Pulse or digital communications – Systems using alternating or pulsating current – Plural channels for transmission of a single pulse train
Reexamination Certificate
1998-08-28
2002-05-21
Vo, Don N. (Department: 2631)
Pulse or digital communications
Systems using alternating or pulsating current
Plural channels for transmission of a single pulse train
Reexamination Certificate
active
06393065
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention concerns a coding method and device, a decoding method and device, and equipment using them. In particular the invention aims to generate code words belonging to a Reed-Solomon code on a Galois field having q elements, the code words generated having all their symbols in a sub-alphabet of this Galois field.
2. Description of the Background
This method is Particularly applied to Reed-Solomon codes on a 256-element Galois field and a sub-alphabet of this field having 64 elements.
Maximum distance separable codes constitute a particularly interesting family of error correction codes. These codes are defined on an alphabet F provided with a Galois field structure GF(q) where q is a power of a prime number p.
Like all linear codes, maximum distance separable codes can be defined by a generator matrix or a control matrix. Known constructions for such matrices effectively corresponding to maximum distance separable codes are the so-called Vandermonde construction or that of Cauchy [Mac Williams and Sloane].
The actual use of a code requires the use of a coder, that is to say a device which, for a code of type (n,k), maps, to each k-tuple of units of information u=(u
1
, . . . , u
k
on GF(q), a coded n-tuple v=(v
1
, . . . , v
n
), referred to as a “coded word”, which represents and which is transmitted in its place. From this point of view, a distinction: between systematic coders and non-systematic coders is established. A coder is referred to as systematic if the k components u
1
of u appear unmodified as a component v
j(l)
of the coded word v representing u.
It should be noted that if k≧4 or k≦n−4, maximum distance separable codes on GF(q) are known only for n≧q+1, and that the case n=q−1 is of particular interest. There are, on the electronic component market, many decoders decoding maximum distance separable codes and operating on an alphabet with 256 elements, each of these elements being identified with a different binary octet, and the said alphabet being structured as the Galois field having 256 elements and often denoted GF(256).
For the remote transmission of information, quadrature amplitude modulations allow a high transmission rate. These modulations have, for example, a 64-signal constellation, such that each of the two components carried by the phase quadrature amplitudes can take eight different values. The natural alphabet associated with this type of modulation therefore has 64 elements.
Persons skilled in the art who wish to use 64-element quadrature amplitude modulation are first of all tempted to use a Reed-Solomon code defined on a 64-element Galois field. However the number of symbols in the code words is limited to 65, which may be too low for certain applications.
A code known to persons skilled in the art under the name BCH defined on the 64-element Galois field can also be used. However, this implies that the decoder works on an alphabet with 2
12
=4096 elements, which is not implemented in a conventional technology. Furthermore, for a given correction capability, the redundancy is then most often close to twice what it is in the case of Reed-Solomon codes, since on GF(64), x
4095
−1 factorises into the product of 63 first degree polynomials and 2016 irreducible second degree polynomials.
BRIEF SUMMARY OF THE INVENTION
The present invention intends notably to specify a systematic procedure for encoding sequences of binary information such that the words of the code are words of a maximum distance separable code on the 256-element Galois field, referred to as the “second alphabet”, and, in addition, satisfy the condition that only 64 of the 256 symbols of this alphabet can be used, both as redundant symbols and as information symbols. The 64 symbols of the second alphabet which are used in this way are called the “first alphabet”.
Thus the decoder can be implemented with a commercial component already produced, at the date of the invention, in large quantities and, consequently, of low cost, while using a transmission channel with quadrature amplitude modulations having 64 elements.
For a given correction capability, the redundancy necessary will then be equal to four thirds of that necessary with a Reed-Solomon code using a 256-element alphabet.
The document EP-0 290 349 (Weng Lih-Jih) is known. In this, given a 256-element sub-alphabet of a 1024-element Galois field, each unit of information to be encoded is represented by k-l symbols of the sub-alphabet to which l arbitrary units of pseudo-information are added, testing the sequences of l arbitrary units of information until the code words contain only symbols of the sub-alphabet, the number l being chosen with the aim that at least one such sequence gives the result sought.
The aim of this document EP-0 290 349 is to keep an octet format for the information and the redundancies, and to construct efficient error correction codes with little redundancy, for encoding long sequences of information.
The document EP-0 290 349 has many drawbacks: it does not suggest using a decoder working on a 256-element Galois field, determination of the units of pseudo-information is not optimised, the number of these units of pseudo-information is not known when the search for them is started, and the said search is empirical and based on a series of tests and checks. The successive test procedures to be used for determining the sequence of l units of pseudo-information are lengthy and they therefore do not allow rapid encoding of the information. Another embodiment disclosed by the document EP-0 290 349 presents the use of a look-up table, which implies the use of a read-only memory whose capacity, at the date of the present invention, is impracticable except for very small values of redundancy.
The invention intends to remedy these drawbacks by proposing, in a single step, to determine a code work all the symbols of which belong to a 64-element sub-alphabet.
This procedure can be matched with the article “Codes between BCH and RS codes”, Ch. Couvreur an, Ph. Piret, from the PHILIPS JOURNAL OF RESEARCH n°. 39, pages 195-205, published in 1984. In this article, codes of determined dimension satisfying the same constraints were suggested within the context of unequal error protection, that is to say within the context of a technical problem with no relation with the present invention.
To that end, the invention relates, according to a first aspect, to a coding device supplying code words, the symbols of which are capable of modulating a physical quantity on a transmission channel making use of symbols of a first alphabet, the decoding of these code words using symbols of a second alphabet containing the first alphabet, the cardinal of the second alphabet being strictly greater than that of the first alphabet and not being an integer power of the cardinal of the first alphabet, a device characterised in that it has:
an input of “primary” symbols belonging to the first alphabet;
processing means adapted to:
determine redundant symbols capable of allowing decoding of the code words composed of primary symbols and redundant symbols, by a decoder working on the second alphabet;
solve a system of equations expressing the constraints to be met so that the said redundant symbols are in the first alphabet.
an output of the symbols of the code words.
Correlatively, the present invention relates, according to a second aspect, to a coding method supplying code words, the symbols of which are capable of modulating a physical quantity on a transmission channel making use of symbols of a first alphabet, the decoding of these code words using symbols of a second alphabet containing the first alphabet, the cardinal of the second alphabet being strictly greater than that of the first alphabet and not being an integer power of the cardinal of the first alphabet, a method characterised in that it has:
a step of inputting “primary” symbols belonging to the first alphabet;
a step of determining re
Le Dantec Claude
Piret Philippe
Canon Kabushiki Kaisha
Fitzpatrick ,Cella, Harper & Scinto
Vo Don N.
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