III US005708665A
`
`Patent Number:
`11
`45 Date of Patent:
`
`5,708,665
`Jan. 13, 1998
`
`5,430,743 7/1995 Marturano et al. ....................... 37/43
`
`Primary Examiner Phung Chung
`Attorney, Agent, or Firm--Kevin L. Daffer; Conley, Rose &
`Tayon
`ABSTRACT
`57
`A communications receiver system is presented for detecting
`burst errors and providing erasure information to the block
`decoder (outer decoder), thereby effectively doubling the
`conventional correction capability of the block decoder with
`only a minimal increase in complexity. In one embodiment,
`this mechanism takes the form of a circuit which re-encodes
`the output of the inner decoder, compares it with the
`received sequence of code symbols, and flags a portion of
`the inner decoder output for erasure when an excessive
`number of code symbol errors are detected. In a second
`embodiment, this mechanism takes the form of a circuit
`which makes hard symbol decisions on the channel signal,
`compares the hard decisions to the channel signal to deter
`mine a noise level, and thereafter flags the channel output in
`regions with excessive noise levels.
`
`14 Claims, 4 Drawing Sheets
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`O
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`United States Patent 19
`Luthi et al.
`
`54 DIGITAL RECEIVERUSING
`EQUALIZATION AND BLOCK DECODING
`WITH ERASURE AND ERROR
`CORRECTION
`
`75) Inventors: Daniel A. Luthi, San Jose; Ravi
`Bhaskaran, Santa Clara; Dojun Rhee,
`San Jose; Advait M. Mogre. Fremont,
`all of Calif.
`(73) Assignee: LSI Logic Corporation, Milpitas,
`Calif.
`
`21 Appl. No.: 701,710
`22 Filed:
`Aug. 22, 1996
`51) Int. Cl'........................................... G06F11/00
`(52) U.S. C. ............................... 371/5.1; 371/41; 371/45;
`371/39.1; 37.5/229
`(58) Field of Search up 40 on
`Povopose adds who woodoo 371/5.1, 41, 43,
`371/44, 45, 37.1, 38.1, 3. 2.2.
`y
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`56)
`
`References Cited
`U.S. PATENT DOCUMENTS
`4,829,525 5/1989 Sugiyama et al. ........................ 371/38
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`1
`DIGITAL RECEIVER USING
`EQUALIZATION AND BLOCK DECODING
`WTH ERASURE AND ERROR
`CORRECTION
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`BACKGROUND OF THE INVENTION
`1. Field of the Invention
`This invention relates to the field of digital communica
`tion systems such as those that might be used for satellite
`transmission channels and cable channels, and in particular
`to the decoding of error correction coded signals.
`2. Description of the Relevant Art
`The history of error correction coding begins in 1948 with
`Claude Shannon. Shannon demonstrated that any commu
`15
`nications channel has a calculable capacity such that infor
`mation transmission at a rate which does not exceed the
`capacity can be achieved with as small an error rate as
`desired. This information transmission is accomplished via
`the use of error correction coding. Unfortunately, Shannon's
`proof was based on ensemble averages, and consequently
`did not provide a useful code construction technique. During
`the 1950's, an extensive amount of effort was put into
`developing explicit code constructions which would provide
`asymptotically vanishing error rates, without success. The
`class of Hamming codes was introduced in 1950, but these
`block codes were only capable of correcting single errors.
`Other codes were developed in the 1950's, but they were
`accompanied by no general construction theory. In the late
`1950's, a probabilistic approach to the decoding problem led
`to the development of tree codes, which have been primarily
`represented by convolutional codes. Then around 1960,
`Reed-Solomon codes and the more general Bose-Chadhuri
`Hocquenghem codes provided a large class of multiple error
`correcting codes, which comprise one of the most important
`classes of block codes today. However, the performance of
`these codes suffers when extended to large block lengths. In
`1967, the invention of the Viterbi decoder provided a
`replacement for the sequential decoding of tree codes,
`thereby strengthening the feasibility of convolutional cod
`ing. Finally, in the 1970's the Justesen and Goppa code
`families were introduced which provided good codes with
`long block lengths.
