DE10307775B4 - Patterned code with robust decoding, in particular signal code, decoding method, decoding device, reading device, and data carrier with program - Google Patents

Abstract

Signal code with one-dimensionally or two-dimensionally arranged cells of signal sections of different signal course, which are assigned to the correspondingly different symbols of an alphabet of N symbols, with N> = 2,
characterized in that
In a one-dimensional arrangement of the cells, in particular in time signals with time signal sections as cells, in an arbitrary section of f consecutive cells of the signal, f set with f> = N * 2 f <= N * N * 4, each of the N symbols at least twice , preferably at least three times.
respectively.
In the case of a two-dimensional arrangement of the cells, in particular in the case of markings of surfaces, preferably in the case of deforming markings, at least one of the following conditions a) to c) is fulfilled:
a) - The cells are arranged in row packets of at least z rows of cells, with z => 2,
Within a row packet, in an arbitrary section of f successive cells, f is set with f> = N * 2 / z f <= N * N * 4 / z, each of the N symbols at least ...

Description

The The invention relates to channel coding and the associated decoding of signals, to one-dimensional signals (e.g., timing signals) as well as for two-dimensional signals (e.g., images). Especially the invention relates to a signal code, a decoding method, a decoding device, a reading device and a data carrier with Program. For reasons of better vividness and simplicity The description will describe the methods and arrangements by means of a two-dimensional example, a matrix code. The described problems, solution methods and arrangements apply mutatis mutandis to one-dimensional signals.

The Term formation used here is based on [Bos].

advance basic concepts from the literature are explained play an important role here, and such concepts and conceptual Distinctions made here for the purpose of simplifying the presentation be introduced.

terms:

• - multidimensional Signal / multidimensional features: An image is called two-dimensional Signal denotes a time signal as a one-dimensional signal. at one-dimensional signals in which the signal values after several Dimensions are simultaneously modulated (e.g., by amplitude and Phase simultaneously or in quadrature amplitude modulation) here for the distinction of several feature dimensions spoken (although these signals in the encoding literature are simply "multidimensional Called signals " become). A color image signal is accordingly as a two-dimensional Signal addressed, for example, in the three independent Feature dimensions Color angle, saturation and intensity modulated is.
• - Alphabet / Symbols: The alphabet is the set of symbols used in the code. Examples: A decimal encoding the alphabet {0, 1, 2, ... 9} with the numbers 0, 1, ..9 as symbols. A binary encoding has the alphabet {0, 1}. A dot matrix code may e.g. the alphabet {dot printed, Dot not printed}.
• - codeword / character / string: A codeword of length n consists of n characters, each character is an element of the alphabet in question. Example: the third character a binary codeword has as concrete value one of the symbols "1" or "0". Code: set of code words. Any sequence of characters is used in literature as a drawing vector (or - misleading - as a code sequence) referred to here as "string". We differentiate here exactly between "string" and "codeword", as follows: Not All conceivable strings to the alphabet must be codewords be included in the code (example: a code with parity bit contains no strings with an odd number of symbols "1". Even numbered strings Symbols "1" are code readers). Instead of "codeword" is sometimes here also, synonymously, "possible Codeword "written. Each codeword is a string, but not every string is a codeword. Sign "follow" does not imply a one-dimensional sequence; It can also be quite a multi-dimensional Act arrangement, e.g. a matrix of characters.
• - When Signal code becomes a code together with a symbol-specific modulation rule denotes, e.g. "0" = "printed," 1 "= unprinted, or" 0 "=" low frequency, "1" = high frequency ".
• - Dimension k of a code: If the code is binary, the code contains 2 high k Codeweerter, with ternaerer coding 3 high k Codewoerter etc.
• - minimum distance d of a code: the smallest possible Hamming distance [Bos] between any two code words of the code.
• - Length of a code: Number of symbols in a code word.
• - Information signs / redundancy signs: With so-called systematic coding, the k becomes information-bearing Character n-k redundancy characters added (e.g., parity bits).
• - Demodulator in the Transmission channel is the transmitted signal to the received Symbols demodulated. Example of two-tone method for time signals: It is estimated, which of the two possible frequencies are available and accordingly decided on the symbols "0" or "1". Example barcode for image analysis: From the image information is estimated, whether it is broad / narrow Line or gap acts. In general, it is possible for the decision to provide a reliability information. In Special cases can equal the reliability information in the form be interpreted by probabilities.
• - Algebraic / reliability optimizer Decoding method; Hard Decision / Soft Decision: At algebraic Decoding, regardless of the demodulation, is due to transmission errors, solely due to the present code redundancy an error correction carried out. Include - um a small selection of practically very common methods too call: HammingCode, CRC, Reed-Solomon. Stand (if necessary complementary) Compared with the methods of correction of errors due to To perform reliability information that the demodulator in the Transmission channel delivers. The entirety of these procedures will here "reliability-optimizing" decoding method called. The prerequisite for this is that the demodulator - at least partly - not irreversible decisions but a plurality of possible ones (Pre-) Decisions gives reliability values. Then speak one of Soft Decision as opposed to Hard Decision.
• - Viterbi algorithm Especially in conjunction with convolutional codes is by means of on the principle Dynamic optimization based Viterbi algorithm Decoding performed at minimum distance without all possible Code words must be listed individually. The underlying code Structure is preferably in a transition network (Trellis) deposited. At the previous hard decision can be an optimization only exploit the minimum inherent in the code and decide on minimum distance to the possible codewords. at preceding soft decision, indicating reliability information To the individual decisions, Viterbi decoding can be the Optimize overall reliability, e.g. also with codes with d = 2 make corrections.
• - Interleaving Lots Codes can easily correct statistically independent single errors, but not in Pulks occurring errors (bundle errors). Out The literature is the so-called interleaving for one-dimensional signals known (realized by line-by-line writing of the characters in a memory and column-by-column read-out). This allows individual Buendelfehler transformed into several (correctable) single errors become. A similar concept can be found in the bitwise Distribution of redundant codes on separate disks (RAID disks) with the Effect of the reconstruction possibility of the information during the crash a single hard disk.
• - matrix code: Matrix-like arrangement of patterns, mounted on a surface, For example, printed, stamped, scratched, cast-on nubs ... The single pattern on the matrix will be here matrix cell (short cell) called. They differ due to differences in the processing or appearance, e.g. pronounced vs. unembossed; scratched around vs. squared angular, horizontal stroke vs.. vertical stroke .... There have been matrix codes with analog values (gray values or Color) modulated cells known ("hue code"). A matrix cell itself is again a "little one Image "(i.e. a matrix) with a two-dimensional array of pixels; the pixels have gray values that can be between 0 and 255, for example. The Matrix cell corresponds to a (temporal) one-dimensional signal Signal portion T to be demodulated into a symbol. "Cell" and "signal section" are relevant here to regard the basic procedure as synonymous. Under Matrix code does not get here, as occasionally in the encoding list to find a generalization of convolutional codes.
• - pixels: The term pixel is to be understood here generally as one of i.a. several samples of the signal to be demodulated, usually within a cell or a period of time. The scan is on the one hand a local (temporal) and on the other hand in As a rule, it is also based on a value-based quantization. Is the quantum quantization binaer, as one speaks in image processing from Binaer pictures.
• - Synchronization: at the sampling of a one-dimensional source signal must be the Signal are divided into cells or signal sections, which are from Demodulator separately processed and (at least tentatively) symbols be assigned. These in their difficulty in practice not task to be underestimated is called synchronization and corresponds the segmentation task in the pattern recognition and especially the Localization task when reading matrix codes.
• - median: For Averaging can be used instead of arithmetic or geometric Using the median calculate. Sorting readings according to their Size and select the mean value, you get the median. For example, the median of the values {1, 4000, 20, 18, 17} is the Value 18. The median is robust against individual outliers.

• – gemusterter Codes, die einerseits unterschieden werden in
• – triviale gemusterte Codes,
• – durch vollzaehlige Aufzaehlung definierte gemusterte Codes,
• – iterative gemusterte Codes, andererseits in
• – kontextfreie gemusterte Codes,
• – kontextsensitive gemusterte Codes.
• – Inselcode.
• – systematische Platzierung.

