Abstract: In a first inter-image prediction mode in which information on a motion vector is used, a first mode detection unit constructs a first candidate list from a plurality of reference block candidates based on a first predetermined order, assigns indices for designating reference block candidates added in the first candidate list, and outputs the indices of the plurality of reference candidate blocks. In a second inter-image prediction mode in which is used a motion vector difference between a motion vector predictor based on information on a motion vector, and a motion vector of a coding target block, a second mode detection unit constructs a second candidate list from a plurality of reference block candidates based on a second predetermined order, assigns indices for designating reference block candidates added in the second candidate list, and outputs the indices of the plurality of reference block candidates and motion vector differences.

Abstract: An LED light and communication system in communication with a broadband over power line communications system. The LED light and communication system includes at least one optical transceiver. The optical transceiver includes a light support having a plurality of light emitting diodes and at least one photodetector attached thereto, and a processor. The processor is in communication with the light emitting diodes and the at least one photodetector. The processor is constructed and arranged to generate a communication signal. The at least one optical transceiver is engaged to a clock, and the clock is in communication with the broadband over power line communications system.

Abstract: A video encoder may include a context-adaptive binary arithmetic coding (CABAC) encode component that converts each syntax element of a representation of a block of pixels to binary code, serializes it, and codes it mathematically, after which the resulting bit stream is output. A lookup table in memory and a context cache may store probability values for supported contexts, which may be retrieved from the table or cache for use in coding syntax elements. Depending on the results of a syntax element coding, the probability value for its context may be modified (e.g., increased or decreased) in the cache and, subsequently, in the table. After coding multiple syntax elements, and based on observed access patterns for probability values, a mapping or indexing for the cache or the table may be modified to improve cache performance (e.g., to reduce cache misses or access data for related contexts using fewer accesses).

Abstract: A method for determining a layer stoppage in LDPC decoding is provided. The method may include determining the occurrence of the layer stoppage to detect and record a convergence of a layer arithmetic unit after the performance of a layer decoding operation using LDPC decoding, and in a subsequent iteration operation stopping an operation of the layer arithmetic unit that has converged and repeating determining the layer stoppage for the layer arithmetic unit that has not yet converged. An output of the non-convergent layer may be diverted to the next non-convergent layer while bypassing the convergent layer without interrupting the subsequent iteration operation while maintaining the overall error correction capability.

Abstract: A method for decoding a video frame includes receiving a slice header of at least one of a plurality of slices, identifying a type of a first slice and a type of a second slice, and initializing a first context associated with the first slice and a second context associated with the second slice using one of a first initialization method and a second initialization method. The first initialization method or the second initialization method is selected according to the type of the first slice and the type of the second slice.

Abstract: A method for decoding a video frame includes receiving a slice in a video decoder, identifying the slice as one of at least a first predicted slice and a second predicted slice, receiving information used to determine a context initialization method corresponding to the slice, and initializing, based on the received information, one of a first context initialization method and a second context initialization method associated with the slice, and decoding the video frame using the slice and one of the first context initialization method and the second context initialization method.

Abstract: Images are divided into image regions. The image regions are processed in encoding cycles such that during an encoding cycle, entropy encoding is carried out in a plurality of parallel encoding branches. In each encoding branch the symbols of an image region are encoded by entropy encoding, which is based on one or more probability models, which take into account the frequencies of symbols occurring in image regions. The probability models are adapted on the basis of the symbols occurring in the image region. A common set of probability models is updated at predetermined time intervals on the basis of frequencies that are adapted in at least one temporally preceding encoding cycle.

Abstract: A compression algorithm based on Huffman coding is disclosed that is adapted to be readily implemented using VLSI design. A data file may be processed to replace duplicate data with a copy commands including an offset and length, such as according to the LV algorithm. A Huffman code may then be generated for parts of the file. The Huffman code may be generated according to a novel method that generates Huffman code lengths for literals in a data file without first sorting the literal statistics. The Huffman code lengths may be constrained to be no longer than a maximum length and the Huffman code may be modified to provide an acceptable overflow probability and be in canonical order. Literals, offsets, and lengths may be separately encoded. The different values for these data sets may be assigned to a limited number of bins for purpose of generating usage statistics used for generating Huffman codes.