`Error control codes function by accepting input data
`symbols and processing them in such a way as to add some
`redundancy to the symbol sequence. All error control codes
`can be formulated so that this coding process takes the form
`of adding check symbols to the data symbol sequence. With
`this formulation, the encoder accepts an input word of k data
`symbols at each time step and produces a code word with n
`symbols, k of which are the input data symbols, and n-k of
`which are the check symbols. An example of such a code
`word 10 having k data symbols 12 and n-k check symbols
`14 is shown in FIG. 1. The redundancy added by the check
`symbols serves to increase the distance between valid code
`symbol sequences. A common measure of the distance
`between code words is the number of symbols in which they
`differ, defined herein as the Hamming distance. Shown in
`FIG. 2 are two code words 16 and 18 which are selected
`from the set of valid code words that make up an example
`block code. A comparison of two code words 16 and 18,
`shown in FIG. 2 reveals three symbol positions which differ:
`D. D., and D. Thus the Hamming distance between code
`words 16 and 18 is three. The minimum Hamming distance
`between any two sequences of code words is called the
`minimum Hamming distance of the code, and is often
`denoted d. For a block code, each code word is unrelated
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`to other code words, so this distance corresponds to the
`minimum Hamming distance between any two code words.
`In FIG. 2, the code words 16 and 18 are the nearest valid
`code words, so for this code d'=3.
`When code words are transmitted across a noisy channel,
`they are often subject to corruption. This corruption typi
`cally takes the form of symbol errors in the code word.
`Usually the locations of these errors are unknown prior to
`decoding, but in some cases it is possible to determine the
`locations of these errors prior to decoding. When this occurs,
`it is advantageous to mark their locations in some manner so
`that these symbols are disregarded in the decoding process.
`When this is done, these errors which are characterized by
`an unknown error value but a known error location can be
`referred to as erasures. The circumstances under which the
`code word will be correctly decoded are provided by the
`following equation:
`
`n+2nsd-1
`where n is the number of erasures and n is the number of
`OS
`To illustrate the above equation, assume that code word
`18 is transmitted and received as a corrupted code word 20
`with two symbol errors. Consider the well known decoding
`algorithm wherein the received code word is compared to all
`valid code words, and the valid code word that is most like
`the received code word is chosen as the correct code word.
`Decoding is then accomplished by simply removing the
`check symbols from the chosen code word. In FIG. 2 code
`word 20 represents a received code word that contains two
`symbol errors. According to the equation, code word 20 may
`be incorrectly decoded, and indeed it differs by only one
`symbol from code word 16. According to the stated decod
`ing algorithm, incorrect code word 16 is chosen, resulting in
`a decoding error. However, when the knowledge of the error
`locations is applied as shown by code word 22, then these
`symbols are ignored in the comparison process and code
`word 22 matches the correct code word 18. Consequently
`code word 22 with erasures is correctly decoded. In general,
`the number of erasures that a code can tolerate without
`making decision errors is twice the number of unerased
`errors that it can tolerate. Further details on the design and
`function of error correction codes may be found in Bernard
`Sklar, Digital Communications: Fundamentals and
`Applications, Prentice Hall, Englewood Cliffs N.J., pp.
`263-365, 1988, incorporated herein by reference.
`While this relation between error and erasure tolerance is
`well known, a practical mechanism for detecting error
`locations before decoding is not. The above equation shows
`that erasures and errors both impair the ability to decode
`correctly, and the only advantage gained by using erasures
`is the provision of additional side information to the decoder.
`When erasures are misapplied, that is, when the location of
`errors is misidentified, then decoding performance worsens.
`The art of code design revolves around optimizing the
`tradeoff between rate reduction and Hamming distance gain
`for a given code complexity. Reed-Solomon codes are
`extremely popular because this family of codes is based on
`a construction that allows for custom tailoring of the infor
`mation rate and Hamming distance properties of the code.
`Furthermore, efficient decoders are easy to design for these
`codes. However at large block lengths, the performance of
`Reed-Solomon codes suffers a loss of efficiency. A technique
`for extending the effective block length of these codes is to
`follow the Reed-Solomon encoder with an interleaver which
`acts to intersperse the symbols from one code word with the
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`symbols from other code words. This is typically done by
`writing the code words into a memory matrix column-wise
`and reading the completed matrix row-wise. The interleaver
`can then be followed by a convolutional encoder which
`further adds redundancy to the symbol sequence. At the
`receiving end the process is reversed, first applying a con
`volutional decoder to the received sequence, next applying
`a de-interleaver, and finally performing the Reed-Solomon
`block decode. Each of the additional steps adds only a
`moderate amount of complexity to the system while signifi
`cantly boosting its performance.
