® J Europäisches Patentamt
`
`European Patent Office
`
`Office européen des brevets
`
`(ÏÏ) Publication number:
`
`0 083127
`B1
`
`®
`
`EUROPEAN PATENT SPECIFICATION
`
`© Date of publication of patent specification: 12.03.86
`
`© Int. CI.4: H 04 N 7/13 //G06F11/10
`
`(B) Application number: 82201597.0
`
`(22) Date of filing: 14.12.82
`
`(H) System for transmitting television picture information using transform coding of subpictures.
`
`(§) Priority: 23.12.81 NL 8105799
`
`@ Date of publication of application:
`06.07.83 Bulletin 83/27
`
`(§) Publication of the grant of the patent:
`12.03.86 Bulletin 86/11
`
`(§) Designated Contracting States:
`DEFRGBSE
`
`(5Î) References cited:
`US-A-3688265
`US-A-3949 208
`
`CONFERENCE RECORD OF THE 1978
`"P"
`flj ' NATIONAL TELECOMMUNICATIONS
`CONFERENCE, vol. 1,3rd-6th December 1978,
`pages 10.6.1 to 10.6.5, Birmingham, Alabama
`(USA); T. OHIRA et al.: "Adaptive orthogonal
`transform coding system for NTSC color
`television signals"
`
`K»,
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`®
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`®
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`Proprietor: N.V. Philips' Gloeilampenfabrieken
`Groenewoudseweg 1
`NL-5621 BA Eindhoven (NL)
`
`Inventor: Driessen, Leonardus M. H. E.
`c/o INT. OCTROOIBUREAU B.V. Prof. Holstlaan 6
`NL-5656 AA Eindhoven (NL)
`
`Representative: Strijland, Wilfred et al
`INTERNATIONAAL OCTROOIBUREAU B.V. Prof.
`Holstlaan 6
`NL-5656 AA Eindhoven (NL)
`
`®
`
`References cited:
`IEEE TRANSACTIONS ON COMMUNICATIONS,
`vol. COM-26, no. 10, October 1978, pages
`1454-1463, New York (USA); T. OHIRA et al.:
`"Orthogonal transform coding system for
`NTSC color television signals"
`
`COMPUTER DESIGN, vol. 19, no. 8, August
`1980, pages 101-108, Concord (USA); R.
`SWANSON: "Matrix technique leads to direct
`error code implementation"
`
`COMPUTER DESIGN, vol. 17, no. 6, June 1978,
`page 132, Concord (USA); "Concatenated
`algebraic decoder"
`
`CO
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`Note: Within nine months from the publication of the mention of the grant of the European patent, any person may
`give notice to the'European Patent Office of opposition to the European patent granted. Notice of opposition shall
`be filed in a written reasoned statement. It shall not be deemed to have been filed until the opposition fee has been
`paid. (Art. 99(1 ) European patent convention).
`
`Courier Press, Leamington Spa, England.
`
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`
`Description
`
`The invention relates to a system for trans(cid:173)
`mitting information of a television picture over a
`medium, said television picture being organized
`in television lines and pixels within each line, and
`being distributed over a plurality of subpictures of
`uniform dimensions, said system comprising a
`transformation device for receiving the informa(cid:173)
`tion of a subpicture for transform into a series of a
`coefficient bits of respective transformation func(cid:173)
`tions, and comprising an encoder for encoding a
`subset of k bits of said a coefficient bits into a
`larger group of n bits by means of a code having
`at least single error correction capability for said k
`bits, said k bits containing at least one bit
`associated to at least one lowest frequency trans(cid:173)
`formation function as most significant bit of the
`associated coefficient, an output of said
`transformation device being connected to an
`input of said medium, said system furthermore
`comprising a display apparatus which is con(cid:173)
`nected to said medium and which comprises a
`decoder for receiving said encoded coefficient
`bits and for therefrom reconstructing the informa-
`tion of the associated subpicture. Such a system
`is known from the article by T. Ohira et al..