Abstract: A video encoder generates a bitstream that includes a syntax element that indicates whether a picture is encoded according either a first coding mode or a second coding mode. In the first coding mode, the picture is entirely encoded using wavefront parallel processing (WPP). In the second coding mode, each tile of the picture is encoded without using WPP and the picture may have one or more tiles. A video decoder may parse the syntax element from the bitstream. In response to determining that the syntax element has a particular value, the video decoder decodes the picture entirely using WPP. In response to determining that the syntax element does not have the particular value, the video decoder decodes each tile of the picture without using WPP.

Abstract: Representative embodiments are disclosed for a rapid and highly parallel decompression of compressed executable and other files, such as executable files for operating systems and applications, having compressed blocks including run length encoded (“RLE”) data having data-dependent references. An exemplary embodiment includes a plurality of processors or processor cores to identify a start or end of each compressed block; to partially decompress, in parallel, a selected compressed block into independent data, dependent (RLE) data, and linked dependent (RLE) data; to sequence the independent data, dependent (RLE) data, and linked dependent (RLE) data from a plurality of partial decompressions of a plurality of compressed blocks, to obtain data specified by the dependent (RLE) data and linked dependent (RLE) data, and to insert the obtained data into a corresponding location in an uncompressed file.

Abstract: An arithmetic decoding method is a method in which a context variable specifying a probability of a possible value of each of elements included in a binary string corresponding to a value of a given variable is initialized and arithmetic decoding is performed, using the context variable. The method includes: determining, from among a plurality of initialization methods as a method of initializing the context variable, an initialization method corresponding to the given variable or a group which includes the given variable; and initializing the context variable using the determined initialization method.

Abstract: A method of parallel decoding for a plurality of communications standards generally including steps (A) to (C) is disclosed. Step (A) may receive a plurality of first words, at least two of the first words generally have a different length than each other. Step (B) may parse the first words into a plurality of memories. Step (C) may generate a plurality of second words by decoding the first words using a plurality of decoders. The decoders generally operate in parallel. The decoding of at least one of the first words may be performed by at least two of the decoders. The decoding is generally based on a signal that identifies a current one of the communications standards used to transfer the first words.

Abstract: The invention relates to a method for coding a data stream (DS), wherein the data stream (DS) comprises a multiplicity of characters which are symbols (S) from an alphabet, wherein the characters of the data stream (DS) are combined to form a plurality of blocks (B), and the blocks (B) are entropy-coded on the basis of a code table (CT) valid for the respective block (B). The method according to the invention is characterized by the fact that the blocks (B), by means of iteration (IT), are associated with a plurality of clusters (CL) on the basis of a clearance (d) which is defined such that the clearance (d) between a block (B) and a cluster (CL) is smaller the less pronounced the change in the entropy (ET) of the cluster (CL) when adding the block (B) to the cluster (CL).

Abstract: A binary arithmetic coding scheme is extended by a functionality to encode and decode non-negative integer values with particular low computational complexity.

Abstract: Information to be transmitted may be compressed using range coding for adaptive arithmetic coding with a virtual sliding window. Cost and complexity of coding may be reduced in some cases.

Abstract: Methods and apparatus for caching neighbor data in a block processing pipeline that processes blocks in knight's order with quadrow constraints. Stages of the pipeline may maintain two local buffers that contain data from neighbor blocks of a current block. A first buffer contains data from the last C blocks processed at the stage. A second buffer contains data from neighbor blocks on the last row of a previous quadrow. Data for blocks on the bottom row of a quadrow are stored to an external memory at the end of the pipeline. When a block on the top row of a quadrow is input to the pipeline, neighbor data from the bottom row of the previous quadrow is read from the external memory and passed down the pipeline, each stage storing the data in its second buffer and using the neighbor data in the second buffer when processing the block.

Abstract: A device comprising a data transfer channel is configured to transfer data between multiple memory devices and a host device. The channel includes multiple decoders and a buffer coupled between the multiple memory devices and the multiple decoders. The buffer is configured to store code words received from the memory devices. Channel control logic is configured to determine availability of one or more of the multiple decoders and to distribute the code words to the one or more decoders based on decoder availability.