`This arrangement is typically used in environments where
`code symbol errors caused by the channel tend to occur
`randomly or in bursts. Burst errors are not random isolated
`errors, but rather burst errors are defined as errors which
`occur in localized groups. For example, in the case of the
`satellite receiver system, the nature of the errors on the
`channel is typically random, although when a concatenated
`decoder is used, errors in convolutional decoding tend to be
`burst errors. A method for detecting bursts errors of the
`convolutional decoder would prove advantageous in assist
`ing the following block decoder. Apart from the random
`noise, other effects may corrupt the transmitted signal. These
`effects are more bursty in nature (examples: microwave
`radiation close to the receiving antenna, lightning, home
`appliance electrical noise, etc.). The de-interleaver acts to
`distribute errors within a group so that they are isolated and
`fewer occur within a given code word. This in turn enhances
`the probability that the number of errors will not exceed the
`correction capability of the Reed-Solomon code.
`Nevertheless, it is still necessary to use Reed-Solomon
`codes of moderate length and complexity to keep the error
`correction capability high enough to preserve their resis
`tance to burst errors.
`Since error correction coding necessitates the transmis
`sion of check symbols in addition to the data symbols, the
`bandwidth available to the data symbols can be decreased to
`make room for the check symbols, or additional bandwidth
`can be allocated for the check symbols. The first option
`results in a reduction of the rate at which data can be
`transmitted, and the second option results in an increase in
`overall channel bandwidth. Typically one of these options is
`required, but the tradeoff is increased manufacturing
`tolerances, increased margin for equipment degradation, a
`reduction of the required signal-to-noise ratio, and an overall
`reduced probability of error.
`SUMMARY OF THE INVENTION
`The problems outlined above are in large part solved by
`a receiver with a mechanism for detecting burst errors and
`providing erasure information to the block decoder, thereby
`increasing the conventional correction capability of the
`block decoder with only a small increase in complexity. In
`one embodiment, a transmission system is provided having
`a transmission channel interposed between a concatenated
`encoder and concatenated decoder. The concatenated
`encoder has an outer block encoder followed by an inter
`leaver followed by an inner convolutional encoder. The
`concatenated decoder has an inner convolutional decoder
`followed by a deinterleaver followed by a outer block
`decoder. The burst error detection mechanism takes the form
`of a circuit which re-encodes the output of the inner decoder,
`compares it with the received sequence of code symbols, and
`flags a portion of the inner decoder output for erasure when
`a number of code symbol errors are detected in a given
`interval.
`65
`In a second embodiment a transmission system is pro
`vided having a transmission channel interposed between an
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`encoder and a decoder. The burst error detection mechanism
`takes the form of a circuit which equalizes the signal, makes
`decisions based on the signal, forms a sequence of differ
`ences between the equalized signal and the decisions, and
`flags a portion of the decoder input signal for erasure when
`the estimated noise level meets one or more criteria in a
`given interval.
`Broadly speaking, the present invention contemplates a
`digital communications system. The digital communications
`system comprises an encoder configured to receive a digital
`signal representing data for transmission. The encoder
`serves to convert the digital signal to a coded digital signal.
`The coded digital signal may then be sent through a trans
`mission channel. An error detector is coupled to the receiv
`ing end of the transmission channel to receive the coded
`digital signal. The error detector determines errors in defined
`locations in the coded digital signal and sets a flag for those
`defined locations. A decoder is coupled to the receiving end
`of the transmission channel to receive the coded digital
`signal. The decoder is also coupled to receive output from
`the error detector indicative of the flag status. The decoder
`then decodes the coded digital sequence using the error
`location flags to increase its error correcting capability.
`According to one embodiment, the decoder takes the form
`of a concatenated decoder in which the output of the inner
`decoder is coupled as a second input to the error detector,
`and the outer decoder is coupled to receive output from the
`error detector indicative of the flag status. The outer decoder
`then decodes the coded digital sequence using the error
`location flags to increase its error correcting capability.
`According to a second embodiment, the error detector
`flags errors on the basis of estimated noise levels. The
`decoder is coupled to receive output from the error detector
`indicative of the flag status. The decoder then decodes the
`coded digital sequence using the error location flags to
`increase its error correcting capability.