This patent application reintroduces the following terms for the purpose of simplifying the description:

• - Patterned codes that are distinguished on the one hand
• - trivial patterned codes,
• - patterned codes defined by a full list,
• - iterative patterned codes, on the other hand in
• Context-free patterned codes,
• - Context-sensitive patterned codes.
• - Island code.
• - systematic placement.

These Terms are explained in detail in the description below.

Was standing:

Of the general state of the art is specified in the basic literature [Bos, Fri, Tsar].

Especially for coding with matrix codes, it should be mentioned:
When labeling paper or films by means of ink-jet or stringent methods, the current coding methods are sufficiently reliable. In direct, especially in deforming marking (inscription), especially unprocessed surfaces by means of laser, Nadelpraegen, scratches and sehnlichen methods, the use of the known coding in practice is currently still very problematic.

• – Die Zellen stellen sich (unter optimalen Bedingungen!) naeherungsweise punktartig dar. Die meisten Codespezifikationen erfordern jedoch spezielle Formen (z.B. Data Matrix: quadratisch beschriftete Zellen); damit wird zumindest die Lokalisierung und teilweise auch die Decodierung solcher Codes sehr schwierig.
• – Speziell fuer punktartige Beschriftung definierte Codierungen sind nicht in der Lage, von der Punktform stark abweichende, wenn auch aufgrund der Beleuchtung systematisch auftretende Formen, sicher zu erkennen. Solche von der Punktform abweichende Formen ergeben sich in der Praxis haeufig, abhaengig von der Praegecharakteristik und der Beleuchtungs-Betrachtungsgeometrie.
• – Einfach auszuwertende Zellen-Bildmuster, insbesondere korrekt platzierte Punkte, sind nur mit aufwendiger Beleuchtung erreichbar.
• – Durch Abnutzen des Praegewerkzeugs oder schwankende Materialeigenschaften aendert sich die Praegecharakteristik im laufenden Betrieb.

On the basis of the (inexpensive) needles the practical problems are explained in more detail:

• - The cells are almost point-like (under optimal conditions!). However, most code specifications require special shapes (eg Data Matrix: square-labeled cells); so that at least the localization and sometimes the decoding of such codes is very difficult.
• - Encodings specially defined for point-like inscriptions are not able to reliably recognize forms that deviate strongly from the point form, even though they are systematically occurring due to the lighting. Such shapes deviating from the dot shape often result in practice, depending on the impression characteristic and the illumination viewing geometry.
• - Easy-to-evaluate cell image pattern, in particular correctly placed points are achievable only with elaborate lighting.
• - By wear of the preheating tool or fluctuating material properties, the impression characteristic changes during operation.

The with time signals occurring disturbances throw in part very similar Problems on: Signal distortions occur unpredictable, nonlinear, but often more similar locally Way (simplest example: fading).

matrix codes so far for realized algebraic decoding, especially for the Reed Solomon Method. Algebraic decoding methods do not use the most in the demodulator available reliability information.

Around at least approximately a reliability-optimizing Decoding is done after [D3] to decode two-dimensional Codes with hard-decision on before by binarization threshold binarized data suggested that determines uncertain image areas whose gray values are close to the binarization threshold, and those tentatively for decoding another Binarisierungswert is assigned as predetermined by the Binarisierungsschwelle.

To [Wi1], appear at defined points of a data strip to be optically read Search pattern built in for comparison with the information-bearing patterns. This information becomes the realization of a decoding process derived on the basis of correlation. (Note: The "cells" after [Wi1] do NOT correspond the cells according to our designation, but rather blocks of Cells, therefore "speak we here from cell blocks).

According to [D1], in order to increase reading reliability, a marking with one or more circles is used proposed annular patterns that the codings each have the same number of color changes on the annulus. Obviously, the security gained by this is very small, as can be seen from the following example: if you change a system with the colors black and white to a bit that has a black neighbor on one side and a white neighbor on the other side, then Does not change the number of color changes.

To [D2] is a machine-readable code in a sequence of columns with arranged per m "areas", consisting of patterns from each n areas (i.e., m> n), the patterns each representing one character and repeated at least once along the column. Template, caused by cyclic shift, represent the same sign. This will make it possible with a reading device that is narrower than m areas, and whose Position along the line can vary, the characters clearly to read, independently from the position of the reader on the column.

After [D4] DE 695 26 915 T2 For example, a stack of bar codes is decomposed into a plurality of packets containing both data and address information. The compact packages are individually decodable and can be scanned with a wider range of angles than is possible with the full width of the code when scanning. Because of the address information, all the code information from the individual packets is easily composable, regardless of the order in which the individual packets were decoded.

On very specific points of the prior art will be referred to to the rest of the cited literature below in the description the advantages received, since according to the description of the here suggested Process the differences become more understandable.

Task:

General The object of the invention is to talk about the possibilities of the past Known, a generally usable, extremely robust To provide coding with associated decoding. The robustness should exceed previously known methods.

Specific The object of the invention is to provide a general task Provide coding when labeling / marking objects, with associated decoding which it u.a. allowed, with direct Lettering (in particular stamped or scratched) and in case of difficult / incorrect Surface and other disturbances, the information is reliable to recognize. It should not be necessary, special search patterns to incorporate into the code as suggested by [Wi1].

In In the industrial environment, often only a small amount of information has to be coded (Example: Specification of the part type, with only a few possible part types), However, this information must be very secure, despite partial very difficult conditions, with no or almost no regrets be read automatically. The one for the accommodation of the code Required space is also an important criterion plays However, compared to the reading security often a subordinate Role.

The The object is achieved according to the invention according to claim 1 and 2.

in the The following are preferred, with the aid of drawings Embodiments of the invention described.

1 shows by way of example the calculation of reliability values for cells, based on average brightness values and simple compactness considerations.

2 shows by way of example the calculation of reliability values for cells with the same mean gray value, due to similarity with other cells with hypothetical significance.

3 shows by way of example the calculation of reliability values for cells solely on the basis of similarity with other cells of hypothetical importance.

4 shows, by way of example, the calculation of reliability values for cells solely on the basis of similarity considerations with several other cells of different hypothetical significance.

5 shows by way of example an iteratively patterned code.

6 exemplifies the trellis to the code 5 ,

7 shows by way of example the selection of comparison cells in the case of iteratively patterned codes.

8th shows by way of example a context-sensitive patterned code.

Description of the coding, based on a example:

The Description will first be made by way of example from the field Matrix code, which was specially chosen to the basic understanding to facilitate the invention.

These Description is expressly as a didactically chosen example to understand; for example, binary codes and certain Bit numbers and local configurations chosen, which, as far as appropriate and factually possible, on codes with larger alphabet and others Configurations can be generalized.

The Example leads step by step to the core of the process, the patterned code (term introduced here), which is then exhaustive to be discribed. The description is thus "from outside to inside".

The starting point is a string of the total length L with an alphabet of up to 2 high k symbols to be coded, eg "0", "1", .. "9", ",", "." , "-", "?", "!", "/" With 16 symbols k = 4 bits per character required.
(With less than 16 symbols, a certain amount of redundancy can already be built in at a same code length in a preprocessing step).

Therefor In a first step, a binary code is defined, the binary one Original code, with length n = k and minimum distance d = 1. Is in For example, if the original code is 16 characters long, the result is initially binary origin code with 16 x 4 = 64 bits.

This Code is optionally a header with a typically small Number of bits expanded, 8 bits in the example. The header carries in particular information about the alphabet of the original code, if necessary also over the length of the original code, if necessary a pre-set Compression method, etc., optionally also about the size of the matrix. The resulting code is called a binary startup code.

Header example

• Header = 00000000: Alphabet = {"0", "1", ... "9", ",", ".", "-", "/"}. redundancy and coding according to example.
• Header = 00000001: Alphabet = {"0", "1", ... "9", "A", "B", ... "Z". ","}. redundancy and coding according to example.
• Header = 10000000: Alphabet as at 00000000, redundancy and coding, however, modified.
• Header = 10000001: Alphabet as at 00000001, redundancy and coding, however, modified. Etc.

in the For example, the header has 8 bits, so the binary start code has 72 Bit.

