , arrives onto a second input of multiplexer  63 . Multiplexer  63  provides a signal shift_value to rearrangement unit  62  indicating how the messages of the read word are to be rearranged. 
   A multiplexer  64 , controlled by a signal S 4 , is connected at a first input to rearrangement unit  62  and at a second input to input memory  28 . According to the value of signal S 4 , multiplexer  64  successively provides processing unit  22  with words stored in input memory  28  or words provided by rearrangement unit  62 . Processing unit  22  is connected at a first output to even RAM  42  and to odd RAM  44  and at a second input to output memory  30 . Conversely to decoder  41  shown in  FIG. 3 , signal shift_value is transmitted to rearrangement unit  62  only. 
   For decoder  60 , a check node message “exchanged” between check node CNj and bit node BNi, obtained at a check node determination step, is not written at the same “location” in one or the other of RAMs  42 ,  44  as the bit node message “exchanged” between the same bit node BNi and the same check node CNj obtained at a bit node determination step. A rearrangement of the messages of each read and written word should then be performed on reading of the words from one or the other of RAMs  42 ,  44  both in a bit node determination step and in a check node determination step. 
   As an example, the rearrangement operation performed by rearrangement unit  62  is a read word shift operation. According to this example, in the check node determination step, rearrangement unit  62  provides messages to processing unit  22  by reading the words from even RAM  42  and odd RAM  44  by performing, on each read word, a rightward shift by a number of shift positions indicated in even ROM  52  and odd ROM  54 . 
   In the next bit node determination step, rearrangement unit  62  provides messages to processing unit  22  by reading the words from even RAM  42  and odd RAM  44  by performing, on each read word, a leftward shift by a number of shift positions indicated in even ROM  52  and odd ROM  54 . 
   After a bit or check node determination step, the new obtained words provided by processing unit  22  are written into even RAM  42  and odd RAM  44  without performing any shift. 
   According to the present example, the number of rightward or leftward shift positions are stored in ROMs  52 ,  54 . Since rearrangement unit  62  performs a circular shift on the read words, a number of rightward shift positions may be stored in ROMs  52 ,  54  in the form of an equivalent number of leftward shift positions. This enables using a rearrangement unit  62  only performing leftward shifts. 
   A more detailed example of the operation of decoder  60  according to the second example of embodiment according to the present invention will now be described for matrix H defined at relation (9) and assuming that even ROM  52  and odd ROM  54  respectively correspond to matrices ROM_EVEN and ROM_ODD defined at relation (13). 
   It is assumed that at the beginning of a bit node determination step, the message distribution in even RAM  42  and odd RAM  44  respectively corresponds to matrices MEM_EVEN and MEM_ODD defined at relation (11). 
   At the next bit node determination step, rearrangement unit  62  provides messages to processing unit  22  by reading the words from even RAM  42  or from odd RAM  44  in the order indicated by even and odd ROMs  52 ,  54  and by performing, for each read word, a leftward shift by the number of shift positions indicated by even and odd ROMs  52 ,  54  as described in relation with the first example of embodiment. As an example, rearrangement unit  62  successively provides the three words (e 0 , e 13 , e 25 ), (e 12 , e 24 , e 1 ), and (e 18 , e 30 , e 6 ) to processing unit  22 . 
   The new obtained words provided by processing unit  22  are then written into even RAM  42  or into odd RAM  44  by following the order indicated by even or odd ROMs  52 ,  54  but without performing any shift. As an example, processing unit  22  successively provides three new words (e 0 , e 13 , e 25 ), (e 12 , e 24 , e 1 ), and (e 18 , e 30 , e 6 ) which are respectively written at line no° 0  of even RAM  42 , at line no° 0  of odd RAM  44 , and at line no° 3  of even RAM  42 . 
   An arrangement of the messages in RAMs  42  and  44  which corresponds to the following matrices MEM_EVEN and MEM_ODD is thus obtained: 
   
     
       