`BRIEF DESCRIPTION OF THE DRAWINGS
`Other objects and advantages of the invention will
`become apparent upon reading the following detailed
`description and upon reference to the accompanying draw
`ings in which:
`FIG. 1 is a code word comprising a structured sequence
`of data symbols and check symbols encoded according to a
`block and/or convolutional encoder;
`FIG. 2 is set of code words exemplifying a correct code
`word, an incorrect yet valid code word, a corrupted version
`of the correct code word with errors, and a corrupted version
`of the correct code word with erasures;
`FIG. 3 is a block diagram of a digital communications
`system having a concatenated encoder and decoder capable
`of providing error correction on transmitted data;
`FIG. 4 is a block diagram of an alternate configuration of
`a digital communications system having an encoder, error
`burst detector, and decoder capable of providing error cor
`rection on transmitted data;
`FIG. 5 is a block diagram of a possible implementation of
`an error burst detector suited for use in the digital commu
`nications system of FIG. 3; and
`FIG. 6 is a block diagram of a possible implementation of
`an error burst detector suited for use in the digital commu
`nications system of FIG. 4.
`While the invention is susceptible to various modifica
`tions and alternative forms, specific embodiments thereof
`are shown by way of example in the drawings and will
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`herein be described in detail. It should be understood,
`however, that the drawings and detailed description thereto
`are not intended to limit the invention to the particular form
`disclosed, but on the contrary, the intention is to cover all
`modifications, equivalents and alternatives falling within the
`spirit and scope of the present invention as defined by the
`appended claims.
`DETAILED DESCRIPTION OF THE
`INVENTION
`Turning now to the drawings, FIG. 3 represents a digital
`communications system 24 which employs a concatenated
`encoding and decoding scheme. Digital communications
`system 24 comprises an equivalent discrete transmission
`channel 26 interposed between an encoder 28 and a decoder
`30. Error burst detector 50 is coupled to channel 26 and
`decoder 30.
`Digital communications system 24 in conjunction with
`encoder 28, decoder 30, and error burst detector 50 serves to
`error correct digital signals sent through channel 26. Error
`correction coding makes the digital signals less susceptible
`to noise and other forms of interference on the channel.
`Digital communications system 24 employs a more efficient
`decoder 30 which can correct a larger number of data
`symbol errors than conventional decoders at a comparable
`level of system complexity. More specifically, decoder 30
`uses additional information provided by error burst detector
`50 to determine the location of suspected code symbol errors
`and thereafter ignores code symbols in those locations upon
`decode. Decoder 30, in conjunction with error detector 50,
`is thereby capable of correcting a larger number of code
`symbol errors than conventional decoders. Decoder 30, in
`conjunction with error burst detector 50, is particularly well
`suited to decoding information transmitted across commu
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`nications channels which are prone to random or burst
`COTS
`Encoder 28 shown in the embodiment of FIG. 3 is a
`concatenated encoder. A preferred concatenated encoder
`hereof employs an inner, convolutional encoder 32, an outer,
`Reed-Solomon block encoder 34 and an interleaver 36
`placed between the encoders. The input data is error cor
`rection encoded and thereafter conveyed across discrete time
`channel 26. Discrete time channel 26 normally comprises a
`modulator 38 and a demodulator 42 operably connected by
`an analog channel 40. Modulator 38 can use any well known
`modulation technique, suitable modulation being amplitude
`modulation, frequency shift keying, phase shift keying, etc.
`Whatever modulation scheme is used, the desired modula
`tion output is one that is less susceptible to interference on
`channel 40.
`Analog channel 40 is typically subject to interference
`which may corrupt signals forwarded therein. The interfer
`ence may cause symbol errors at certain code word locations
`present at the output of demodulator 42. In digital commu
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`nications system 24, analog channel 40 may take the form of
`a transmitting antenna from which microwaves are emitted,
`atmosphere and empty space through which the microwaves
`travel, a satellite which reflects or receives and retransmits
`the microwaves, and a receiving antenna which converts the
`microwaves into an electrical signal. In this case, the chan
`nel interference may result from atmospheric noise, multi
`path interference, and fading. Otherforms of noise may arise
`from electronic circuitry within the modulator 38 and
`demodulator 42. Other channels which might be used in
`communications system 24 include cable transmission chan
`nels and magnetic recording channels.
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`Retrieval of a carrier modulated coded digital signal
`begins with demodulator 42, which serves to reproduce the
`coded digital signal from the carrier waveform. Depending
`on the modulation technique, demodulator 42 may employ
`an amplifier and various filters. Regardless of the form
`chosen, the desired output of demodulator 42 is a coded
`digital signal which is as free of interference as possible.