Of the binary start code is now supplemented by a number of check bits. These check bits are not used for error correction later in decoding, but error detection to reject unrecognizable codes to be able to. Efficient is e.g. the Hamming Code; with him is with little effort a very high residual error probability achievable.

Side note:

at Cancellations can be made for time signals and corresponding protocols Repeats of the transmission are triggered, possibly with changed Transmission rate. This corresponds to the reading in a picture evaluation a new image, if necessary, with changed boundary conditions (lighting, Camera setting etc.).

in the For example, 8 parity bits are used for a total of 72 bits (e.g. Hamming code with 7 check bits plus another check bit that the first 7 check bits included). Basically suffice for smaller claims but also smaller supplements. In the example, the code has now a total of 72 + 8 = 80 bits. This code is now called primary code.

Of the Primary code is now split into as long as possible parts with a certain maximum length, in the example in 16 blocks a 5 bits, called Primaerbloecke. These primary blocks are now called binary numbers interpreted as codes with k = 5, n = 5, d = 1 in the example. The Primaerbloecke are now recoded into so-called extended Primaerbloecke. The amount of extended Primaerbloecke provides a code with n> k and d> 1, extended Called primary code.

These Extension is used during the decoding for error correction.

you note that the parity bits refer to the entire code, while the latter code extension realized in blocks is.

These Code extension can now be done by means of a code delimitation (so-called systematic Code with e.g. Parity bits), but preferably in Form of a so-called non-systematic code, in which between the transmitted information and the redundancy information no longer can be distinguished directly.

Here is an example of a non-systematic extended primary code with k = 5, n = 9 and d = 3: 00000 000000000 10000 100000011 00001 111000000 10001 011000011 00010 100110000 10010 000110011 00011 011110000 10011 111110011 00100 010101000 10100 110101011 00101 101101000 10101 001101011 00110 110011000 10110 010011011 00111 001011000 10111 101011011 01000 110100100 11000 010100111 01001 001100100 11001 101100111 01010 010010100 11010 110010111 01011 101010100 11011 001010111 01100 100001100 11100 000001111 01,101 011001100 11101 111001111 01110 000111100 11110 100111111 01111 111111100 11111 011111111

Here is a simpler non-systematic extended prima code with k = 5, n = 6 and d = 2: 00000 000000 00000 100001 00001 110000 00001 010001 00010 101000 00010 001001 .... .... 01111 011110 01111 111111

in the The following example uses the first highly redundant code. This allows algebraic decoding to correct 1-bit errors become 3-bit errors with reliability-optimized decoding. From the 16 primary code blocks a 5-bit, so 16 blocks of extended Primaer codewords with 9 bits each.

Now an initially conventional interleaving is performed. By swapping lines and Columns will be 16 9-bit bio-corners to 9 16-bit biocoins. The 16-bit blocks can be broken down into smaller blocks, here 4 4-bit blocks each. In the example, 36 blocks of 4 bits each are created. The resulting 4-bit codes are called INTERCODES.

The Intermediate codes are now extended again (systematically or non-systematically), whereby the so-called ISLAND CODE arises.

These Island codes are now systematically placed according to the invention. Systematic placement is further explained below.

island codes are now ENGINEERED CODES according to the invention.

patterned Codes (here newly introduced definition for this invention) are Codes that are very special, explained below, local (temporal) Placement rules for to keep the symbols, with the aim of the best possible diversification the code alphabet within the code words, according to a given system.

• – Die Inselcodes werden bei zweidimensionaler bildhafter Codierung, z.B. einem Matrixcode, als zweidimensionale Anordnung der Bits dargestellt.
• – Die Inselcodes werden bei eindimensionaler Codierung (z.B. Zeitsignalen) in strenger oertlicher/zeitlicher Reihenfolge dargestellt, d.h. ein Vertauschen der Zeichenpositionen ist nicht erlaubt.

(Anmerkung: vertauscht man sonst bei einem Code, der nicht gemusterter Code ist, die Zeichenpositionen immer in gleicher Weise, so hat das auf alle weiteren Eigenschaften keinen Einfluss).The representation of patterned codes is strictly local or time related; When describing an island code, the local / temporal arrangement of the symbols always plays a role.

• - The island codes are displayed in two-dimensional pictorial encoding, such as a matrix code, as a two-dimensional arrangement of the bits.
• - The island codes are displayed in one-dimensional coding (eg time signals) in strict local / temporal order, ie a swapping of the character positions is not allowed.

(Note: if you otherwise swap the character positions for a code that is not patterned code, then the same applies to all other properties).

Annotation: The arrangement need not be rectangular or square; they are arbitrary arrangements with fixed relative geometry Character positions possible. Also, the whole islands, depending on free Definitionmeglichkeit, be arranged arbitrarily rotated; important is only the always consistent RELATIVE arrangement of all Characters among each other.

Here is an example:

There are a total of 16 possible intermediate code words with 4-bit intermediate codes. These are converted into the following island codes, for example, for a matrix coding, with 6 bits in a 2 × 3 arrangement: Example 4 bits intermediate code, 6 bits ISLAND CODE: 0000 011 1000 001 001 101 0001 011 1001 001 010 110 0010 010 1010 011 011 100 0011 101 1011 010 001 101 0100 101 1100 010 010 110 0101 100 1101 101 011 100 0110 110 1110 100 001 101 0111 110 1111 100 010 110

The most essential property of a binary patterned code (and thus of an island code) is the minimum requirement that each of the two symbols occur at least once (when extending to higher quality codes, this must be true for at least two of the symbols, ideally for all symbols). The scattering should be done according to a certain system, so that one can specify rules according to which one in certain local subsets of characters find all symbols at least n times, with n> = 1. Another desire for a good island code is that it should have a minimum distance d> = 2.

purpose the local scattering of the symbols is, during the demodulation process, due to local comparisons of necessarily different symbols (and / or necessarily the same symbols), Reliability mass to deduce

• a) Die Anzahl der Einsen ist immer ungerade. Daher gilt d >= 2.
• b) Jedes Symbol kommt dreimal vor.
• c) in den Zeilen kommt jedes Symbol mindestens einmal vor.
• d) Bei spaltenweiser Betrachtung ist zu erkennen: Entweder – in allen 3 Spalten sind die Symbole jeweils unterschiedlich (→ 3 lokale Vergleiche moeglich) Oder – in einer Spalte sind die Symbole unterschiedlich, in den beiden verbleibenden Spalten, mit jeweils gleichen Symbolen, sind die Symbole von Spalte zu Spalte unterschiedlich. (→ 3 lokale Vergleiche: einmal spaltenweise, zweimal zeilenweise)

Here are the advantageous properties of the island code given above:

• a) The number of ones is always odd. Therefore, d> = 2.
• b) Each symbol occurs three times.
• c) in the lines, each symbol occurs at least once.
• d) For column-by-column observation it can be seen: Either - in all 3 columns the symbols are different (→ 3 local comparisons possible) Or - in one column the symbols are different, in the two remaining columns, each with the same symbols, are the Symbols vary from column to column. (→ 3 local comparisons: once in columns, twice in rows)

A Systematics of patterned codes and thus possible island codes given below.

Systematic placement

The Island codes are inventively (on the matrix or in the Time) systemically placed.

The Island codes have arisen from extended primary codes; every island code is thus assigned to a number of extended primary codes. Systematic placement now means, for island codes, the associated have common extended primary codes, the local (temporal) Minimum distance, exceeds a minimum value or that such island codes, in the context of the possibilities given by the size of the code matrix (or a maximum ertraeglichen cache memory and a delay in the decoding), as far as possible apart to come to rest.

in the In this example, a 6x6 array of 4-bit intermediate codes is obtained (and thus 6-bit island codes), wherein each 2 x 2 arrays of these codes come from different extended primary codes and such Intermediate codes that have at least one (out of 4) extended primary codes have in common, the here maximum distance of 2 placement increments have each other.

ever For application purposes, for example, the middle or the minimum local distance between such island codes is maximized.

