Abstract: A method is dedicated to encoding data that must be transmitted by means of a wave-based transmission infrastructure, and comprises i) a step consisting of creating in parallel M first matrices having T rows and C columns with subsets of data from B successive received bursts, the subsets of data from each burst being distributed within at least two successive first matrices, ii) a step consisting of creating in parallel M second matrices each having T rows and N columns with parity symbols resulting from encoding the data that is respectively contained in the rows of each of the M first matrices, iii) a step consisting of creating in parallel M first matrices having K rows and C columns with parity symbols resulting from encoding the data that is respectively contained in the columns of each of the M first matrices, and iv) a step consisting of distributing by interlacing, firstly, J subsets of parity symbols from each second matrix into J successive sets, and secondly P subsets of parity symbols from each t

Abstract: An arrangement of interleavers allocates bits from an input symbol across sub-symbols transmitted via sub-carriers of multiple orthogonal frequency division multiplex (OFDM) carriers. The input bits are allocated in a fashion to provide separation across subcarriers, and rotation of sub-symbols across the OFDM carriers provides additional robustness in the present of signal path impairments.

Abstract: A multistage difference cyclic permutation unit (106) for performing multistage cyclic permutation, an address administration unit (104) for administering addresses of the cumulative LLR memory (101), a received value arrangement unit (103) for generating records during writing of received values to the cumulative LLR memory (101), and a control unit (110) for generating parameters to control each unit from information of a parity check matrix and the current cyclic permutation size are prepared. The address administration unit (104) controls reading/writing addresses of the cumulative LLR memory (101) based on a reading start address from the cumulative LLR memory (101) corresponding to the column block. After the start of reading of a column block, the control unit (110) generates a reading start address in the next decoding of the column block and stores it into the address administration unit (104).

Abstract: Methods and corresponding systems in an interleaver include loading K symbol data, in a linear order, into a matrix memory having (R·C) storage locations corresponding R rows and C columns. A sequence of interleaved addresses is produced for reading the K symbol data in an interleaved order from the matrix memory. Next, (R·C)?K interleaved addresses are queued in a first-in-first-out (FIFO) memory. After queuing (R·C)?K interleaved addresses in the FIFO memory, symbol data is output using the interleaved addresses in the FIFO memory to address and output the symbol data in the matrix memory in the interleaved order. The FIFO memory can contain at least 234 memory locations.

Abstract: An interleaving method in a mobile communication system is provided. The interleaving method includes encoding a plurality of bits to output encoded bits in a sequence, interleaving the encoded bits based on a modulation order to generate interleaved encoded bits comprising consecutive bits having a size based on the modulation order, the consecutive bits corresponding to consecutive bits of the encoded bits, scrambling the interleaved encoded bits with a scrambling code to generate scrambled bits, and modulating the scrambled bits based on the modulation order to output at least one symbol.

Abstract: Devices and methods for processing wireless high definition video data to be communicated in an uncompressed format over a wireless medium is disclosed. In one embodiment, an encoder includes a first outer encoder that encodes a first portion of a video data stream. A second outer encoder encodes a second portion of the video data stream. A first parser parses the first encoded data stream into first sub-video data streams. A second parser parses the second encoded data stream into second sub-video data streams.

Abstract: A system for execution of a decoding method is disclosed. The system is capable of executing at least two data decoding methods which are different in underlying coding principle, wherein at least one of the data decoding methods requires data shuffling operations on the data. In one aspect, the system includes at least one application specific processor having an instruction set having arithmetic operators excluding multiplication, division and power. The processor is selected for execution of approximations of each of the at least two data decoding methods. The system also includes at least a first memory unit, e.g. background memory, for storing data. The system also includes a transfer unit for transferring data from the first memory unit towards the at least one programmable processor. The transfer unit includes a data shuffler. The system may also include a controller for controlling the data shuffler independent from the processor.

Abstract: A transmitter sends a series of transport bursts, each containing a data burst and possibly also repair data, indicated as distinct from data of the data bursts. Source blocks comprise data from more than one data burst and from those, repair symbols are generated.

Abstract: A method of controlling retransmission in a transmitter, the method provides transmitting a medium access control (MAC) management message to a receiver by hybrid automatic retransmit request (HARQ) and initiating retransmission of the MAC management message when an HARQ process is terminated with an unsuccessful transmission of the MAC management message before an expiration of a retransmission timer for the MAC management message.