Abstract: An image coding method for performing compression-coding on image data includes: binarizing a signal to be coded of the image data, to generate a binary signal; determining a low-order context which is a context associated with a type of the signal to be coded, and a high-order context that is common to the low-order context and a context associated with another type; calculating coding probability information to be used in arithmetic coding of the binary signal, using (i) high-order probability information corresponding to the determined high-order context and (ii) low-order probability information corresponding to the determined low-order context; performing the arithmetic coding on the binary signal using the coding probability information; and updating the high-order probability information and the low-order probability information based on the binary signal.

Abstract: In an example, aspects of this disclosure relate to a method for decoding a reference index syntax element in a video decoding process that includes decoding at least one bin of a reference index value with a context coding mode of a context-adaptive binary arithmetic coding (CABAC) process. The method also includes decoding, when the reference index value comprises more bins than the at least one bin coded with the context coded mode, at least another bin of the reference index value with a bypass coding mode of the CABAC process, and binarizing the reference index value.

Abstract: A method of decoding a video through symbol decoding includes parsing symbols of image blocks from a received bitstream; classifying a current symbol into a prefix bit string and a suffix bit string based on a threshold value determined according to a size of a current block; performing arithmetic decoding of the prefix bit string and the suffix bit string by using respective arithmetic decoding methods determined for each of the prefix bit string and the suffix bit string; performing inverse binarization of the prefix bit string and the suffix bit string by using respective binarization methods determined for each of the prefix bit string and the suffix bit string; and restoring the image blocks by performing an inverse transformation operation and a prediction operation on the current block by using the current symbol restored through the arithmetic decoding and the inverse binarization.

Abstract: An encoding system analyzes a data file to determine if portions of the data file include significant disparities in symbol probability. Huffman coding trees are produced for each of the portions of the data file and the portions are separately encoded according to specific Huffman coding trees. Encoded portions and the corresponding Huffman coding tree are packaged together and transmitted to a decoder. The encoder and decoder processes portions using different Huffman coding trees in parallel via multiple processors or processing cores.

Abstract: An image decoding method includes: arithmetic decoding steps for performing arithmetic decoding processes on decoding target signals according to contexts determined based on the types of the decoding target signals and the symbol occurrence probabilities determined based on the contexts; and a context update step for executing a group of context update processes on the decoding target signals in each of processing units each obtained as a segment having a certain size, according to the decoded signals resulting from the arithmetic decoding processes.

Abstract: A method of decoding a video through symbol decoding includes parsing symbols of image blocks from a received bitstream; classifying a current symbol into a prefix bit string and a suffix bit string based on a threshold value determined according to a size of a current block; performing arithmetic decoding of the prefix bit string and the suffix bit string by using respective arithmetic decoding methods determined for each of the prefix bit string and the suffix bit string; performing inverse binarization of the prefix bit string and the suffix bit string by using respective binarization methods determined for each of the prefix bit string and the suffix bit string; and restoring the image blocks by performing an inverse transformation operation and a prediction operation on the current block by using the current symbol restored through the arithmetic decoding and the inverse binarization.

Abstract: An image processing device that encodes image data including: an encoding unit which, with a small region line including, arrayed in the horizontal direction, small regions obtained by dividing large regions arrayed in the vertical direction of an image, performs encoding of image data of the large region, advancing the encoding order of small regions in the same order as a scan order, and advancing the encoding order of small region lines in an order different from the scan order; and a control unit that controls the encoding unit to encode in accordance with a state of a left small region situated at a left periphery of a small region to be processed, and a state of a lower small region situated at a lower periphery of the small region to be processed. The device suppresses deterioration in encoding efficiency due to high speed image encoding.

Abstract: An image processing device that encodes image data including: an encoding unit which, with a small region line including, arrayed in the horizontal direction, small regions obtained by dividing large regions arrayed in the vertical direction of an image, performs encoding of image data of the large region, advancing the encoding order of small regions in the same order as a scan order, and advancing the encoding order of small region lines in an order different from the scan order; and a control unit that controls the encoding unit to encode in accordance with a state of a left small region situated at a left periphery of a small region to be processed, and a state of a lower small region situated at a lower periphery of the small region to be processed. The device suppresses deterioration in encoding efficiency due to high speed image encoding.

Abstract: A reduction in the number of binarizations and/or contexts used in context adaptive binary arithmetic coding (CABAC) for video coding is proposed. In particular, this disclosure proposes techniques that may lower the number contexts used in CABAC by up to 56.