In addition, another condition should be satisfied:
For patterned codes, as I said, the placement of symbols plays a role. For reasons that will become clearer below (demodulation of patterned codes, see below), the symbols of a single island code itself should, however, be as close together as possible, so the island codes should have as compact a range as possible; for example, the above-mentioned 2 × 3-shape is more favorable a 1 × 6-shape. Generally favorable in the two-dimensional are therefore quadratic or equilateral hexagonal forms.

at the placement of the symbols is thus taken care of: island codes, which originated from common associated extended codes of primacy are, should be as far apart as possible, the symbols On the other hand, a single island code is as close as possible to each other.

DECODE:

Decode the island codes:

The Advantageous exploitation of the properties of patterned codes for Decoding with reliability information is based on here shown island codes shown.

Preliminary remark: Although the minimum distance of this island code is d = 2, 1-bit errors can be corrected by using reliability information (algebraic methods require this) > = 3). It is a general advantage of reliability decoding versus algebraic decoding that, with even minimum spacing, more errors can be corrected in principle than bea algebraic decoding.

designations:

The symbols of the above-mentioned 2 × 3 island code are hereinafter referred to as:
ace
bdf

at not too big island codes can one a "brute force" decoding realize that consists in that all possible code words counted and for each possible codeword the Zugehoerige reliability is calculated. The decoder decides for the codeword with the highest reliability. Based on this, below Brute force decoding The method mentioned below is explained as the reliability values calculate and use advantageous.

The first possible codeword (see above) is
0000 011
001,
that is, a = 0, b = 0, c = 1, d = 0, e = 1, f = 1.

Of the Demodulator now calculates reliability values z each for the results 0 and 1. In the simplest approach this is done from one character each, that is, z (a = 1) = ..., z (a = 0) = .... The sum of these two reliability values does not necessarily have to be normalized. The decoder decides Now on the possible codeword, for which the sum of the reliability values is maximum.

• – Bereits damit ist, da die Mindestdistanz des Inselcodes >= 2 ist, eine Fehlerkorrektur moeglich.
• – Bereits damit ist eine signaladaptive Demodulation moeglich, wie weiter unten beschrieben wird.

This results in:

• Already with this, since the minimum distance of the island code is> = 2, an error correction is possible.
• Already with this, a signal-adaptive demodulation is possible, as will be described below.

An essential improvement according to the invention resulting from the practice of the demodulation task results from the fact that the demodulator calculates reliability values in pairs or tripwisely or quedrupelweise, etc. In the following we consider pairwise consideration:
The demodulator calculates specifically for the code
011 (ace
001 bdf)
(we are in a brute-force decoding), the reliability values for those pairs that have different symbols in this codeword, ie
z (a = 0, c = 1), z (a = 0, e = 1), z (a = 0, f = 1),
z (b = 0, c = 1), z (b = 0, e = 1), z (b = 0, f = 1),
z (c = 1, a = 0), z (c = 1, b = 0), z (c = 1, d = 0),
z (d = 0, c = 1), z (d = 0, e = 1), z (d = 0, f = 1),
z (e = 1, a = 0), z (e = 1, b = 0), z (e = 1, d = 0),
z (f = 1, a = 0), z (f = 1, b = 0), z (f = 1, d = 0).

Now the reliability for the individual results of this codeword is calculated. An obvious calculation rule is the arithmetic mean:
Z (a = 0): = (z (a = 0, c = 1) + z (a = 0, e = 1) + z (a = 0, f = 1)) / 3.
Z (b = 0): = (z (b = 0, c = 1) + ....
...

These Calculation rule automatically leads to a certain error correction. However, according to the invention, a non-linear calculation rule is more advantageous, the single or even several "outliers" in the individual Terms are suppressed. Advantageous are methods that are on the comparison the signals from different, but benign matrix cells are based (automatic local adaptation).

To suppress outliers (maximum once down, at most once up) is proposed according to the invention:
Z (a = 0): = median (z (a = 0, c = 1), z (a = 0, e = 1), z (a = 0, f = 1)).
Z (b = 0): = median (z (b = 0, c = 1), ...

To suppress simple outliers, either down or up, it is suggested:
Z (a = 0): = median ((z (a = 0, c = 1) + z (a = 0, e = 1)) / 2,
(z (a = 0, c = 1) + z (a = 0, f = 1)) / 2,
(z (a = 0, e = 1) + z (a = 0, f = 1)) / 2
).
Z (b = 0): = median ((z (b = 0, c = 1) + ....

The Overall reliability for the codeword typically results from the sum of individual reliabilities.

The System decides on hard decision for the codeword with the highest Gesamtzuverlaessigkeit. The system only provides soft decision for each code word the associated total reliability.

Lies as an example the codeword assumed here (a = 0, b = 0, c = 1, d = 0, e = 1, f = 1), and the matrix cell e or f are arbitrarily disturbed in the signal, nevertheless the signal in Matrix cell a is correctly demodulated and this is done AUTOMATICALLY taking advantage of a comparison procedure with the specifically here to a different and undistorted matrix cell c! That at Hard Decision is the right choice; at Soft Decision, the associated reliability value is correct and correct the interfered matrix cell unaffected, so that a subsequent reliability-optimizing (typically: Viterbi) decoding correct Delivers results.

The basic advantages of decoding patterned codes are already apparent from this simple example:
Low-frequency fluctuations in time signals (fading, phase drift etc), systematic errors in image content (eg image-to-image illumination, illumination inhomogeneity), systematic errors in captions to be read optically, errors in image acquisition (eg blooming), variations in surface properties of the imaged objects, ... A multitude of real problems in demodulation can be partially or completely solved with patterned coding.

We have now reached the core of the procedure:
Patterned codes, as explained in more detail below, allow for distributed self-referencing or self-normalization in demodulation, to which they owe these possibilities. Self-referencing takes place during demodulation; Due to the distribution, it is again fault tolerant. The distributed reference is (except for trivial patterned coding, see below for definition) not a simply interspersed additional reference signal, but part of the error correction on a higher level, anyway redundantly coded signal itself.

The Self referencing happens primarily locally, as always different symbols of a patterned codeword preferably located in compact local / temporal areas; this results an automatic adaptation to low-frequency fluctuations or systematic deviations.

Vice versa however, the coded information is due to the systematic Placement spread as far as possible, making local buendelhafte Problems that still can not be resolved at the local level are corrected can be.

One have a simple example of fault tolerant self referencing we already in the above-described suppression of outliers met by median surgery. The principle is outlined below under "self-referencing" using examples Explained in more detail.

at big island codes, the brute force decoding forbids naturally, because the effort grows exponentially with the length of the code words. Non-brute force decoding of island codes is below "iterative patterned Codes "in the section" scheme of patterned Codes "based on a Example described.

Out The decoding of the island codes thus creates the intermediate codes.

With Each intermediate code can optionally have its reliability value passed on (Soft Decision) to then another reliability-optimizing To enable decoding:

Further decoding steps:

By Reversal of the placement and interleave rule arise the extended Primaerbloecke, which are now decoded to the Primaerbloecken.

• a) mit bekannten Methoden, unter Vernachlaessigkeit der eigentlich zur Verfuegung stehenden Zuverlaessigkeitsinformation
• b) zuverlaessigkeitsoptimierend, mittels bekannter Verfahren, die typischerweise auf Dynamischer Optimierung beruhen.

This can happen

• a) using known methods, neglecting the reliability information actually available
• b) reliability-optimizing, by means of known methods, which are typically based on dynamic optimization.

The remaining decoding steps are immediate:
Compilation of the primer blocks, checking of the parity bits (resulting in rejection if necessary), removal of the header, (possibly dependent on the header) return coding into the original code.