Abstract: An interleaving method to which time-first-mapping is applied in a mobile communication system is provided. The interleaving method includes writing coded bits into an interleaver on a row-by-row basis, and reading the coded bits written in the interleaver on a column-by-column basis, wherein the coded bits are written by groups having a size according to a modulation order.

Abstract: A loss correction encoding device having an improved capability of loss correction using LDPC-CC is disclosed. In the loss correction encoding device (120), a rearranging unit (122) rearranges information data contained in n information packets according to the constraint length Kmax and the encoding rate (q?1)/q of a cheek polynomial of the loss correction code used in a loss correction encoding unit (123). Specifically, the rearranging unit (122) rearranges the information data in such a way that continuous Kmax×(q?1) pieces of information data after rearrangement are contained in different information packets. The rearranging unit (122) distributes the information data to information blocks from n information packets (n satisfies formula (1)). Kmax×(q?1)?n??(1).

Abstract: Handling burst error events with interleaved Reed-Solomon (RS) codes. A received signal, that has undergone convolutional interleaving sometime before, is received from a burst noise affected communication channel. The signal undergoes convolutional deinterleaving and the codewords generated there from undergo appropriate successive cyclic shifting to arrange burst noise affected symbols of various codewords into at least some common symbol locations. For example, at least two codewords have burst noise affected symbols in common symbol locations. An ensemble decoder jointly decodes multiple codewords during a same time period (i.e., processes multiple codewords simultaneously). By processing multiple codewords simultaneously, the ensemble decoder has greater error correction capability than a decoder that processes a single codeword at a time.

Abstract: A transmitter cyclic pattern having a pattern length of N bits is generated and converted into an M-bit transmitter parallel data stream, where N?M. A bit-sequence altered transmitter parallel data stream is generated by performing a transmitter altering process, converted into a serial data and transmitted together with a clock signal. The serial data is received and converted into an M-bit receiver parallel data stream, and a bit-sequence restored parallel data stream is generated by performing a process opposite to the transmitter altering process. A receiver cyclic pattern is generated by using bits in the bit-sequence restored parallel data stream and converted into an M-bit reference parallel data stream, and a bit-sequence altered reference parallel data stream is generated by performing a process same as the transmitter altering process and compared with the received parallel data to test if the data is correctly received.

Abstract: A communications device including a low-density parity check (LDPC) encoder and a transmitter. The LDPC encoder is configured to (i) receive data, and (ii) in response to the received data, generate encoded data using a predetermined LDPC matrix, in which the predetermined LDPC matrix is specified by a predetermined base matrix. The transmitter is configured to transmit the encoded data over a communications channel.

Abstract: In cable modem termination systems (CMTS) and other information transmission systems, a method for changing the interleave depth associated with each data stream is provided. This may be done dynamically, and for any subset of downstream devices such as modems. The interleave depth may be set on an individual device level. Embodiments may decrease data receiving latency on devices that do not suffer from error rates, such as caused by burst noise, while maintaining throughput on devices with high error rates.

Abstract: An interleaver that implements the LCS turbo interleaver algorithm utilized by the CDMA2000 standard is described. The interleaver includes a first computation unit for receiving an input address and computing a first sequential interleaved address during a first clock cycle in response thereto. A second computation unit is included for receiving an input address and computing a second sequential interleaved address during the first clock cycle in response thereto. The interleaver further includes a comparator for determining whether the first or the second sequential interleaved address is invalid and generating a signal in response thereto. The output of the comparator provides a control signal to a switch which selects the first or the second sequential interleaved address as an output interleaved address for the first clock cycle. The interleaver is further designed to move in a forward direction or a reverse direction.

Abstract: Disclosed herein is a receiving apparatus, including: a decoding section configured to receive and decode a low density parity check code; and a decoding control section configured to control a frequency of the decoding on the basis of conditional information that is an index indicative of a communication condition that influences power consumption in the decoding section.

Abstract: The present invention provides systems and methods for an efficient, parallel implementation of burst error correction codes, such as the Fire code. The present invention includes a FEC decoder which is pipelined to simultaneously perform syndrome computation, error trapping and syndrome normalization, and error correction. The pipelined implementation can apply to shortened and full-length codes. Advantageously, the present invention yields a design which is approximately 1/20th the size of conventional parallel approaches.