`Orthogonal Transform Coding Systems for NTSC
`Colour Television Signals,
`IEEE Transactions
`Communications, Vol. COM-26, No. 10, October
`1978, pages 1545—63. The transmission medium
`may be a transport medium, for example, a
`bundle of telephone lines, or a storage medium,
`for example, a magnetic tape within a video
`cassette recorder. The encoding serves to limit
`the redundancy of the picture information so that
`the bit rate of the information to be stored or
`transferred is diminished. The reduction may for
`example be by a factor of four without lessening
`the subjective display quality. Suitable trans-
`formation
`function are Hotelling, Fourier,
`Hadamard or Haar functions, hereinafter only the
`use of Hadamard functions is treated by way of
`example. The reduction of the redundancy leads
`to a higher susceptibility to errors. The citation
`protects eleven bits by a single error correction
`code having a minimum Hamming-distance of
`three.
`
`It has been found that under certain circum(cid:173)
`stances single bit error correction is insufficient.
`On the other hand, protection of all k coefficient
`bits by a code of increased correction capability =
`would raise the number of bits by a too large
`amount. It is an object of the invention to provide
`improved error protection for certain coefficient
`bits while leaving the protection of other coeffi(cid:173)
`cient bits at their earlier levels. The object of the
`invention is realized in that it is characterized in
`that said code has a minimum Hamming-distance
`of four to allow for at least single error correction,
`double error detection within said k bits, in that
`said code has a second,
`larger, minimum
`Hamming-distance of at least five to allow for at
`least double error correction within a subset of at
`least two bits of said k bits.
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`In itself an extended error protection system is
`disclosed in US—A—3,949,208. This document,
`however, relates to a memory for general use and
`therefore the particular relevance of each stored
`bit is not known beforehand. Therefore, according
`to this citation all bits have to be equally well
`protected.
`Coefficient bits are to be understood to mean
`herein the bits which are applied to the encoder of
`the error correction code in order to be encoded.
`Code bits are to be understood to mean herein the
`bits which form the output result of the encoder
`or the information supplied for the decoder. The
`bits which
`result
`from
`the analog-to-digital
`conversion of the picture information before it is
`applied to the transformation device will not be
`considered, and the bits which are formed after
`the implementation of the error correction code in
`order to adapt the signal to be transmitted to the
`specific properties of the transmission medium
`(modulation bits) will not be considered either.
`In a particular embodiment of a system of the
`kind described in the preamble, it is proposed to
`activate the encoder selectively, under the control
`of subpicturewise
`received
`television picture
`information, to operate in one of a plurality of
`transformation modes, each mode having a
`respective set of coefficient bits applied to the
`medium plus a mode signalling bit group to
`indicate the transformation mode thus activated.
`This is described in the prior unpublished Nether(cid:173)
`lands Patent Application 8003873. The earlier
`system has a normal mode in which information
`is transported only as a small number of bits, for
`example, as a 0 bit or a 1 bit. In incidental cases
`this is not sufficient and for one (or some) blocks a
`change-over is made to such an incident mode.
`For some transformation functions the number of
`coefficient bits is then increased at the expense of
`other transformation functions. It is attractive to
`include said signalling bit group in the error
`protection code so that the selection of the
`incident modes is protected.
`In a further particular embodiment of a system
`of the kind described
`in the preamble it is
`proposed, for use with colour television picture
`information which is sampled in the converter
`with a sample frequency fs which equal twice the
`color subcarrier frequency fsc at instants which
`coincide with the phase positions
`
`i-Mn,
`
`±
`
`4
`
`in which M=0, 1, 2,..., of the colour information
`signal u(t) in the line signal, that the trans(cid:173)
`formation functions are Hadamard functions. This
`is described in the prior unpublished Netherlands
`Patent Application 8004521. According to the
`earlier system, the colour difference signal is
`embodied
`in only a very small number of
`coefficients, for example, in only two coefficients.
`In that case it is attractive to include the most
`significant coefficient bit of each of the two
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`Figure 11 shows a block diagram of a decoder
`transformation functions representing the colour
`for the specimen code,
`difference information
`in the error correction
`Figure 12 shows a detail of the decoder.
`code.
`Figure 13 shows a table with syndrome words
`Preferably, said extra-protected coefficient bits
`and associated error indication bits.
`comprise the most significant coefficient bits of
`Figure 14 shows a detail of the decoder.