Consideration of code rates

In the example shown here, the matrix code has a total of 24 × 24 = 576 bits, while the binary start code has a total of 72 bits. This corresponds to a relatively low code rate of 72/576, ie 12.5%, but with very high security of the decoding:
Roughly speaking, in this example, if you consistently use reliability-optimizing decoding, each of 9 disjoint groups of islands, each of three islands may be completely disturbed (d = 3 for extended primary code) and, in addition, a matrix cell may be massively disturbed in all remaining islands ( possibly even two) or virtually all matrix cells of the island may be slightly disturbed due to the corrective effect of demodulating; IN ADDITION, ALL of the matrix cells of each island, globally or island-wise, may be TERRITORALLY LIKELY disturbed! About the parity bits the possibility of a rejection, if the signal is disturbed even more.

ever according to the scope of the original alphabet, the maximum permitted size the matrix (of the time period) and as required to the Certainly, the procedure can be analogous with lesser or still higher redundancy can be realized.

For this In particular, a lower redundancy in the transition from Use primary code for extended primary code (the one given above 5-to-9-bit extension code is not-optimal; he was in Example only for the convenience of the explanation chosen).

Example 1:

A d = 2 extension of the 80-bit primary code, construed as 16 × 5 bits, on 6 bits leads to 16 × 6 = 96 bit extended binary code. With a width of the intermediate code of 6 bits, spread over 4 × 4 = 16 positions, which is extended to 8-bit island codes, result in a total of 16 × 8 = 128 bits for the matrix. Ie. the code rate is 72/128 accordingly about 0.57 percent.

Example 2:

A d = 2 extension of the 80-bit primary code, construed as 16 × 5 bits, on 6 bits leads to 16 × 6 = 96 bit extended binary code. With a width of the intermediate code 8 bits, spread over 3 × 4 = 12 positions, which is extended to island codes with 9 bits each, result in a total of 12 × 9 = 108 bits; Code rate 72/108 corresponding to approx. 0.66 percent.

The Code rates when using the method, for by complete Aufzaehlung the codewords defined patterned codes, according to these So calculation examples are typically 10% ... 65%.

The In general, iterative patterned codes introduced below have more favorable code rates than defined by listing the code words patterned codes.

self-referencing:

About Self referencing is signal adaptive demodulation possible.

See also 1 , The cells are either "black" or "white". The mean gray values of a cell are between g = 0 (black) and g = 10 (white). For each cell, individual reliability values are calculated, ranging between z = 0 (very unreliable) and z = 10 (very reliable).

• Fall 1, siehe 1: Berechnung alleine aus den einzelnen Zellinhalten. Die Zuverlaessigkeitswerte ergeben sich direkt aus den mittleren Grauwerten (1 oben; Zuverlaessigkeit alleine vom mittleren Grauwert abhaengig), gegebenenfalls unter Beachtung weiterer Kriterien wie z.B. eines Homogenitaetskriteriums (1 unten; unterschiedliche Zuverlaessigkeiten z bei gleichem mittleren Grauwert g).
• Fall 2, siehe 2: Berechnung unter Beachtung weiterer Zellen (betrachtet werden im Beispiel zwei Zellen in der Naehe), mit der Hypothese dass diese Nachbarzellen schwarz bzw. weiss sind. Dabei werden, wie im Fall 1, lediglich die mittleren Grauwerte betrachtet, gegebenenfalls unter Beachtung weiterer Kriterien wie z.B. eines Homogenitaetskriteriums.
• Fall 3, siehe 3: Berechnung unter Beachtung weiterer Zellen und Hypothesen, wie im Fall 2, jedoch ohne Beachtung der mittleren Grauwerte, ausserdem erfolgt ein pixelweiser Bild- (bzw Signal-)Vergleich. Bei dieser Vorgehensweise erfolgt nicht nur eine automatische Adaption an Eigenschaften wie z.B. Kontrastschwankungen, sondern auch eine Adaption an sich systematisch aendernde lokale Formen.

Reliability is calculated separately for black and white and does not have to be 10.

• Case 1, see 1 : Calculation alone from the individual cell contents. The reliability values result directly from the mean gray values ( 1 above; Reliability depends solely on the average gray value), if appropriate taking into account further criteria such as eg a homogeneity criterion ( 1 below; different reliability z at the same mean gray value g).
• Case 2, see 2 : Calculation taking into account further cells (considered in the example two cells in the vicinity), with the hypothesis that these neighboring cells are black or white. In this case, as in case 1, only the mean gray values are considered, if appropriate taking into account further criteria such as eg a homogeneity criterion.
• Case 3, see 3 : Calculation taking into account further cells and hypotheses, as in the case of 2, but without observing the mean gray values, in addition, a pixel-wise image (or signal) comparison is carried out. In this approach, not only an automatic adaptation to properties such as contrast fluctuations, but also an adaptation to systematically changing local forms takes place.

4 shows a procedure 3 , but there are several comparison cells (5 each in the example) available for the different symbols. The median of the individual comparison results is used to calculate the reliability.

By the comparison-based reliability mass will be as desired Local adaptation achieved, both to fluctuating averages as well Concerning waveforms.

Of the Decoder looks at such cell pairs for each possible codeword, have the hypothetical same or different symbols calculated the corresponding reliability values and calculated on it based on the total reliability for each codeword, as above by means of sum or median or other mean value operators, and decides on the codeword with the highest overall reliability.

• – faelschlicherweise schraeg eingestelle Beschriftungseinrichtung: z.B. Strichrichtung +55/-35 Grad anstelle von +45/-45 Grad,
• – Verdrehung durch Synchronisationsfehler beim Lokalisieren der Matrix,
• – falsch eingestellte Tintenmenge bei der Beschriftungseinheit, Tinte geht zur Neige,
• – schwankende Helligkeit der Hintergrundflaeche,
• – bei verformend aufgebrachter Markierung der Oberflaeche mittels Ritzen oder Praegen ist das Erscheidnungsbild der einzelnen Striche stark von der Beleuchtungsrichtung abhaengig (z.B. werden aus punktfoermigen Mustern kreisfoermige oder Sichelfoermige); die Veraenderungen verhalten sich lokal in gleicher oder sehnlicher Wiese, d.h. Zellen mit gleichen Symbolen sehen lokal untereinander sehnlich aus, obwohl sie, je nach Beleuchtung, sehr unterschiedlich aussehen koennen.

In this way, the overall reliability measure of a codeword automatically adapts to local and / or systematic errors such as contrast reduction, fading, page jitter, changing the characteristic pictorial appearance within a cell (blooming in bright highlights, blurring of printer swirls with misadjusted inkjet, pre-emption characteristics worn preshare tool). Example: Binaer coded matrix code with cells in which lines of different directions (+ 45 degrees, - 45 degrees) are located, as described in [XER] (but not as a patterned code). The following errors are calculated using the procedure specified here:

• - erroneously schraeg set label device: eg line direction + 55 / -35 degrees instead of + 45 / -45 degrees,
• - skew due to synchronization error when locating the matrix,
• - incorrectly set ink quantity at the labeling unit, ink is running out,
• - fluctuating brightness of the background area,
• In the case of deformed applied marking of the surface by means of scratches or engraving, the image of the formation of the individual lines is highly dependent on the direction of illumination (eg, dot-like patterns become circular or sickle-shaped); the changes behave locally in the same or sinewy way, ie cells with the same symbols look very close to each other locally, although they may look very different depending on the lighting.

The Method is always applicable because of the properties of patterned ones Codes is guaranteed to be safe in a certain environment cell pairs exist with the same and those with different symbols, according to known laws.

at Good patterned codes exist within a certain range always a certain number of symbols of each kind. Thereby In addition, the outlier tolerant property of the Median operators, as described above.

In the examples given so far there are always at least 2 symbols of each variety, so it is always at least one similarity measure for a certain cell with at least one cell of hypo the same and different varieties are possible. However, even with patterned codes in which each symbol only occurs at least once, this can advantageously be exploited: if only one comparison cell with a hypothetical symbol is available in a specific constellation, a single comparison is also useful for the calculation of a meaningful reliability value.

System of patterned codes:

• – triviale gemusterte Codes
• – durch vollzaehlige Aufzaehlung definierte gemusterte Codes
• – iterative gemusterte Codes

To facilitate the explanation, we introduce the following distinction:

• - trivial patterned codes
• - patterned codes defined by a full list
• - iterative patterned codes

A Another distinguishing feature is the division into context-free and context-sensitive patterned codes. When placing the icons of context-sensitive patterned codes are the symbol placement rules from far before (e.g., one line before, line by line) placed adjacent symbols in the neighborhood.