Abstract: The method allows to obtain, starting from an initial S-random interleaver permutation stored in memory devices and having a size N, a final S-random permutation having a smaller size K<N by successive pruning operations which yield the final permutation, through an iterative process which is performed by using electronic processing devices, and in which in successive steps selected elements are eliminated in accordance with predetermined criteria. The final permutation is generated using a reference vector having a dimension or size equal to that of the initial permutation. Said reference vector is generated by said processing devices in such a way that for each pruning step, if the element has been eliminated on the basis of a predetermined criterion, one element of the reference vector is generated in such a way that the value and the position thereof in the reference vector are indicative of the value of the element eliminated.

Abstract: A transmitting device encrypts DMR voice superframes using encryption parameters and sends the encryption parameters in at least one of the voice superframes by: identifying a selected number of bits from a plurality of vocoder frames the voice superframe; replacing each of the identified bits with a corresponding bit of a first encryption parameter; placing at least one encryption parameter in an embedded signaling field of the voice superframe; and transmitting the voice superframe with the encryption parameters to a receiving device. The receiving device extracts the encryption parameters, which can be a key identifier, an algorithm identifier, and an initialization vector for use in decrypting messages from the transmitting device.

Abstract: In a communications system that demultiplexes user data words into multiple sub-words for encoding and decoding within different subword-processing paths, the minimum distance between bit errors in an extrinsic codeword can be increased by having corresponding interleavers/deinterleavers in the different subword-processing paths use different interleaving/deinterleaving algorithms.

Abstract: A clock and data recovery device recovers data from a sequential stream of data that includes bursts of data separated by gaps. Each burst of data arrives with its own phase and with its own deviation from a nominal frequency. The bursts of data begin with a preamble that is utilized to determine the timing of the burst. The clock and data recovery device determines the timing of a burst of data using signals from one or more demultiplexers or samplers. At the start of each burst of data, sampled input signals are analyzed by an edge detector to determine a sample phase for the burst. A selector utilizes the sample phase determined by the edge detector to choose which of the sampled input signals to use to produce output data signals from the clock and data recovery device.

Abstract: A digital data recording/reproducing method includes the steps of: interleaving data on a PI code for each PI code of a 208-row ECC block; and converting a short burst error into random errors by dispersing errors on the PI codes. Moreover, the digital data recording/reproducing method increases correction capability against several bytes to several tens bytes of errors generated at random without changing burst error correction length by performing this processing for respective PI codes by using interleave rules that are different as much as possible from one another.

Abstract: Various embodiments include apparatus, methods, and systems that operate to extend the processes of reading, modifying, and writing data stored in or being provided to a memory array without interrupting a continual stream of data to be written into the memory array. Embodiments may include an apparatus comprising a memory array, and an error code module coupled to the memory array with a data buffer having a plurality of data burst registers operable to receive a plurality of data bursts to be written to the memory array on a corresponding plurality of consecutive clock cycles. The error code module is operable to perform a read/modify/write process on each of the plurality of data bursts within a time period no longer than a period of two consecutive cycles of the plurality of consecutive clock cycles.

Abstract: An arrangement of interleavers allocates bits from an input symbol across sub-symbols transmitted via sub-carriers of multiple orthogonal frequency division multiplex (OFDM) carriers. The input bits are allocated in a fashion to provide separation across subcarriers, and rotation of sub-symbols across the OFDM carriers provides additional robustness in the present of signal path impairments.

Abstract: The invention is directed to a method and apparatus for decoding encoded data symbols. The invention is also directed to corresponding encoding methods. The decoder arrangement comprises an input for receiving encoded data and an identifier associated with a coding scheme used to create said encoded data. A processor in the decoding arrangement determines from the identifier, a mapping between said encoded data and the original data. A decoder uses the mapping to extract the original data from the encoded data. The operation of the decoder is independent of the coding scheme used in the encoding process.

Abstract: A network communication device includes a host interface, which is coupled to communicate with a host processor, having a memory, so as to receive a work request to convey one or more data blocks over a network. The work request specifies a memory region of a given data size, and at least one data integrity field (DIF), having a given field size, is associated with the data blocks. Network interface circuitry is configured to execute an input/output (I/O) data transfer operation responsively to the work request so as to transfer to or from the memory a quantity of data that differs from the data size of the memory region by a multiple of the field size, while adding the at least one DIF to the transferred data or removing the at least one DIF from the transferred data.