`the transformation function which indicate the
`Figure 15 shows a table with feasible (n, k)
`mean luminance of the relevant subpicture. it has
`code, and
`been found that the protection of these most
`Figure 16 shows the generator matrix of a (12,
`significant bits offers a good subjective result.
`4) code.
`The number of bit errors to be corrected pre(cid:173)
`Figure 17 shows the relationship between code
`ferably equals the number of bits forming the
`bits and (guessed) data bits for the Figures 6, 9.
`third number of coefficient bits.
`The invention also relates to a picture convert(cid:173)
`ing device for use in a system of the described
`kind in which the encoder forms a non-systematic
`code. It has been found that, contrary to many
`other cases, the non-systematic code then offers
`an attractive compromise between means and
`results. Preferably, the number of data bits pro(cid:173)
`tected by the error correction code amounts to six
`and said second number preferably also amounts
`to six. This results in a simple implementation
`with usually adequate correction possibilities.
`The
`invention also
`relates
`to a display
`apparatus for use in a system of the described
`kind in which the decoder forms a feasible series
`of data bits on the basis of at least one series of a
`number of code bits which has been found to be
`incorrect but not correctable. Sometimes the
`correction is then correctly performed but some(cid:173)
`times also incorrectly. However, it has been found
`that in many cases the extra-protected coefficient
`bits can still be correctly recovered.
`The invention also relates to a decoder for use
`in a system or a display apparatus of
`the
`described which is constructed as a switching
`module. It may be a single integrated circuit or,
`for example, a module consisting of several
`integrated circuits.
`
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`Brief description of the system
`Figure 1 diagrammatically shows a system in
`which the invention can be incorporated. Element
`120 is a camera tube. The signal which is scanned
`line-wise is converted into a digital representation
`in element 122. Transformation device 146 first of
`all comprises a Hadamard transformation device
`124 and an encoder 126 for an error correction
`code as will be described hereinafter. Block 128
`represents an interleaving device for spreading
`over a larger time interval faults cause by burst
`errors. Block 130 represents a modulator
`for
`converting the series of code bits received into
`channel symbols: this series is thus adapted to
`the properties of the transmission medium. For
`example, given lower limits are implemented as
`regards the length of intervals without transitions
`(run length limitation). Line 144 represents the
`transmission medium which may be a storage
`medium or,
`for example, a communication
`channel. The elements 120 to 130 may together
`form part of a picture converting device, for
`example, a camera. Block 132 represents a
`demodulator for recovering the code bits from the
`series of channel symbols regenerated. Element
`134 represents the opposite member of the block
`128 and serves for de-interleaving. Element 136
`represents the decoder for reconstructing or
`choosing the data bits from the code bits. Element
`138 forms the opposite member of the block 124
`for cancelling the Hadamard transformation and
`for recovering a binary coded amplitude signal
`per pixel. Element 140 represents a digital-to-
`analog converter. Element 142 represents the
`display element which is in this case constructed
`as a cathode ray tube. The elements 132 to 142
`may form part of a display apparatus.
`
`Description of the transformation functions
`For background information Figure 2 shows
`some possibilities for the encoding of a sub-
`picture by means of so-called Hadamard func(cid:173)
`tions. The first eight Hadamard functions are
`shown over a unit time interval at the left of the
`Figure with bivalent amplitude (0, 1). This row of
`functions can be indefinitely continued. It can be
`demonstrated that an arbitrary function can be
`approximated with any desired accuracy over the
`unit interval by means of a series of Hadamard
`functions with adapted amplitude. The same is
`applicable to a two-dimensional subpicture, four
`of which are denoted by the reference numerals
`
`Brief description of the figures.
`The invention will be described in detail herein(cid:173)
`after with reference to some Figures.
`Figure 1 diagrammatically shows a system in
`which the invention can be incorporated,
`Figure 2 shows, as background information,
`some possibilities for the coding of a subpicture
`by means of Hadamard functions.
`Figure 3 shows more relevant information for a
`subpicture consisting of 4x4 pixels.