Abstract: A video decoder converts a block-based LSC indicator into a scan-based LSC indicator. The block-based LSC indicator indicates coordinates of a last significant coefficient of a block of transform coefficients according to a scanning order. The scan-based LSC indicator indicates an ordinal position of the LSC according to the scanning order. The video decoder may decode, based on the scan-based LSC indicator, a significance map for the block.

Abstract: A video encoder is configured to determine a first and second binary string for a value indicating the position of the last significant coefficient, within a video block of size T. A video decoder is configured to determine a value indicating the position of a last significant coefficient within a video block of size T based on a first and second binary string. In one example, the first binary string is based on a truncated unary coding scheme defined by a maximum bit length defined by 2 log2(T)?1 and the second binary string is based on a fixed length coding scheme defined by a maximum bit length defined by log2(T)?2.

Abstract: Techniques for generating synchronized dictionaries for sparse coding to facilitate coding of video content are presented. During a communication session, an encoder associated with a first terminal generates a dictionary that is synchronized with a corresponding dictionary maintained by a decoder associated with a second terminal. The decoder uses the dictionary to facilitate decoding video content, based on sparse coding, received from the encoder. During a subsequent communication session between the first terminal and a third terminal, the dictionary is made available to a decoder associated with the third terminal. The encoder associated with the first terminal and decoder associated with the third terminal signal each other to identify the dictionary as being common between the encoder and decoder, and this common dictionary is used for coding content communicated between the encoder and decoder. The encoder and decoder can update the dictionary based on the subsequent video session.

Abstract: A method and system are disclosed in which a signaling message conforming to a GMPLS signaling protocol and associated with an optical connection is generated and transmitted by a transmit node to a receive node to change the size of a connection bandwidth in a network. The message may include information indicative of a number of spectral portions which correspond to frequencies of selected ones of the plurality of optical signals, selected ones of the plurality of optical signals being available to carry data from the transmit node to the receive node; and information indicative of a change in the number of selected ones of the plurality of optical signals. The transmit node may resize the connection while data traffic continues to be transmitted over the connection in the Optical Transport Network without service disruption to the client attached to the connection being resized.

Abstract: A method of converting first data into second data includes: determining a target symbol corresponding to the first data by utilizing a determining unit; and generating the second data corresponding to the determined target symbol. One of the first data and the second data is a syntax element, and the other of the first data and the second data is an entropy-coded result of the syntax element. The target symbol corresponding to the first data is determined adaptively according to occurrence probability of candidate syntax element values of the syntax element.

Abstract: The present invention extends to methods, systems, and computer program products for iteratively calculating standard deviation for streamed data. Embodiments of the invention include iteratively calculating standard deviation in a current computation window based on the standard deviation calculation for a previous computation window. Iteratively calculating standard deviation avoids visiting all previous input and performing redundant computations thereby increasing calculation efficiency. In general, streaming data is added to a buffer of size n until the buffer is filled up. Once the buffer is filled, a sum and standard deviation are calculated for the first n data points. As new data elements are received, a new sum is calculated by reusing the prior sum and a new standard deviation is calculated by reusing the prior standard deviation.

Abstract: A method for decoding a video frame includes receiving a slice in a video decoder, identifying the slice as one of at least a first predicted slice and a second predicted slice, receiving information used to determine a context initialization method corresponding to the slice, and initializing, based on the received information, one of a first context initialization method and a second context initialization method associated with the slice, and decoding the video frame using the slice and one of the first context initialization method and the second context initialization method. The first context initialization method is a method for initializing a context associated with the first predicted slice and the second context initialization method is a method for initializing a context associated with the second predicted slice.

Abstract: An invention is disclosed for performing entropy encoding in a parallelized manner, using a GPU. In embodiments, an input sequence of integers is received, and run-length encoding is performed on any runs of zeros in parallel operations on the GPU. Then, a plurality of parallelized operations are performed on the run-length encoded sequence to entropy encode the sequence. The value N may be entropy encoded using only N and the value that precedes it in the sequence, N?1, so the encoding may be sub-divided into multiple operations that may be performed in parallel on the GPU. After entropy encoding is performed, a bitstream may be produced using parallelized operations on the GPU.