         
           
             
               
                 
                   MEM_EVEN 
                   = 
                   
                     
                       ( 
                       
                         
                           
                             
                               e 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               0 
                             
                           
                           
                             
                               e 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               13 
                             
                           
                           
                             
                               e 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               25 
                             
                           
                         
                         
                           
                             
                               e 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               26 
                             
                           
                           
                             
                               e 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                           
                             
                               e 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               14 
                             
                           
                         
                         
                           
                             
                               e 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               4 
                             
                           
                           
                             
                               e 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               16 
                             
                           
                           
                             
                               e 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               29 
                             
                           
                         
                         
                           
                             
                               e 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               18 
                             
                           
                           
                             
                               e 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               30 
                             
                           
                           
                             
                               e 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               6 
                             
                           
                         
                         
                           
                             
                               e 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               31 
                             
                           
                           
                             
                               e 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               8 
                             
                           
                           
                             
                               e 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               20 
                             
                           
                         
                         
                           
                             
                               e 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               33 
                             
                           
                           
                             
                               e 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               10 
                             
                           
                           
                             
                               e 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               22 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       
                         
                           0 
                         
                       
                       
                         
                           1 
                         
                       
                       
                         
                           2 
                         
                       
                       
                         
                           3 
                         
                       
                       
                         
                           4 
                         
                       
                       
                         
                           5 
                         
                       
                     
                   
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   
 
                 
                 ⁢ 
                 
                   MEM_ODD 
                   = 
                   
                     
                       ( 
                       
                         
                           
                             
                               e 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               12 
                             
                           
                           
                             
                               e 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               24 
                             
                           
                           
                             
                               e 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                           
                         
                         
                           
                             
                               e 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               15 
                             
                           
                           
                             
                               e 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               27 
                             
                           
                           
                             
                               e 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               3 
                             
                           
                         
                         
                           