`Figure 4 shows some configurations of sub-
`pictures comprising 4x4 pixels,
`the
`for
`Figure 5 shows
`five possibilities
`numbers of coefficient bits used for the elements
`of the series of transformation functions.
`Figure 6 shows the generator matrix of a
`specimen code.
`
`Figure 7 shows the set of code words formed
`for this code.
`Figure 8 shows an encoder for this code,
`Figure 9 shows the parity check matrix for the
`specimen code,
`Figure 10 shows a table with the syndrome
`words which can be formed,
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`luminance of a subpicture, because each
`20, 22, 24, 26, with bivalent density (white and
`Hadamard function has the same mean value,
`shaded). Block 20 has an intensity which varies in
`that is to say half the luminance "white" in Figure
`the horizontal direction according to the function
`3. The combination of column 60 of Figure 5 and
`38 and in the vertical direction according to the
`function 30: code 3830. The other blocks have the
`the subpicture configuration 44 shown in Figure 4
`following codes 22: 4034; 24: 3236; 26: 4242. In
`represents an attractive realization for a PAL
`the approximation of an arbitrary monochrome
`system in which the colour difference signals are
`intensity distribution
`in
`the subpicture,
`the
`embodied in the coefficients of the Hadamard
`coefficients of the higher order Hadamard func(cid:173)
`functions C6 and C7 of Figure 3. The five columns
`tions are almost always relatively small. Such a
`52 through 60 shown in Figure 5 represent the
`code can also be used for a polychrome picture
`numbers of transformation modes in which the
`(generally trichrome in the case of television
`picture can be represented. Notably the first four
`pictures). In addition to the luminance signal two
`columns represent as many selectable cases.
`colour difference signals are applicable (for red
`Column 52 represents a "normal" situation with
`and for blue). The variation of these colour
`an "average" picture, and the other columns
`difference signals can also be approximated by
`represent cases in which a coefficient which is
`means of a series of Hadamard functions with
`normally small is "large" in a special case. Such a
`suitable coefficients.
`coefficient can then be represented bar a larger
`number of bits so that it is emphasized.
`As a continuation Figure 3 shows the sixteen
`Column 54 emphasizes C5, C9, C13
`feasible Hadamard functions for approximating a
`subpicture comprising 4x4 pixels. It is to be noted
`Column 56 emphasizes C5, C9, C13,
`that this can also be done with subpictures which
`Column 58 emphasizes C5, C6, C13, C9,
`are not square. However, hereinafter only sub-
`the emphasis being at the expense of mainly CO.
`pictures
`comprising
`4x4
`pixels will
`be
`It is to be noted that such different trans-
`considered. Generally, the number of picture lines
`formation modes can also be realized when the
`and the number of pixels per picture line pre(cid:173)
`combination of the column 60 represents the
`ferably equals a power of the number two. The
`normal mode. The selection from the four (or
`number of feasible Hadamard functions for a
`possibly another number) transformation modes
`one-dimensional interval of p pixels (or lines)
`is signalled by a signalling bit group (of two bits in
`equals p. Figure 4 shows four feasible disposi(cid:173)
`the case of realization according to the columns
`tions of a subpicture of 4x4 pixels, a shift of one
`52... 58 of Figure 5). The subpicture of 16 pixels is
`half pixel period being allowed between the
`thus coded by 40 data bits, 38 of which are
`pixels of two successive picture lines. Figure 4,
`coefficient bits; this means 2\ bit per pixel. Other
`example 44, shows an attractive configuration of
`adaptive transformation methods are also known
`a subpicture for a PAL system and identical
`per se.
`configurations of the subpictures; it has been
`found that the colour difference signals are then
`embodied in the functions C6 and C7 of Figure 3
`(Figure 3 does not show the shift of the picture
`lines; furthermore, the subpicture concerns only a
`single frame). Figure 4, block 46, shows an
`attractive configuration of a subpicture for an
`NTSC system and identical configurations of the
`subpictures; it has been found that the colour
`difference signals are then embodied
`in the
`functions C5 and C7 of Figure 3.
`By combinations of the subpictures shown in
`Figure 4 and possibly of their mirror images, a
`picture can be divided in many ways; within one
`picture, subpictures of mutually
`different
`configuration may also occur. For further details,
`reference is made to the cited Netherlands Patent
`Application 8004521.