1) trivial patterned codes

at trivial patterned code becomes the codeword of a normal code (e.g., binary number with / without parity bit; as described herein Application preferably the intermediate code) within a region locally unrestricted placeable symbols, supplemented by one or more Icons (supplement icon).

• a) Ein Ergaenzungssymbol: – Das Ergaenzungssymbol hat den gegenueber einem speziell festgelegten Zeichen des Codes invertierten Wert (bei laengerem Alphabet kann man z.B. jeweils zyklisch um einen Schritt weiter gehen im Alphabet). – das Ergaenzungssymbol kann vorteilhafterweise auch gegenueber dem im Code am haeufigsten vorkommenden Symbol invertiert sein.
• b) Zwei Ergaenzungssymbole: – Es handelt sich um die Symbole "0" und "1" an festgelegter Position. Diese Ergaenzungssymbole koennen nun als Referenzsymbol fuer den Vergleich bei der Demodulation verwendet werden. – Das Codewort wird um ein erstes Symbol ergaenzt, das gegenueber dem im Codewort am haeufigsten vorkommenden Symbol invertiert ist und dann um ein weiteres Symbol ergaenzt, das gegenueber dem nun im Codewort UND dem ersten Ergaenzungssymbol am haeufigsten vorkommenden Symbol invertiert ist.
• c) Mehrere Ergaenzungssymbole wurch wiederholtens Anwenden der Regeln a) und/oder b).

According to the invention, the extension takes place according to the following rules:
(Definitions based on alphabet {"0", "1"}):

• a) An addition symbol: - The addition symbol has the value inverted with respect to a specially defined character of the code (in the case of a longer alphabet, for example, one can cyclically move one step further in the alphabet). - The supplement symbol may advantageously also be inverted compared to the symbol most frequently occurring in the code.
• b) Two addition symbols: - These are the symbols "0" and "1" at the specified position. These addition symbols can now be used as a reference symbol for comparison during demodulation. The codeword is supplemented by a first symbol, which is inverted compared to the symbol most frequently occurring in the codeword and then supplemented by another symbol, which is inverted compared to the symbol which is most frequently occurring now in the codeword AND the first supplemental symbol.
• c) Several supplementary symbols by repeatedly applying the rules a) and / or b).

trivial Patterned codes have the disadvantage that, with a small amount of supplementation (Cases a, b) the demodulator is "dependent" on the immobility of all supplementary symbols, he wants them to use as reference symbols, or that in case c) a significant Extension of the code length comes about, you want a robust Allow decoding (several potential reference symbols for Choice).

Annotation: In [DM1], under "redundancy data integrity enhancer ", Simple to arrange symbols in a freer but more reproducible way Arrangement possibility. The symbols remain the same, the minimum requirement that in an environment each symbol occurs at least once, is not fulfilled. So this is not one (trivial) patterned code.

2) defined by counting in full patterned codes

Such Codes become simple by listing all possible code hosts defined, indicating the geometric arrangement of the symbols in the picture or in the signal.

One An example of such a code has been exemplified of the coding procedure applied here (transition from Intermediate code to the island code).

However, the design of more extensive patterned codes, defined by a full list, is relatively difficult; as well as the conversion into an adapted decoding method, one wants to avoid complete Aufzaehlung when decoding. Computer-aided design procedures could be used here useful, but the design is simpler following the approach of the iterative patterned codes described below.

3) iterative patterned codes

Iterative patterned codes are based on the example 5 to 7 explained.

Of the patterned code is composed of blocks of three each placed symbols. The bloecke are, each on the right anfuegend, arranged next to each other in any number of N.

For the selection of symbols within a block, the following rule applies:
For a block to be added to the right, at least two symbols must be different from the corresponding symbols of the previous block. 5 Below is an example where placement on the far right is not allowed. 6 above shows the belonging Trellis.

• – alle Symbole gleich bleiben (trifft fuer ein Codewort zu), oder
• – genau ein Symbol sich aendert (trifft fuer 3 Codewoerter zu).

Thus, of the possible per se 2 high 3 code words of the new block excluded those in which

• - all symbols remain the same (applies to a codeword), or
• - exactly one symbol changes (applies to 3 codewords).

It So four (= 2 to the power of 2) out of eight (= 2 to 3) code domains are excluded. Thus, the code rate is about 2/3.

takes one block of 5 with the provision that in a similar way at least change at least 3 of the 5 symbols, so is the code rate roughly 3/5, if at least each of at least 2 of the 5 symbols change the code rate is roughly 4/5. With iteratively patterned codes So you can, while retaining all the advantages, very good code rates achieve.

Due to the constantly changing symbols in at least two out of three positions, the demodulator has the option of selecting local reminder symbols. The handling is analogous to the procedure given in the original example for codes that are defined by counting in full, except that now not the entire code is considered, but always only a few (sufficient: two) adjacent code blocks. The use of more than 2 comparison blocks is described below with reference to 7 ,

The Decoding preferably takes place by means of dynamic optimization, under On the basis of the trellis, whereby as the mass of mass reliability will be consulted, as described above, only now not in one step over all possible codewords of the island code but it becomes a total reliability measure in a corresponding manner Calculated over the codeweeler of the blocks, which looked at the just Transition in the network are involved.

Anmerkufg: The usual procedure for the dynamic optimization of a Guetemasses is as follows: you go through the trellis in columns, calculates for each node the predecessor accounts with which together the maximum value is created and stores this value and a backward pointer to this predecessor node. At the end determine in the last column the global maximum total; from the node in question back through the stored Pointer you get the solution (the codeword) with the maximum Total Dumaguete.

7 illustrates the selection of reference symbols (referencing see examples) 3 and 4 ) for the code 5 and 6 : The bold arrow indicates the currently considered edge transition of the trellis. To calculate reliability values for the question mark cell, four comparison cells with a hypothetical value "s" and a comparison cell with a hypothetical value "w" are available directly at the edge transition.

A problem exists if one wants to have available several comparison cells of every possible hypothetical value in order to be able to produce sufficient interference safety, for example via the median operator. Simply adding more blocks of code and listing variants would result in a combinatorial explosion. The solution according to the invention consists in following the dynamic optimization especially for the currently considered one Originated backspace pointers (dashed arrow) and used the other cells found there with the hypothetical value given there; this is possible since the return path seen by the source cell under consideration will be the final solution just then, if the source cell is trod on determining the global solution by backtracking the set pointers. In this way, in the determination of reference cells, the already performed dynamic optimization is advantageously exploited to prevent a combinatorial explosion. In 7 By reversing along the dashed arrow, one finds a code word with two usable cells with a hypothetical value "w", so that a total of three such cells are available for comparison.

It the question remains about the minimum distance d.

Nice at d = 1, it does so because of the patterned code given redundancy and the referencing ability, a good one Error correction.

Around a certain minimum distance d> 1 to be able to ensure, it is proposed according to the invention to demand a parity after a certain number of blocks. This parity can affect the valence of blocks or all Cells or separately according to different cells (e.g. the 1st and the second line of a block separated). The flying explanation happens cell-related, about all cells over the number of "ones".

• a) n1 MOD 2 = 1 (Anzahl ungerade), oder → d = 2
• b) n1 MOD 2 = 0 (Anzahl gerade), oder → d = 2
• c) m1 MOD 4 = 0 (Anzahl durch 4 teilbar) → d = 3
• d) m1 MOD 4 = 2 (Anzahl durch 4 teilbar mit Rest 2) → d = 3 etc.

With binary codes with alphabet {0,1}, for example, the requirement can be made that
with n1 = number of "ones" applies:

• a) n1 MOD 2 = 1 (number odd), or → d = 2
• b) n1 MOD 2 = 0 (number even), or → d = 2
• c) m1 MOD 4 = 0 (number divisible by 4) → d = 3
• d) m1 MOD 4 = 2 (number divisible by 4 with remainder 2) → d = 3 etc.

• – bei aktuell gerader Anzahl im Block den "geraden Zeiger",
• – bei aktuell ungerader Anzahl im Block den "ungeraden Zeiger".