                             
                               e 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
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   The bit determination step may substantially be carried out according to the same sequence as that indicated in previously-described table II. However, the columns entitled “SC 4 ” and “Shift_value (write)” are not to be taken into account since no shift is performed on the words written into even RAM  42  or into odd RAM  44 . 
   In the next check node determination step, rearrangement unit  62  successively reads words from even and odd RAMs  42 ,  44  according to a regular read order and performs, for a word read from even RAM  42  or from odd RAM  44  at a determined line number, a circular shift to the right, by the number of shift positions indicated at the same line number of one of ROMs  52 ,  54 . The new words provided by processing unit  22  are then written into even RAM  42  or into odd RAM  44  in the normal order of the lines of these memories with no shift. An arrangement of the messages in even and odd RAMs  42 ,  44  corresponding to matrices MEM_EVEN and MEM_ODD defined at relation (11) is then found again. The check node determination step may be performed according to the same sequence as that indicated in Table I by however providing that a shift operation is to be performed on each read word. 
   The arrangement of the messages in even and odd RAMs  42 ,  44  is thus different after a check node determination step and after a bit node determination step. 
     FIG. 5  shows a third example of embodiment of a decoder  70  according to the present invention. 
   Conversely to decoder  60  shown in  FIG. 4 , the output of multiplexer  50  is, further, connected to a first input of a multiplexer  72  and the output of multiplexer  51  is, further, connected to a second input of a multiplexer  72 . Multiplexer  72  is controlled by a signal SM 4  provided by control unit  46 . Multiplexer  72  thus provides one of the following signals add_r, add_w, even_out, and odd_out to a shift control unit  74  which provides, for each signal representative of a received address, a shift value shift_value to rearrangement unit  62 . Only data representative of addresses of RAMs  42 ,  44  are then stored in even and odd ROMs  52 ,  54 . The operation of decoder  70  is further identical to the operation of decoder  60 . 
     FIG. 6  shows a more detailed example of the forming of one of even or odd ROMs  52  or  54  of the second example of embodiment of the present invention. ROM  52 ,  54  is capable of receiving a signal L 1  equal to add_r or to add_w and which is representative of an initial line number of the associated RAM  42 ,  44  and of providing a signal L 2  (even_out or odd_out) representative of a new line number of RAM  42 ,  44 , a signal D_NB representative of a number of shift positions to be used in a bit node determination step, and a signal D_NC representative of a number of shift positions to be used in a check node determination step. The decoder comprises a multiplexer  76 , controlled by a binary control signal SC 6  provided by control unit  46 , receiving signal D_NB at a first input and signal D_NC at a second input and providing a signal Decal age, corresponding to the signal shift_value_odd or shift_value_even transmitted to rearrangement unit  62  for the second example of embodiment. As an example, when signal SC 6  is high, which indicates that a check node determination step is going on, signal Decal age is equal to D_NC and when signal SC 6  is low, which indicates that a bit node determination step is going on, signal Decal age is equal to D_NB. 
     FIG. 7  shows a more detailed example of the forming of shift control unit  74  for the third example of embodiment of decoder  70  according to the present invention. Each ROM  52 ,  54  of decoder  70  according to the third example of embodiment only provides an address signal even_out, odd_out. Multiplexer  72  provides shift control unit  74  with a signal representative of an address of one of even or odd RAMs  42 ,  44  and which may correspond to one of signals add_r, even_out, or odd_out. Shift control unit  74  comprises a memory  78  capable of receiving the signal representative of an address and of providing the number of shift positions D_NB adapted to the carrying out of a bit node determination step. Shift control unit  74  comprises a unit  80  capable of determining the number of shifts D_NC to be used in a check node determination step based on D_NB. A multiplexer  82 , controlled by signal SC 7 , receives signal D_NB at a first input and signal D_NC at a second input and provides signal shift_value to rearrangement unit  62 . As an example, when signal SC 7  is high, which indicates that a check node determination step is going on, signal shift_value is equal to D_NC and when signal SC 7  is low, which indicates that a bit node determination step is going on, signal shift_value is equal to D_NB. 
   For the second and third examples of embodiment of the decoder according to the present invention, decoder  60 ,  70  comprises but a single rearrangement unit  62 . Since the surface area necessary to the forming of shift control unit  74  is negligible, the surface area taken up by a rearrangement unit is practically completely freed with respect to decoder  41 . Further, rearrangement unit  62  of decoder  60 ,  70  according to the second or the third example of embodiment may have a structure identical to that of a conventional rearrangement unit  34 ,  38 . 
   According to a variation of the second and third examples of embodiment, rearrangement unit  62  is placed between processing unit  22  and RAMs  42 ,  44  downstream of processing unit  22  according to the data flow direction. Rearrangement unit  62  is then capable of writing a word into RAMs  42 ,  44  based on a word provided by processing unit  22  by modifying the position of the messages in the word provided by processing unit  22 . In a bit node determination step or a check node determination step, the message at the first position of each read word is provided to first elementary processing unit Mod 1 , the message at the second position of each read word is provided to second elementary processing unit Mod 2 , etc., and the message at the last position of each read word is provided to the last elementary processing unit Mod NB . Rearrangement unit  62  then modifies the message position in each word provided by processing unit  22  so that all messages to be provided to a same elementary processing unit Mod i , i ranging from 1 to NB, at the next determination step are at the same position in each word. A different distribution of the bit node messages and of the check node messages is then obtained in RAMs  42 ,  44 , respectively after a bit node determination step or a check node determination step. 
   Of course, the present invention is likely to have various alterations, modifications, and improvements which will readily occur to those skilled in the art. In particular, the rearrangement unit may perform an operation other than a shift. It may for example perform permutations. 
   Such alterations, modifications, and improvements are intended to be part of this disclosure, and are intended to be within the spirit and the scope of the present invention. Accordingly, the foregoing description is by way of example only and is not intended to be limiting. The present invention is limited only as defined in the following claims and the equivalents thereto.