Abstract: In an embodiment, a source device encodes source information corresponding to a frame, assembles an initial data frame that includes the encoded data blocks, and transmits the initial data frame to a destination device. The destination device decodes the encoded data blocks and assembles a restored version of the initial data frame. The destination device identifies corrupted data blocks and uncorrupted data blocks within the restored version, stores the uncorrupted data blocks, generates a message that identifies the corrupted data blocks, and transmits the message to the source device. In response, the source device encodes source information corresponding to the corrupted data blocks identified in the message, assembles a responsive data frame, and transmits the responsive data frame to the destination device. The destination device produces a corrected data frame from the retransmitted data blocks and the previously-stored uncorrupted data blocks.

Abstract: An apparatus and method for transmitting and receiving symbols in a mobile communication system, in which a multiplexer and burst mapper divides each of first and second group data blocks into a plurality of sub-blocks, the symbols including the first group data block and the second group data block, the second group data block having a different priority level from the first group data block, and maps a combination of one of the first group data sub-blocks and one of the second group data sub-blocks to each burst. A modulator maps a bit of the first group data sub-block and a bit of the second group data sub-block to a symbol according to a bit reliability pattern of modulation symbols in each burst.

Abstract: An error correction code includes a separate error code portion for each of two or more separate burst erasure durations (or burst error durations). For each burst erasure duration, the code can be employed to recover from the burst erasure with a different delay time. Each error code portion has a particular parameter for burst duration (B) and delay (T), meaning that the code can be used to recover from a burst erasure of duration B with delay T. Each error code portion is based on separating the source symbols into sub-symbols and diagonally interleaving the sub-symbols based on the (B,T) parameters for the error code portion. Accordingly, different burst erasures are recovered from with different delays.

Abstract: A method, a device, and an apparatus for correcting bursts are disclosed. The method includes: calculating a correction vector according to a received codeword and a check matrix, wherein the check matrix is an Overlapped Quasi Dual Diagonal Matrix; determining a length and position of a burst according to a longest zero element vector between two nonzero elements in the correction vector when the correction vector is nonzero; and calculating out an error mode according to the correction vector and the length of the burst, obtaining an error mode polynomial according to the error mode, correcting the received codeword according to the error mode polynomial, and obtaining a corrected codeword polynomial. The PBC-based implementation method for cyclic codes herein can correct more burst errors than the conventional cyclic code decoding method.

Abstract: An apparatus and method of an outer Forward Error Correcting (FEC) code for a mobile broadcast service based on TD-SCDMA network is disclosed.

Abstract: A decoding apparatus for a high-density recording medium includes a demodulator, a long-distance code (LDC) processing module, a burst indicator subcode (BIS) processing module, an erasure code generator, and a decoder. The demodulator demodulates data from a high-density recording medium to obtain a demodulated data and a demodulation error flag. The LDC processing module and the BIS processing module deinterleave the demodulated data to respectively obtain an LDC data and a BIS data. The erasure code generator sets an erasure flag corresponding to the LDC data according to the demodulation error flag and the BIS error flag. The decoder decodes the LDC data according to the erasure flag. Further, the decoder decodes the BIS data to obtain the BIS error flag.

Abstract: The present invention is a device for detecting short burst errors. The device includes a first signal input, wherein the first signal input is configured to receive a first signal. The device includes a second signal input, wherein the second signal input is configured to receive a second signal. The device includes a logic gate, wherein the logic gate is operable for receiving the first signal via the first signal input, receiving the second signal via the second signal input, and generating a logic output gate signal based on the received first signal and the second signal. Furthermore, the device includes a filter, wherein the filter is configured for receiving the logic output gate signal from the logic gate and generates a filter output signal based upon the received logic output gate signal, wherein the filter output signal is operable for flagging errors.

Abstract: A receiving system and a data processing method are disclosed. The receiving system includes a signal receiving unit, an FIC handler, a manager, and a decoding unit. The signal receiving unit receives multiple Reed-Solomon (RS) frames comprising desired mobile service data for multiple ensembles and fast information channel (FIC) data including an indicator field, wherein the indicator field indicates whether or not the desired mobile service data are delivered through the multiple ensembles. The FIC handler obtains the indicator field from the FIC data. The manager determines at least one ensemble based upon the indicator field. And, the decoding unit decodes IP streams of the desired mobile service data from the RS frame of the determined ensemble.