In the case of optimization, this means in case a (or b) that you have to do a "double entry" on each node when going through the trellis: you store the respective optimum and the corresponding backward pointer both for the case "number of ones so far "as well as in the case" number of ones so far odd ". This is necessary because in each column both an even and an odd number of ones can be added. At the very end, you choose the optimal even (or odd) solution, and choose when going back through the hands

• - if the number is currently even in the block, the "straight pointer",
• - if the number is currently odd in the block, the "odd pointer".

In Case c) or d) accordingly requires a "quadruple bookkeeping", etc.

With iteratively patterned codes, large code lengths can be generated, while maintaining the internal local pattern. Do you give such long codes with or a few parity bits with, you get very good Code rates. Example: 5-bit block with the restriction that in successive blocks at least two bills occur If you have to, you get, as already explained above, a code rate from just over 4/5: we have neglected that one at the very first block has no restriction. If you end up in the end adding a single parity bit, this neglects it just canceled and the code rate is exactly 4/5.

The Adding a single parity bit would give the given block structure to disturb. Instead, you can just as well for the last to be added Block the restriction of compliance with the parity. This does not change anything when considering the code rate.

at iteratively patterned codes will be the whole - possibly with parity - completed Code interpreted as a code word.

Context-sensitive patterned codes:

at Context-sensitive patterned codes are not just the blocks of depending on the block placed immediately before.

A simple example with context-sensitive patterned codes may suffice ( 8th ):
The 2 × 2 code blocks are set line by line, with the rule that no completely black 2 × 2 blocks and no completely white 2 × 2 blocks may be created, not left to the previous page (insofar it is an iterative patterned code) but also not up to the already much-placed neighbor (this placement can not be reversed). There are therefore additional situation-dependent restrictions: it can happen that EITHER blocks with "2 × above black" OR that blocks with "2 × above white" are prohibited.

context-sensitive Codes offer due to their strict pattern in all directions in addition to the strictest possible Self-referencing simplifications for the synchronization of two-dimensional Codes.

Additions:

• – Eine erfindungsgemaesse Erweiterung besteht darin, bei zweidimensionalen Signalen die Parities so zu verteilen, dass daraus Orientierungsinformation ableitbar ist. Beispielsweise kann man die obere Haelfte (bzw. die Inselcodes der oberen Haelfte) eines Matrixcodes mit gerader Paritaet und die untere Haelfte mit ungerader Paritaet absichern. Vorteile: es wird fuer diese Information kein extra Platz benoetigt; aufgrund der Verteilung der Information auf den gesamten Code ist die Decodierung fehlertolerant.
• – Komprimieren des Ursprungscodes – mit oder ohne Header – vor der ersten Erweiterung. Dann ist bei fest vorgegebenem Raum fuer den Gesamtcode normalerweise eine groessere Redundanz erreichbar.
• – gestufte Redundanz: Aufteilen der Ursprungsinformation in wichtigere und unwichtigere Information; wichtigere Information erhaelt hoehere Redundanz als unwichtigere. Unwichtige Information ggf. direkt, ohne Redundanz codieren.
• – Die oben angegebene MEDIAN-Funktion kann erfindungsgemaess ersetzt werden durch eine Funktion, die aus n Werten nicht den mittleren Wert herausgreift, sondern beispielweise den Zweit-Groessten oder Viert-Kleinsten oder x-groessten, mit x als einer Funktion von n und x <= n.

The following possible additions to the procedure are mentioned:

• An extension according to the invention consists in distributing the parities in the case of two-dimensional signals in such a way that orientation information can be derived therefrom. For example, the upper half (or the upper half island codes) of a matrix code with even parity and the lower half with odd parity can be secured. Advantages: no extra space is needed for this information; because of the distribution of information over the entire code, decoding is error tolerant.
• - Compress the source code - with or without header - before the first extension. Then, given a fixed space for the overall code, usually greater redundancy is achievable.
• - tiered redundancy: splitting source information into more important and less important information; more important information gets higher redundancy than less important. If necessary, directly encode unimportant information without redundancy.
• According to the invention, the MEDIAN function given above can be replaced by a function which does not pick the mean value out of n values but, for example, the second-largest or fourth-smallest or x-largest, with x as a function of n and x < = n.

Advantages:

at the known reliability-optimizing method provides the Demodulator only a Zuverlaessigkeitsin formation from the Signal of single characters. The method presented here is the information about a comparison process over the Signal portions of several characters won, with a known Minimum number of character pairs must be the same or different; This results in a differentiated signal analysis and a better adaptation to changeable, locally similar Signal interference.

This Advantage becomes even stronger the more cells are included in a comparison. Especially preferred In a local area, each symbol occurs at least three times.

at Trellis coded modulation (TCM) after [Ung] becomes the encoding optimized with respect to the signal constellation, i. coded sequences of signal points should have maximum Euclidean distance (see, e.g. [Frie] p. 309 ff). In TCM, in principle, in extreme cases Modulation values for consecutive symbols (or groups of symbols) all the same with the same codeword.

at By contrast, patterned coding ensures that within of the same codeword always a certain dispersion over different Symbols takes place. From this derive the closed possibilities the heightening of the security of failure by self-referencing.

The Method corrects both local and propagated errors (Bundle defect) and automatically adapts itself lansomely or systematically changing circumstances.

Fluctuations in the signal quality (eg fading in time signals, brightness fluctuations in image signals, temporal changes in the image characteristics in the case of image sequences) can be excluded due to the direct comparability, see the examples listed above, with automatic adaptation to the signal characteristic. When decoding images with mapped codes such as matrix codes / bar codes, flat surface defects such as dark spots due to self-referencing are corrected while local errors such as scratches due to the combination of built-in error correction with systematic placement are corrected. Both measures work together and support each other. The method also automatically adapts to systematic signal changes, such as the visual appearance of a round impression impression, the systematically depending on the lighting direction can change from circular shape over circular ring shape and sickle shape to contrast reversal. Automatically, the corrections take place locally at the signal level, at the global level more at the logical level.

• – iterative gemusterte Codes werden nach endlicher Zahl von Iterationsschritten abgebrochen (d.h. sie sind Blockcodes). Daher kann es ueber groessere Bereiche grundsaetzlich keine Probleme mit der sog. katastrophalen Fehlerfortpflanzung geben.
• – Innerhalb des Codes werden die Zuverlaessigkeitswerte vorzugsweise durch lokale Betrachtung berechnet; Zuverlaessigkeitswerte haengen nicht unbedingt von weiter entfernten Zuverlaessigkeitswerten ab. Auch aus dieser Sicht gibt es sogar innerhalb der Codes keine Fehlerfortpflanzung.
• – Gute Faltungscodes koennen nur computergestuetzt entworfen werden; es gibt keine systematischen Entwurfsmethoden fuer "gute" Faltungscodes (ja selbst die Definition eines Guetekriteriums ist schwierig). Es gibt andererseits systematische Entwurfsmethoden fuer iterative gemusterte Codes mit angestrebten Eigenschaften, und fuer die Bewertung der Codes, wae anhand der Beispiele aufgezeigt.
• – Grundsaetzlich koennte man versuchen, die iterativ gemusterten Codes durch Faltung zu erzeugen. Viel einfacher und durchschaubarer ist jedoch die oben geschilderte Vorgehensweise des Entwurfs per Zustandsdiagramm, woraus sich direkt die zugehoerige Trellis-Struktur zum Decodieren ableitet.
• – Faltungscodes sind insbesondere deshalb beliebt, weil sie mittels Trellisdecodierung "online" decodiert werden koennen (wobei allerdings oft eine kuenstliche Beschneidung der Betrachtungstiefe stattfinden muss). Iterative gemusterte Codes sind ebenfalls mittels Trellis-Decodierung decodierbar, mit dem zusaetzlichen Vorteil der sich exakt wiederholenden Trellis-Struktur, was zusaetzliche Vorteile fuer eine hardwarenahe Realisierung bringt: a) aufgrund der exakt begrenzbaren notwendigen Betrachtungstiefe, b) aufgrund der exakten Wiederholung fuer eine Parallelisierung.