`The information of each subpicture is trans(cid:173)
`formed by means of the set of Hadamard func(cid:173)
`tions which
`is symbolized
`in Figure 3, the
`coefficients being represented by a bit group.
`Figure 5 shows five examples for the assignment
`of a given number of bits to each of these
`coefficients. The digits in the column 62 corres(cid:173)
`pond to the order of the Hadamard function in
`Figure 2. The total number of bits in each column
`(being the sum of the numbers in the column)
`always equals 38 in Figure 5. This means that the
`same total dynamics can be realized for the
`
`Description of the error protection code.
`In the embodiment
`in accordance with the
`invention, six of said 40 data bits which represent
`the relevant subpicture information are protected
`by a non-systematic (n, k)=(12, 6) code, which
`means that the number of bits is increased by six;
`however, within the set of twelve bits all bits are
`code bits and an original data bit may not be
`recovered from one associated code bit. As
`regards the first four columns of Figure 5, these
`six data bits may represent
`the four most
`significant bits of the coefficient CO plus the two
`bits of the signalling bit group. Alternatively, in
`the columns 54, 56 and 58, the three most
`significant bits of CO plus the most significant bit
`of C8 may be selected. In column 60 of Figure 5,
`the six protected bits may be the four most
`significant bits of the coefficient of the trans-
`formation function CO and the most significant
`bits of the functions C6, C7 which represent the
`colour difference signals.
`Figure 6 shows the generator matrix of the
`specimen code used and Figure 7 shows the table
`with the 12-bit code words thus formed (column
`64) on the basis of the relevant data words
`(column 66). Column 68 states the weight of the
`associated code word, i.e. the number of code bits
`having the value " 1 ".
`Ignoring the code word
`which consists entirely of " 0" bits, the minimum
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`weight of a code word equals four. This means
`tions, and the syndrome word "48" by a large
`that the minimum Hamming distance of the code
`number of
`feasible combinations of
`three
`also equals four, so that at all times one error bit
`incorrect code bits. Because the code is linear, the
`can be corrected in a code word and two error bits
`effect of disturbances may be summed. The error
`can be detected. Figure 8 shows an encoder for
`pattern (4, 8) and the error pattern (5, 9) may be
`implementing the generator matrix of Figure 6.
`summed and produce
`the syndrome word
`The six data bits arrive in parallel on the inputs
`"000011". However, this syndrome word now
`72; the twelve code bits are also outputted in
`indicates the error pattern (0, 1), and the error
`parallel on the outputs 74. The matrix is imple(cid:173)
`pattern (4, 5, 8, 9) is not considered. The same
`mented by means of EXCLUSIVE-OR elements
`syndrome word "000011" is also found by bit(cid:173)
`such as the element 70. It is alternatively possible
`wise modulo-2 addition of the syndrome words
`to perform the coding operation by means of a
`"111111" (63) and "111100" (60), and also by
`read-only memory which comprises (at least) six
`addition of the syndrome words "111101" (61)
`inputs and twelve outputs. The
`interleaving,
`and "111110" (62). The table states all twelve
`modulation
`and
`parallel/series
`conversion
`error words which contain only one incorrect
`mechanisms have been omitted in this Figure.
`code bit, and also all 66=ix 12x11
`incorrect
`words which contain two incorrect code bits. It
`When a code word is received which comprises
`appears
`that
`the
`following errors can be
`two incorrect bits, it can be detected as being an
`corrected:
`incorrect code word. In that case there are a
`number of code words which are situated from
`a) a single incorrect code bit in a code word is
`the relevant code at a Hamming distance which
`always corrected because a unique syndrome
`equals two. For the decoding of this incorrect
`word is associated therewith,
`code word it is not relevant to determine the
`b) two incorrect code bits in a code word are
`correct code word from the feasible choices.
`also always corrected if they do not both belong
`However, it is important that the most likely
`to the even code bits of the code word or both to
`correct data word is selected in the case of an
`the odd code bits of the code word,
`incorrect code word. It appears that the table of
`c) when two code bits of the code word are
`Figure 7 can be divided into four subtables. All
`incorrect, both bits having an even or an odd
`data words of each subtable have the same value
`order number, the two most significant data bits
`for the two extreme left (most significant) bits.