Abstract: Handling burst error events with interleaved Reed-Solomon (RS) codes. A received signal, that has undergone convolutional interleaving sometime before, is received from a burst noise affected communication channel. The signal undergoes convolutional deinterleaving and the codewords generated there from undergo appropriate successive cyclic shifting to arrange burst noise affected symbols of various codewords into at least some common symbol locations. For example, at least two codewords have burst noise affected symbols in common symbol locations. An ensemble decoder jointly decodes multiple codewords during a same time period (i.e., processes multiple codewords simultaneously). By processing multiple codewords simultaneously, the ensemble decoder has greater error correction capability than a decoder that processes a single codeword at a time.

Abstract: A system and method for detecting burst noise during quadrature amplitude modulation (QAM) communications are provided. A QAM signal is acquired at a receiver in communication with a network. The QAM signal is demodulated at the receiver to identify a plurality of symbols. Amplitudes for each of the plurality of symbols are determined, and are compared to a predetermined threshold. For each amplitude that is greater than the predetermined threshold, information is recorded at the receiver relating to a burst noise event. The magnitude of the burst noise can be determined by measuring a difference between a received constellation point and a perimeter constellation point closest to the received constellation point. The information about the burst noise event can be transmitted to an error correction module for reducing future burst noise in the network. Equalizer coefficients and tracking loop performance can be adjusted/enhanced using the burst noise information.

Abstract: A cascade encoding method and apparatus are applied to a handheld television system or other fields. The method includes the following: A. Reed-Solomon (RS) encoding is performed on inputted Medium Access Control (MAC) packets, and coded MAC packets are outputted; and B. Low density parity check code (LDPC) encoding is performed on the coded MAC packets, and LDPC encoding blocks are outputted. The apparatus includes an RS coder and an LDPC coder. The RS encoding and LDPC encoding are cascaded to encode an inputted code flow, so as to reduce an error rate. Meanwhile, bytes in one RS encoding data block are dispersed into different LDPC blocks to be encoded through byte interleaving, thereby sufficiently utilizing error code characteristics of the RS encoding and the LDPC encoding for decoding, and improving error correction capability of a system.

Abstract: A storage subsystem monitors one or more conditions related to the probability of a data error occurring. Based on the monitored condition or conditions, the storage subsystem adjusts an error correction setting, and thus the quantity of ECC data used to protect data received from a host system. To enable blocks of data to be properly checked when read from memory, the storage subsystem stores ECC metadata indicating the particular error correction setting used to store particular blocks of data. The storage subsystem may be in the form of a solid-state non-volatile memory card or drive that attaches to the host system.

Abstract: In cable modem termination systems (CMTS) and other information transmission systems, a method for changing the interleave depth associated with each data stream is provided. This may be done dynamically, and for any subset of downstream devices such as modems. The interleave depth may be set on an individual device level. Embodiments may decrease data receiving latency on devices that do not suffer from error rates, such as caused by burst noise, while maintaining throughput on devices with high error rates.

Abstract: A digital communication device is provided for decoding a data stream to generate a receiver output. In the digital communication device, a burst error detector determines burst noise locations corresponding to the data stream according to an error-check equation and accordingly generates a burst error indicator. Thereafter, an inner decoder decodes the data stream to generate an inner decoded stream, comprising an erasure marker for performing an erasure marking process on the inner decoded stream based on the burst error indicator to generate an erasure indicator corresponding to the inner decoded stream. An outer decoder then decodes the inner decoded stream with reference to the erasure indicator to generate the receiver output.

Abstract: A multiple-input multiple-output (MIMO) transmitter including a scrambler and a forward error correction encoder. The scrambler is configured to receive user data and generate scrambled data in response to the user data. The forward error correction encoder is configured to generate encoded data, in response to the scrambled data, using a low density parity check (LDPC) matrix, wherein the LDPC matrix is derived from a specified base matrix.

Abstract: An assignment scheme exploits the Media Access Control (MAC) layer protocol features under various MAC layer call scenarios. In one embodiment, the Hamming distance between pairs of critical Data Units are assigned to codewords with a minimum distance of dmin2=8 bits, thereby increasing the hard decision error correcting capability from 1 bit to 3 bits when deciding between these pairs of Data Units. The method for assigning data unit identification (DUID) codes by a radio operating within a wireless communication system includes determining by the radio whether an expected burst is a 4 Voice Burst with Encryption Synchronization Signaling (4V); when the expected burst is 4V, decoding the DUID within the received burst using an increased minimum distance; and when the expected burst is not 4V, decoding the DUID within the received burst using a minimum distance.

