Method of correcting residual errors at the output of a...

Details Method of correcting residual errors at the output of a... Method of correcting residual errors at the output of a...

2000-02-09

2003-06-10

Decady, Albert (Department: 2133)

Error detection/correction and fault detection/recovery

Pulse or data error handling

Digital data error correction

C714S781000

Reexamination Certificate

active

06578171

ABSTRACT:

BACKGROUND OF THE INVENTION
Field of the Invention
The invention lies in the general field of communication systems. It concerns in particular an external code which permits the correction of residual errors at the output of a turbodecoder, taking account of the constraints imposed by the use of a turbocode in general terms, and more particularly a turbocode based on an interleaver of the so-called “x to x
e
” type.
It applies equally well to the coding of data representing a physical quantity, to the coding of data in the form of codes able to modulate a physical quantity, to the decoding of data-modulated signals as data, and to the decoding of data representing physical quantities. These data can, for example, represent images, sounds, computer data, electrical quantities or stored data.
SUMMARY OF THE INVENTION
The invention finds an application in the field of convolutional codes. When the latter are used to implement an iterative decoding, these codes are greatly improved when their coders contain a permutation device (“interleaver”). In this case, they are normally referred to as “turbocodes” and the corresponding iterative decoder is referred to as a “turbodecode”. For convenience.
the operation performed by the turbocoder is referred to as a “turbocoding” and this operation supplies a so-called “turbocoded” sequence.
the operation performed by the turbodecoder is referred to as “turbodecoding” and this operation supplies a so-called “turbodecoded” sequence.
On these subjects, documents which serve as a reference are, on the one hand, the article by C. BERROU, A. GLAVIEUX and P. THITIMAJSHIMA entitled “
Near Shannon limit error
-
correcting coding and decoding:turbocodes
” published in the proceedings of the conference ICC'93. 1993, pages 1064 to 1070, and on the other hand the article by C. BERROU and A. GLAVIEUX entitled “
Near optimum error
-
correcting coding and decoding:turbo
-
codes
” published in IEEE Transactions on Communications, Volume 44, pages 1261 to 1271, in October 1996.
A parallel turbocoder (
FIG. 1
) with an efficiency equal to ⅓ can be considered as a pair of systematic recursive convolutional coders with divisor polynomials such that the first coder
120
produces a check sequence from the sequence of symbols to be coded
a
and the second coder
122
produced a check sequence of a sequence
a
* obtained by interlacing (or “permutation” in an interleaver
121
) of the sequence
a
.
In this context, the simultaneous return to zero of the two codes is a classic problem.
One way of resolving it has been found by one of the inventors and is summarised below.
For the purpose of clarity, it will be assumed hereinafter that the two divisor polynomials of the turbocoder are equal and termed g(x). Let m be the degree of the polynomial g(x) and let N
0
be the smallest integer such that g(x) is a divisor of the polynomial 1+x
No
.
For reasons described below, a polynomial g(x) is chosen where no divisor is the square of a polynomial of degree equal to or greater than 1, and this means that N
0
is an odd number.
Let N be the size of the sequence
a
chosen so that it is an odd multiple of N
0
:N=M·N
0
.
Any sequence of information symbols
a
for being turbocoded can then have a polynomial representation u(x) with binary coefficients of degree N-m-1. This sequence u(x) is precoded (or “formatted”) as:
a
⁢
(
x
)
=
u
⁢
(
x
)
+
∑
i
=
N
-
m
N
-
1
⁢
 
⁢
a
i
⁢
x
i
where the m binary symbols a
1
are chosen so that a(x) is a multiple of g(x). As a consequence of this formatting (preceding) and the chosen values of the parameters, if a(x) is a multiple of g(x), then a*(x)=a(x
c
) modulo 1+x
N
is also a multiple of g(x) for any value of e which is a power of 2. It is necessary to consider that g(x) has no multiple factor since, in general, a*(x) has the guarantee of being divisible only by the irreducible factors of g(x).
In the remainder of the description, the type of permutations and interleavers disclosed above are referred to as “x to x
e
”.
With general turbocodes, decoding is essentially an iterative procedure (see in this regard the document by C. BERROU and A. GLAVIEUX, “
Near optimum error
-
correcting and decoding:turbocodes
”, IEEE Trans. On Comm., Vol. COM-44, pages 1261-1271, October 1996).
Two prior-art documents have a few points of similarity with the problem to be resolved with regard to the correction of residual errors at the output of a turbodecoder.
A patent U.S. Pat. No. 4,276,646 of Texas Instruments describes a method and device for detecting and correcting errors in a set of data. In this patent a method is described consisting of putting the information in the form of subsets and adding to each subset a CRC (Cyclic Redundancy Check) so as to correct said subset.
An article by J. Andersen (“
Turbocoding for deep space applications
”, Proc. IEEE 1995 International Symposium on Information Theory, Whistler, Canada, September 1995) proposes the use of a BCH code for the correction of residual errors at the output of a turbodecoder.
These two documents present solutions which have a fairly limited effectiveness in the correction of residual errors, notably if they are applied to turbocodes of the type “x to x
e
”. There are two main reasons for this:
The first reason relates to the fact that they do not take account of the structure of the residual errors. In fact a study of turbodecoders with an interleaver of the type “x to x
e
”, by one of the inventors, revealed that the residual errors have a particular structure, provided that the iterations of the decoder are continued until their results stabilises.
The second reason is that the solutions proposed above supply coded sequences whose associated polynomial is not divisible by the divisor polynomial g(x) (their outputs are not formatted). A formatting function is therefore necessary before turbocoding.
The aim of the invention is therefore to remedy the aforementioned drawbacks in efficacy of residual error correction at the output of a turbodecoder.
To this end the invention proposes a method of transmitting binary data
u
by a sender to a receiver through a transmission channel, characterised in that said method includes a formatting function integrated in an external coding function for the binary data
u
.
This invention can be used in many telecommunication systems.
It applies in particular in cases where the sender uses a turbocoder with an “x to x
e
”, interleaver, and the receiver uses a turbocoder with an “x to x
e
” interleaver.
According to an even more particular embodiment, the binary data
u
are stored in an initial matrix U of L rows and K columns, L and K being predetermined, and an error correction code (N
0
, K) is allocated to each row, thus forming an intermediate matrix U
1
.
According to an even more particular embodiment, an error detection code (M, L) is allocated to each column of the intermediate matrix U
1
, thus forming a formatted matrix A, having M rows and N
0
columns.
This arrangement makes it possible to detect the columns in error, on the principle of a product code.
According to a more particular embodiment, the error detection code (M, L) is produced by adding five additional bits calculated with the generator polynomial g
1
(y)=(1+y)(1+y+y
4
), where y=x
No
, N
0
being the number of columns in said formatted matrix A.
It will be understood that y is a binary variable evaluated along the columns of the matrix A.
The term (1+y) of the generator polynomial g
1
(y) ensures that the coding of the binary data
u
by the codes (N
0
, K) and (M, L) supplies a sequence which is divisible by the polynomial g(x). The term (1+y+y
4
) is an example of a polynomial used for error detection.
In a particular implementation, the error correction code (N
0
, K) has a minimum distance (d) greater than a predetermined number, representing the number of columns which can be corrected by the received matrix A′.
The invention also relates to a method of formatti

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