Further advantages of iteratively patterned codes compared to convolutional codes:

• Iterative patterned codes are aborted after a finite number of iteration steps (ie they are block codes). Therefore, there can be no major problems with so-called catastrophic error propagation over larger areas.
• Within the code, the reliability values are preferably calculated by local consideration; Reliability values do not necessarily depend on more distant reliability values. Even from this point of view, even within the codes there is no error propagation.
• - Good convolutional codes can only be designed with computer assistance; there are no systematic design methods for "good" convolutional codes (even the definition of a criterion is difficult). On the other hand, there are systematic design methods for iterative patterned codes with desired properties, and for the evaluation of the codes, as shown by the examples.
• - Basically, one could try to generate the iteratively patterned codes by convolution. Much simpler and more transparent, however, is the above-described procedure of the design by state diagram, from which directly derives the associated trellis structure for decoding.
• Convolutional codes are particularly popular because they can be decoded "online" by means of trellis decoding (although often an artificial curtailment of the viewing depth has to take place). Iterative patterned codes are also decodable by means of trellis decoding, with the added advantage of the exactly repeating trellis structure, which provides additional advantages for hardware-near realization: a) due to the exact delineation required depth, b) due to the exact repetition for parallelization ,

The Procedure is for multidimensional signals (especially pictures) as well can be used as for one-dimensional signals (especially time signals).

at patterned code results in the overall picture approximate homogeneous grid of constantly changing symbols. bigger Areas with always the same symbols are avoided.

• – Moeglichkeit zur Selbstsynchronisation; Beispiel: die Abbildung eines gemusterten Matrixcodes fuehrt zu einer Struktur, deren Grundraster man beispielsweise ueber eine Fouriertransformation bestimmen kann. Die fuer eindimensionale Signale bekannte Vorgehensweise der Quadrierung des Signals mit nachfolgender schmalbandiger Filterung wird aufgrund der Gemustertheit des Signals effizienter. Dies gilt insbesondere, wie oben erwähnt, für kontextsensitiv gemusterte Codes. Dieses Selbstsynchronisationsverfahren ist global und entpricht nicht dem laufenden Nachführen entprechend der Lage von Kanten oder inneren Strukturen, wie in [Wi2] wegen welliger/verzogener Papiervorlage vorgeschlagen.
• – homogenes Erscheinungsbild; aus groesserer Entfernung betrachtet verschwimmen die Zellen; Bei einer Hell-Dunkel-Modulation bilden sich keine hellen oder dunklen Inseln. Die Codierung eignet sich daher auch –
• – als Grund"farbe" von groesseren, frei gestalteten Elementen,
• – Als Steanographisches Codierungsmittel in der Kryptographie (aufgrund der Gemustertheit und aufgrund der Stoersicherheit).

This results in the following advantages:

• - possibility for self-synchronization; Example: the image of a patterned matrix code leads to a structure whose basic grid can be determined, for example, by means of a Fourier transformation. The procedure known for one-dimensional signals of squaring the signal with subsequent narrow-band filtering becomes more efficient due to the patternedness of the signal. This applies in particular, as mentioned above, for context-sensitive patterned codes. This self-synchronization method is global and does not correspond to the ongoing tracking according to the location of edges or internal structures as suggested in [Wi2] for wavy / warped paper original.
• - homogeneous appearance; seen from a greater distance, the cells blur; In a light-dark modulation, no light or dark islands form. The coding is therefore also suitable -
• As a reason "color" of larger, free-form elements,
• - As a Steanographic coding means in cryptography (due to pattern quality and due to the security against interference).

There patterned codes over the entire signal (or most of the Signal) across a pattern according to certain rules, can be ensured that in the absence of Signal always a rejection takes place, or the detection of presence a signal is very simple.

To [Wi1] appear at defined locations of a data strip to be optically read Search pattern built in for comparison with the information-bearing patterns. This will be patterned (that would be here cell blockwise) Reliability information e.g. derived by correlation.

The method presented here allows a reliability-optimizing decoding without having to install special search patterns. In addition, as we work here cell by cell, a much more differentiated, non-linear evaluation is made possible here. Due to the global reliability-optimizing approach, preferably implemented by means of dynamic optimization, it is not necessary to have unambiguously correct recognitions in any places, in order to make a decision feedback to others To be able to realize patterns.

In More recently, the so-called turbo codes have been introduced [Ber] and successfully used. Turbo codes are two concatenated convolutional codes, separated by interleaving, iteratively using soft-in-soft-out Viterbi decoding decoded.

turbo Codes require infinite impulse response convolutional codes (IIR = infinite impulse response). It is thus the above about convolutional codes Said. The operation of turbo codes specifically is very difficult to see through, therefore, the design and the optimization is designed very difficult. The iterative approach leads to unpredictable Computing time.

Sources:

• [Bos] M. Bossert: Channel Coding. Teubner 1998.
• [Fri] B. Friedrichs: Channel coding. Springer 1996.
• [Tsar] R.H. Morelos-Zaragoza: The Art of Error Correcting Coding. Wiley & Sons, April 2002.
• [Ber] C. Berrou, A. Glavieux: Near Optimum Error Correcting Coding and Decoding: Turbo Codes. IEEE Trans. To Communications, Vol. 44, no. 10, Oct. 1996, pp. 1261-1271.
• [Ung] G. Ungerboeck: Channel Coding with Multilevel / Phase Signals. IEEE Trans. An Information Theory, Vol. IT-28, no. 1, Jan. 1982, Pp. 55-67.
• [DM1] U.S. Patent 5,324,923
• [XER] European Patent Application 0 469 864 A2
• [W i1] DE 199 26 194 C2
• [Wi2] DE 199 26 197 C1
• [D1] DE 197 33 466 A1
• [D2] WO 81/00476 A1
• [D3] DE 101 23 406 A1
• [D4] DE 695 26 915 T2

Claims (6)

Signal code with one-dimensionally or two-dimensionally arranged cells of signal sections of different signal course, which are assigned to the correspondingly different symbols of an alphabet of N symbols, where N> = 2, characterized in that - in one-dimensional arrangement of the cells, in particular in time signals with time signal sections as cells, in an arbitrary section of f consecutive cells of the signal, f with f> = N * 2 f <= N * N * 4, each of the N symbols occurs at least twice, preferably at least three times. or - in the case of a two-dimensional arrangement of the cells, in particular in the case of markings on surfaces, preferably with deforming markings, at least one of the following conditions a) to c) is fulfilled: a) the cells are arranged in row packets of at least z rows of cells, with z => 2, - Within a row packet comes in any section of f consecutive cells, f set with f> = N · 2 / zf <= N · N · 4 / z, each of the N symbols at least once, preferably at least twice, more preferably at least three times before. b) - The cells are arranged in row packets of at least z rows of cells, with z => 2, - Within a row packet, change from column to column in any section of f consecutive cells, f fixed with f> = N · 2 / zf <= N · N · 4 / z, at least one, preferably at least two, more preferably at least three characters to another symbol. c) - within an arbitrary range of adjacent cells, f and g fixed with f> = 2 and g> = 2 and f · g <= N · N, each of the N symbols comes at least once, preferably at least twice, more preferably at least three times before. A signal code decoding method according to claim 1 or a signal code described as follows: cell blocks of at least each of two-dimensional cells of signal sections of different waveforms corresponding to the correspondingly different symbols of an alphabet of N symbols of N> = 2 2 × 2 cells arranged two-dimensionally, in which each of the N symbols in each of the cell blocks occurs at least twice, preferably at least three times, characterized in that - the decoding at least over a part of the total signal is carried out reliability optimizing optimization of a Gesamtgütemasses, preferably by means of dynamic optimization, - in the Gesamtgütemaß at least one single quality measure received, - the Einzelgütemasse be calculated from one or more comparison functions in the Receive signals from at least two different, preferably adjacent cells. Decoding device with a decoding method according to Claim 2. Reading device with a decoding after Claim 2. disk program for realizing a signal code according to claim 1. disk with a program for decoding signals by means of a decoding method according to claim 2.