`However, interference cannot be entirely eliminated from
`the encoded signal, which consequently motivates the use of
`error correction coding.
`According to the advantages hereof, output from demodu
`lator 42 is forwarded to decoder 30, but also to error burst
`detector 50. Decoder 30 decodes the coded digital signal
`preferably using an inner Viterbidecoder 44, a deinterleaver
`48, and an outer Reed-Solomon decoder 46. In addition,
`decoder 30 accepts output from error burst detector 50
`which flags locations of suspected symbol errors in the
`coded digital signal. With the additional information pro
`vided by the determination of the symbol errors, outer
`decoder 46 is able to correct a larger number of symbol
`errors than a conventional decoder of similar complexity.
`It should be emphasized that the symbol error locations
`must be known prior to decoding before erasures may be
`used to an advantage.
`In systems where the prevalent error type is burst errors,
`the main benefit of erasures is to be gained by the outer
`decoder 46. The inner decoder is normally designed to
`correct isolated random errors. However the burst errors
`may only be dealt with by codes with large Hamming
`distances. This motivates the presence of the outer decoder
`in a concatenated decoder design. Since the use of erasures
`permits the use of codes with reduced Hamming distances,
`implementation complexity of the outer decoder is signifi
`cantly reduced.
`In systems where concatenated decoders are not desired,
`a second embodiment shown in FIG. 4 may be used. Error
`burst detector 58 functions to measure the noise level on
`discrete time channel 26 and thereafter set symbol error flags
`based on criteria related to the noise level. Such criteria may
`include the noise level or a time averaged measurement of
`the noise level exceeding a predetermined threshold value.
`Alternatively, the error burst criteria might include sudden
`changes in the noise level, or a combination of the value and
`derivative of the noise level. In any case, the symbol error
`locations are determined prior to decoding, and hence may
`be used to advantage by the entire decoder 56. Decoder 56
`may be implemented in the form of a block decoder, a
`convolutional decoder, or a concatenated decoder.
`Returning to FIG. 3, de-interleaver 48 reverses the inter
`leave operation performed by interleaver 36. Flag informa
`tion from error burst detector 50 is processed so that symbols
`flagged at the input to the de-interleaver 48 remain flagged
`at the output of the de-interleaver 48. One method for doing
`this is to simply add a flag bit to each symbol as it is written
`into a de-interleaving mechanism modified to handle the
`augmented symbols. Then as the augmented symbols exit
`the de-interleaver the flag status of a given symbol is easily
`determined.
`As shown in FIG. 5, error burst detector 50 accepts output
`symbols from inner decoder 44 and re-encodes the output
`symbols using an inner encoder 60 which implements the
`same encoding function as inner encoder 32. The resulting
`code symbol sequence output from inner encoder 60 serves
`as an approximation of the input to discrete time channel 26.
`Location of symbol errors is easy to achieve by comparing
`the input to channel 26 and output from channel 26.
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`Although the input to channel 26 is not readily available, the
`approximation provided by the output of encoder 60 will be
`faithful when isolated random symbol errors occur. This is
`true since isolated random symbol errors are within the error
`correction capability of the inner decoder. The decoding and
`re-encoding of the channel output effectively implements the
`error correction.
`The approximation of the input to discrete time channel
`26 will be extremely poor when many symbol errors occur
`in a small amount of time (i.e. burst errors). Since the error
`correction capability of the inner decoder is overwhelmed by
`the number of errors present in a burst error, the decoding
`and re-encoding of the channel output effectively results in
`wild guesses as to the input of the channel. These guesses are
`wrong more often than right, but more importantly, the
`correspondence with actual channel output is low. This
`characteristic permits the identification of the portions of the
`channel output signal sequence in which burst errors occur.
`For reasons outlined later, this results in a reliable identifi
`cation of symbol error locations.
`Data delay line 62 serves to store the output signal from
`channel 26 until the inner decoder 44 and inner encoder 60
`have produced an approximation of the input signal to
`channel 26. Comparator 64 compares the approximation of
`the input signal to the output signal and determines the
`presence or absence of a symbol error. This determination is
`passed in the form of a signal to a windowing filter 66 that
`determines the number of symbol errors in an interval which
`includes a predetermined number of code symbols. A signal
`representing this number is sent to threshold detector 68
`which functions to determine whether the number of symbol
`errors in the specified interval exceeds a predetermined
`threshold. Threshold detector 68 outputs an error flag signal
`representing the presence or absence of a burst error in the
`specified interval. De-interleaver 48 is coupled to receive the
`error flag signal, and will use it to attach a flag bit to a subset
`of the code symbols that reside in the specified interval.