Abstract: In an information processing device, error detection information is generated from additional information and a header is generated from error detection information. An encoded header is then generated by appending a header-error correction code to the header and encoded additional information is generated by appending an information-error correction code to the additional information. Finally, an information-appended image is generated by integratedly appending the encoded header and the encoded additional information to the target image.

Abstract: A digital broadcasting system and a method for controlling the same are disclosed. A method for controlling a digital broadcast receiving system includes the steps of receiving a broadcast signal having mobile service data and main service data multiplexed therein, extracting transmission parameter channel (TPC) signaling information and fast information channel (FIC) signaling information from a data group within the received mobile service data, by using the extracted fast information channel (FIC) signaling information, acquiring a program table describing virtual channel information and service of an ensemble, the ensemble being a virtual channel group of the received mobile service data, by using the acquired program table, detecting a descriptor defining basic information required for accessing the received service, and, by using the detected descriptor, controlling the receiving system to enable access to the corresponding service.

Abstract: A method of recovering data in a line signal which is predicted to be subjected to repetitive noise impulses, the line signal comprising a series of data frames, the method comprising the steps of: predicting a group comprising one or more frames in said line signal which are expected to be corrupted by a noise signal; blanking said group of one or more frames which are predicted to be corrupted; determining the preceding and succeeding frames adjacent to said group; and including in each said group of one or more frames one or more parity blocks wherein if said noise signal deviates from its predicted timing interval or duration and corrupts the data carried in one or more of said frames adjacent to said group, the corrupted data is recovered using one or more of said parity blocks of said group of blanked frames and the other one of said adjacent frames.

Abstract: An interleaving method to which time-first-mapping is applied for a plurality of channel-coded and rate-matched code blocks in a mobile communication system is provided. The interleaving method includes determining sizes of a horizontal area and a vertical area of an interleaver, generating modulation groups with adjacent coded bits in a vertical direction according to a modulation scheme, sequentially writing the modulation groups in the horizontal area on a row-by-row basis, and sequentially reading the coded bits written in the interleaver in the vertical area on a column-by-column basis.

Abstract: The present invention is a device for detecting short burst errors. The device includes a first signal input, wherein the first signal input is configured to receive a first signal. The device includes a second signal input, wherein the second signal input is configured to receive a second signal. The device includes a logic gate, wherein the logic gat is operable for receiving the first signal vial the first signal input, receiving the second signal via the second signal input, and generating a logic output gate signal based on the received first signal and the second signal. Furthermore, the device includes a filter, wherein the filter is configured for receiving the logic output gate signal from the logic gate and generates a filter output signal based upon the received logic output gate signal, wherein the filter output signal is operable for flagging errors.

Abstract: An error correction coding device includes a time divider for dividing field data of L packets into N data packets and (L-N) parity packets, a first RS (Reed-Solomon) encoder adding parities of a predetermined number of bytes to the data packets, respectively, a storage unit for storing the data packets, and a second RS encoder generating parity packets corresponding to the stored data packets. An error correction decoding device includes a first RS decoder correcting errors in a horizontal direction of the field data using parities of the predetermined number of bytes included in the L packets, a storage unit storing the error-corrected data packets, and a second RS decoder correcting errors in a vertical direction of the field data using the parity packets. Thus, the error correction can be strongly performed using parities existing in the horizontal and vertical directions with respect to the field data.

Abstract: An error correction coding device includes a time divider for dividing field data of L packets into N data packets and (L-N) parity packets, a first RS (Reed-Solomon) encoder adding parities of a predetermined number of bytes to the data packets, respectively, a storage unit for storing the data packets, and a second RS encoder generating parity packets corresponding to the stored data packets. An error correction decoding device includes a first RS decoder correcting errors in a horizontal direction of the field data using parities of the predetermined number of bytes included in the L packets, a storage unit storing the error-corrected data packets, and a second RS decoder correcting errors in a vertical direction of the field data using the parity packets. Thus, the error correction can be strongly performed using parities existing in the horizontal and vertical directions with respect to the field data.