Abstract: The invention relates to an estimator for estimating a probability distribution of a quantization index generated from a source coder encoding a source signal, into a sequence of quantization indices, the source signal being described by a signal model, the source coder providing a current quantization index and current side information, the estimator being configured to obtain auxiliary parameters based on a configuration of the source coder and the current available side information and the signal model, the estimator being further configured to adaptively update the probability distribution of a quantization index upon the basis of a probability density function relating to a previous state of the estimator, the auxiliary parameters, the current quantization index and the current side information.

Abstract: A particular implementation receives geometry data of a 3D mesh, and represents the geometry data with an octree. The particular implementation partitions the octree into three parts, wherein the symbols corresponding to the middle part of the octree are hierarchical entropy encoded. To partition the octree into three parts, different thresholds are used. Depending on whether a symbol associated with a node is an S1 symbol, the child node of the node is included in the middle part or the upper part of the octree. In hierarchical entropy encoding, a non-S1 symbol is first encoded as a pre-determined symbol ‘X’ using symbol set S2={S1, ‘X’} and the non-S1 symbol itself is then encoded using symbol set S0 (S2?S0), and an S1 symbol is encoded using symbol set S2. Another implementation defines corresponding hierarchical entropy decoding. A further implementation reconstructs the octree and restores the geometry data of a 3D mesh from the octree representation.

Abstract: A check node processing unit updates an extrinsic value ratio based on a prior value ratio for each row of a parity check matrix with respect to input data. An identifying unit identifies, based on an element of the parity check matrix that can be identified by a row and column associated with the updated extrinsic value ratio, a next-target element in the same column and in a different row. The identifying unit identifies an element to be updated in the next step by the check node processing unit, from among multiple elements included in the same column. A variable node processing unit updates, based on the extrinsic value ratio, a prior value ratio associated with the identified next-target element after the check node processing unit completes the updating of each row. The check node processing unit and the variable node processing unit alternately and iteratively execute their operations.

Abstract: According to one embodiment, method for decoding encoded data comprises a hardware module including circuitry to process a data stream. The data stream includes one or more encoded symbols each including a code assigned to a corresponding symbol. A set of least frequently occurring symbols are assigned a common code to encode those symbols within the data stream. Data blocks are generated each containing a data stream portion. One or more encoded symbols within each data block are identified by comparing data block portions to maximum code values for corresponding code lengths to determine a code length for each data block portion. A starting location for the identified encoded symbols within each data block is determined based on the determined code lengths.

Abstract: An entropy decoder and method for decoding code words with an indication of associated probability for each code word. The decoder can be operable to receive code words and the indication of associated probability. A branch node block can be in communication with a leaf node block. The branch node block comprising one or more branch node lookup tables and branch node control logic. The branch node control logic operable to process a code word in the input buffer using a selected table from the one or more branch node lookup tables to obtain leaf node information and a bit count of a code word size, the branch control logic further operable to refresh the input buffer to replace the bit count of the code word size and to make the leaf node information and the table selection available to the leaf node block.

Abstract: Methods and devices for encoding and decoding that involve sorting bins according to their respective estimated probabilities to form subsequences, each subsequence having an associated estimated probability. Subsequences are encoded to form codewords. Ordered sets of phrases of known length are then formed from the codewords. Each first of the phrases in a set contains at least part of one codeword. The first phrase has an associated estimated probability and the probability estimates associated with each of the other phrases in the set are determined based upon the probability estimate associated with the first phrase, which permits the phrases to be decoded in parallel.

Abstract: An encoder for encoding a sequence of symbols is described which has an assigner configured to assign a number of parameters to each symbol of the sequence of symbols based on information contained within previous symbols of the sequence of symbols; a plurality of entropy encoders each of which is configured to convert the symbols forwarded to the respective entropy encoder into a respective bitstream; and a selector configured to forward each symbol to a selected one of the plurality of entropy encoders, the selection depending on the number of parameters assigned to the respective symbol.

Abstract: A system, method and computer program product having optimal matching to a known or measured probability distribution encodes data without the use of an excessively large lookup table. An encoder constructed according to the present invention uses two or more different encoding methods in combination. In one embodiment, Huffman coding by table lookup is combined with computational generation, such as by using an exponential Golomb equation. The most commonly occurring elements are looked up in a small Huffman table, while the remaining elements are coded with the equation. In another embodiment, data is encoded using two or more equations. In yet another embodiment, data is encoded using multiple tables in conjunction with one or more equations.