`are correct or will be properly corrected. In the
`Each code word of a subtable
`then has a
`case of eight different results for the syndrome
`Hamming distance of at least 5 from each code
`word (sixteen feasible error patterns in the code
`word of each other subtable. For the code word
`word), one data bit must be guessed. In the case
`which consists entirely of zeros, this can be
`of six other different results for the syndrome
`verified most easily. Consequently, the two most
`word (fourteen feasible error patterns in a code
`significant data bits are protected by a code which
`word), two data bits must be guessed. In the case
`corrects two bit errors. It also appears that when
`of one different result for the syndrome word
`two bit errors occur in a code word, one in an
`(several feasible error patterns), the entire data
`even position and one in an odd position, correc(cid:173)
`word must be guessed because in that case at
`tion is also feasible. This appearsfrom the fact
`least three code bits are incorrect.
`that there is no code word having the weight " 4"
`with a " 1" in an even bit position as well as in an
`odd bit position.
`Figure 9 shows the parity check matrix [H] of
`the specimen code which satisfies [G] • [H]=0.
`Multiplication of a twelve-bit word by the parity
`check matrix [H] produces a six-bit syndrome
`word. If the twelve-bit word is an error-free code
`word, the syndrome word consists exclusively of
`" 0" bits. Figure 10 shows a table with
`the
`syndrome words. The first two columns state the
`digital and the binary representation of
`the
`syndrome words. The further column states the
`order of incorrect code bits (0—11) causing the
`relevant syndrome word. If there are several
`possibilities, they are separated by a semicolon.
`For all feasible 212=4k different incorrect words,
`only those comprising the lowest number of
`incorrect bits are indicated for each syndrome
`word. For example, the syndrome word " 4" is
`caused by an error in code bit "10", the syndrome
`word " 6" by an error in the code bits 3 and 8, the
`syndrome word "24" by two feasible combina(cid:173)
`tions of two incorrect code bits, the syndrome
`word "16" by three of such feasible combina(cid:173)
`
`Description of the decoder.
`Figure 11 shows a block diagram of a decoder
`for use with the described code. The correct or
`incorrect twelve-bit code words t arrive on input
`76. Element 78 is the syndrome generator which
`generates a six-bit syndrome word on output 80
`by means of the parity check matrix [H], and
`which conducts the six most significant code bits
`on output 82. Element 84 is a read-only memory
`which is addressed by the six syndrome bits; a
`synchronizing clock system has been omitted for
`the sake of simplicity. The read-only memory 84
`outputs nine error indication bits: six on output 86
`and three further error indication bits on output
`88. The first six error
`indication bits e0...es
`indicate the errors detected in the six most
`significant code bits; for (64-8-6-1 )=49 different
`syndrome words
`this
`is the only correction
`required. In the multiple EXCLUSIVE-OR element
`87 these error indication bits are modulo-2 added
`to the associated, more significant code bits
`C0...CS. In element 90, the six-bit data word m' is
`reconstructed from the six repaired code bits
`received. The described circuit elements, exclud-
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`HTC EX1011, Page 5
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`ing read-only memory 84, are shown in detail in
`data word. The further guessing in the element 96
`Figure 12. Figure 13 shows a table with syndrome
`can be performed in various ways:
`words and the associated groups of error indica(cid:173)
`a. guessing implies: assuming to be one: the
`tion bits. The first column of the latter Figure
`output signal of Figure 14 is bit-wise combined
`contains a decimal representation of the syndrom
`with the associated data bits in an OR-function.
`words while the second column contains a binary
`b. analogously, guessing may imply: assuming
`representation. The third column states the six
`to be "zero".
`error
`indication bits appearing on output 86
`c. guessing implies that the treatment depends
`(Figure 11 ) which provide the primary correction.