`The windowing filter 66 serves to determine the number
`of symbol errors in a specified interval. This is done to
`identify burst errors which are characterized as many errors
`occurring in a localized interval. The number of errors and
`the size of the interval which are used to differentiate a burst
`error from a series of random errors are specified by the
`system designer based on measured channel characteristics.
`One implementation for filter 66 is a shift register of a
`specified length that stores the output of comparator 64, and
`a summer that sums the contents of the shift register.
`The intent of the error flags is to mark as errors all of the
`code symbols that occur during an error burst on the basis
`that the symbols represent guesses by the inner decoder 44
`and are most likely wrong. The probability of a particular
`symbol not being in error during an error burst is dependent
`on the statistics of the channel 26 and the decoder 30, but in
`general the probability is inversely proportional to the
`cardinality of the symbol set. For the large symbol sets
`normally used in Reed-Solomon codes, the probability of
`symbol error approaches 100%. Consequently, the erasure of
`these symbols is advantageous and leads to significant
`improvement in decoding performance of outer decoder 46.
`FIG. 6 illustrates one possible configuration for an error
`burst detector 58. Error burst detector 58 comprises a
`decision element 72, and a comparator 74 with inputs
`coupled to the input and output signals of decision element
`72. The output of the comparator may take the form of an
`absolute value of the difference between the input signals or
`perhaps the square of the difference between the input
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`signals. Error detector 58 may further comprise a window
`ing filter 76 and a threshold detector 78. Windowing filter 76
`forms a signal determined by a weighted moving average of
`the comparator output signal. Windowing filter 76 is
`designed such that the resulting signal has a significant
`correlation with the presence of errors in the demodulated
`signal stream. Threshold detector 78 asserts an error flag
`whenever the windowing filter output exceeds a config
`urable threshold. Error burst detector may additionally com
`prise an equalizer 70. Equalizer 70 would then serve to
`remove intersymbol interference from the demodulator out
`put and/or improve the signal-to-noise ratio.
`Decision element 72 may take the form of one or more
`comparators, each of which simply determines whether the
`channel output signal is greater than or less than a given
`value. The given values are chosen to be the midpoints
`between modulation points in the signal constellation. In this
`manner, the decision element is able to find the modulation
`point closest to the channel signal, and arbitrarily "decides"
`that the closest modulation point is the correct one. This is
`often referred to as making a hard decision.
`The distance between the channel output signal and the
`correct modulation point is determined by the interference of
`the channel. If the channel were perfect, the channel output
`signal would be equal to the correct modulation point. By
`taking the absolute value or square of the distance, a signal
`representing the level of the noise on the channel is gener
`ated. This noise signal can then be processed in one of
`severalmanners. An estimated noise power can be generated
`by averaging a fixed number of past noise signals. It is
`expected that an error burst will be characterized by a
`sudden jump in the difference between the current and
`previously estimated noise power. When threshold detector
`78 to detects this sudden jump, the corresponding symbol
`locations in the channel output have an error flag set.
`Equalizer 70 is typically used to combat sources of
`channel interference which are not random, such as
`intersymbol interference. This simplifies the implementation
`of the decision element for complex channels and permits a
`more accurate estimation of noise.
`The communications system configuration of FIG. 4
`might generally be preferred for high-order constellations,
`i.e. when the signal can consist of many signal points. In this
`case a greater need exists for equalization to improve the
`receiver's ability to distinguish between signal points.
`The communications system configuration of FIG. 3
`might generally be preferred for channels which necessitate
`a large coding gain. These include power limited channels
`such as satellite channels are prone to a higher probability of
`error, and consequently require a code with a higher error
`correction capability.
`Numerous variations and modifications will become
`apparent to those skilled in the art once the above disclosure
`is fully appreciated. It is intended that the following claims
`be interpreted to embrace all such variations and modifica
`tions.
`What is claimed is:
`1. A communications system comprising:
`an encoder configured to receive a digital signal and
`thereafter convert said digital signal to a coded digital
`signal;
`a transmission channel through which said coded digital
`signal is transmitted;
`a decoder coupled to said transmission channel to receive
`said coded digital signal, configured to correct erasures
`and errors in said coded digital signal, and configured
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`ERICSSON v. UNILOC
`Ex. 1033 / Page 9 of 10
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