Abstract: A data predicted value generating unit generates a predicted value (data predicted value) for original data intended to be encoded, based on a history of original data which is floating-point data. A data predicted value modifying unit adjusts a mantissa value of the data predicted value by aligning an exponent value of the data predicted value with an exponent value of the original data. A first residual generating unit generates a residual (first residual) between new original data and the data predicted value after being adjusted. A first residual predicted value generating unit generates a predicted value for the first residual (first residual predicted value), based on a history of first residuals. A second residual generating unit generates a residual (second residual) between the first residual and the first residual predicted value. A residual encoding unit generates encoded data by encoding the second residual.

Abstract: An image coding apparatus provides a run-length encoding unit RLE1 that subjects quantized coefficients obtained by quantizing frequency components of an image signal to a variable length coding process by using a run value Run that indicates the number of successive zero coefficients and a level value Lev that indicates a value of a non-zero coefficient following the zero coefficients. The run-length encoding unit RLE1 includes a reordering unit Lreodr for reordering level values Lev; a variable length coder LVLC for coding reordered level values ROLev by using a code table selected according to the value of a quantization parameter QP; a reordering unit Rreodr for reordering run values Run from high frequency component of the quantized coefficients to low frequency component; and a variable length coder RVLC for coding reordered run values RORun by using a code table selected according to the number of already-processed run values.

Abstract: Embodiments relate to data compression using dictionary encoding. An aspect includes subdividing a table of uncompressed data into a first block and a second block of complete rows. Another aspect includes determining information about a frequency of occurrence of different values for each column of the first block. Another aspect includes selecting a row of the first block to be removed out of the first block using frequency of occurrence-information. Another aspect includes removing the a row out of the first block to form an updated first block and determining information about a frequency of occurrence of different values for each column of the updated first block. Another aspect includes deriving a dictionary containing code-words for encoding the values of the updated first block. Another aspect includes encoding the values of the updated first block based on the code-words. Another aspect includes adding the removed row to the second block.

Abstract: Data compression using a combination, of content independent data compression and content dependent data compression. In one aspect, a method for compressing data comprises: determining whether or not a parameter or attribute of data within a data block is identified for the data block wherein the determining is not based solely on a descriptor that is indicative of the parameter or attribute of the data within the data block; and compressing the data block with at least one encoder associated with the parameter or attribute of the data within the data block to provide a compressed data block.

Abstract: An encoder for encoding a sequence of symbols is described which includes an assigner configured to assign a number of parameters to each symbol of the sequence of symbols based on information contained within previous symbols of the sequence of symbols; a plurality of entropy encoders each of which is configured to convert the symbols forwarded to the respective entropy encoder into a respective bitstream; and a selector configured to forward each symbol to a selected one of the plurality of entropy encoders, the selection depending on the number of parameters assigned to the respective symbol.

Abstract: Method, apparatus, and systems employing novel delayed dictionary update schemes for dictionary-based high-bandwidth lossless compression. A pair of dictionaries having entries that are synchronized and encoded to support compression and decompression operations are implemented via logic at a compressor and decompressor. The compressor/decompressor logic operatives in a cooperative manner, including implementing the same dictionary update schemes, resulting in the data in the respective dictionaries being synchronized. The dictionaries are also configured with replaceable entries, and replacement policies are implemented based on matching bytes of data within sets of data being transferred over the link. Various schemes are disclosed for entry replacement, as well as a delayed dictionary update technique. The techniques support line-speed compression and decompression using parallel operations resulting in substantially no latency overhead.

Abstract: A digital information encoder including a divider configured to divide a block of information into a plurality of sub-parts, an initial bit allocator configured to perform an initial allocation of bits to a KTH sub-part of said plurality of sub-parts, a processor configured to compute an estimated number of bits for encoding said KTH sub-part, and a bit allocation adjuster configured to obtain an adjusted bit allocation for said KTH sub-part by adjusting said initial allocation of bits to said KTH sub-part based, at least in part, on said estimated number of bits, wherein the encoder encodes said KTH sub-part using said adjusted bit allocation for said KTH sub-part.

Abstract: A method for wireless communication is disclosed that includes selecting a plurality of probabilities for a symbol based on a bit-to-symbol mapping; calculating a conditional mean of the symbol based on the plurality of probabilities; and, generating a signal representative of the symbol based on the conditional mean of the symbol. An apparatus for performing the method is also disclosed.