`on the data content, for example, the value for the
`The fourth column states the further error indica(cid:173)
`preceding subpicture
`is substituted. Typical
`tion bits on output 88 which serve to solve
`properties of the transmission may also be taken
`ambiguous cases. The decimal representations of
`into account, for example, the fact that an error
`the latter three error indication bits are shown in
`from 0 to 1 is more probable than vice versa, or
`the last column. The meaning of the latter three
`the effect of neighbouring bits may be
`error indication bits is as follows:
`considered. This is not elaborated herein.
`Figure 15 shows a table of (N, K) codes with at
`most twelve code bits and at least 2 data bits, with
`unequal protection among the data bits. The first
`column states the length of a code word, i.e. the
`value of N. The second column states the length
`of a data word, i.e. the value of K. The third
`column states the degree of error protection for
`each of the series data bits as expressed in the
`minimum Hamming-distance D; it is well known
`that
`the minimum Hamming-distance
`is a
`convenient way of expressing the error protection
`capability of a code. A value of D=2 implies that
`single bit errors may be detected, at D=3 single
`bit errors may be corrected, and so on. The
`minimum Hamming-distance as defined for a
`certain bit implies that the correction or detection
`capability with respect to reproduction of the
`correct value of this bit is assured even if the
`maximum amount of errors covered by this value
`of D occurs. Therefore, for a (11,4) code the two
`most significant bits are protected against two
`incorrect code bits, while an additional incorrect
`bit can be detected. The protection for the other
`two data bits is less. For some cases more
`possibilities exist, for example, for the (11, 2)
`code. Sometimes more than two protection levels
`are feasibly, for example, in the (12,4) code. Thus,
`one data bit may be reconstructed even if three
`errors occur, a second data bit may be recon(cid:173)
`structed even
`if two errors occur, while an
`additional error is signalled correctly in that case,
`two
`further data bits may be
`reconstructed
`correctly if one error occurs, while an additional
`error is signalled correctly. The generator matrix
`of the latter code is shown in Figure 16.
`The code already described with reference to
`the Figure 6,9 represents a special case of a class
`of [N, K]=[4n, 2n] code with n^3 and Hamming
`distances for the relevant data bits of (n+2, n+2,
`4,4,...) where
`the differences between
`the
`Hamming distances are attractive. A very
`favourable generator matrix for such a code is
`given by:
`
`0: after the operation by means of the six first
`error indication bits, no further modification of
`the data content of the six most significant
`code bits is required.
`1 : (in this case no correction has been performed
`in element 87): the entire data word must be
`guessed because there are more than two
`incorrect code bits.
`2: in addition to the correction performed by the
`first group of error indication bits, the data bits
`m2 must be guessed.
`3: in addition to the correction performed by the
`first group of error indication bits, the data bit
`rria must be guessed.
`4: the correction by the first group of error
`indication bits has not taken place, data bit rrv
`must be guessed.
`5: the correction by the first group of error
`indication bits need not be performed, data bit
`m5 must be guessed.
`6: the data bits m2 and m4 must be guessed.
`7: the data bits 1x13 and ms must be guessed.
`
`The connections 76, 80, 82 and 86 of the circuit
`shown in Figure 12 have already been mentioned.
`The logic operations are again performed by
`means of EXCLUSIVE-OR-elements. Connection
`92 represents the output of the multiple EXCLU-
`SIVE-OR element 87 of Figure 11. In block 90 of
`Figure 11, a provisional six-bit data word is
`reconstructed from the first six code bits thus
`provisionally corrected, said reconstructed data
`word being presented on output 94. The latter
`connection is also shown in Figure 12, together
`with the internal construction of the element 90.
`The latter can be constructed in the described
`manner by means of only four exclusive-OR-ele-
`ments and by cross-wiring in order to modify the
`sequence of some code bits. In block element 96,
`the data bits which are not unambiguously
`defined are guessed under the control of the three
`last error indication bits. The decoding of the
`error indication bits is shown in Figure 14. The
`circuit shown
`in Figure 14 comprises
`two
`inverters, such as the element 98, a logic OR-gate
`101, and five logic AND-gates such as the element
`100. On the outputs 102... llOthe signals necessi(cid:173)
`tating the guessing operation successively appear
`for the data bits m2, ma, m4, ms and for the entire
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`HTC EX1011, Page 6
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`Therein, en, 0n and 1n are vectors having