2D PRODUCT CODE AND METHOD FOR DETECTING FALSE DECODING ERRORS

Priority is claimed to U.S. Provisional Application No. 61/255,271, filed 27 Oct. 2009.

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1. Technical Field of the Invention

The present invention discloses a two-dimensional (2D) product code for forward error correction (FEC) and a method for detecting false decoding errors in digital communication systems.

2. Background of the Invention

Long-distance digital communication systems, such as optical submarine cable systems, are responsible for the transmission of significant amounts of data. This data is transmitted across great distances, often from continent to continent. During transmission, data can become corrupted from noise within transmission channels, faults in transmission or receiving devices, or data errors from reading from and writing to an elastic store. Therefore, FEC is employed to minimize the error probability of transmitted data.

Claude Shannon first suggested a maximum possible channel throughput which developed into a theorem of error correction describing the addition of redundant data to payload data for the correction of errors from channel noise or interference during transmission. This FEC increases the reliability of transmitted data by encoding a block of payload data with redundant data bits through an algorithm generated at the transmitter, which allows a decoder to determine if an error has occurred. The decoder employs the code generated by the encoder to identify what information, if any, has been corrupted by noise or interference during transmission, and the decoder can in turn correct these errors.

As known in the art, FEC can be implemented as a product code. A product code may be two-dimensional (2D), where every bit within the transmission frame is subject to two separate, but intersecting, codes; one row code and one column code. A FEC codeword (n), or block of symbols, is comprised of data bits or information symbols (k) and parity bits or redundant symbols (r). Generally, any errors in long-distance data transmission are uniformly random. Such errors can be remedied by interleaving bits for transmission; therefore, errors are scattered across transmission frames so that de-interleaving the data shows random, individualized errors which are easy to detect and correct.

Presently, prior art teaches the use of cyclical redundancy check (CRC) codes to detect false errors. However, appending CRC parity to the data increases both the overhead and the redundancy of the system. Therefore, it is an object of the present invention to provide a method to detect and correct false errors without the use of CRC codes.

The present invention discloses a method and apparatus for performing forward error correction with a multi-dimensional product code, and a method for detecting false decoding errors in frame-based data transmission systems. The present invention discloses a 2D product code comprised of two Bose Ray-Chaudhuri Hocquenghem (BCH) codes. BCH codes are cyclic, error-correcting, digital codes of variable lengths which are able to correct errors in transmitted data. BCH codes typically employ a polynomial over a finite field, and a BCH codeword consists of a polynomial that is a multiple of the generator polynomial. Transmitted data is input into decoder which contains a syndrome to process each code and determine if any errors exist. The syndrome sends the data to a buffer and concurrently, through the use of a 2D BCH product code, sends the data through both a row decoder and a column decoder. Employing such iterative decoding allows the row decoder to correct any remaining errors not corrected by the column decoder, and/or allows the column decoder to correct any remaining errors not corrected by the row decoder. In addition, the row codes may correct all column code data and parity, and the column codes may correct all row code data and parity. Once the data has been fully decoded, or the row decoder and/or the column decoder have been stopped, the detected errors from the decoders and the data from the buffer are passed to the error correction element to correct data using the supplied error information.

Due to the limited amount of redundant information the decoder can sometimes detect errors incorrectly; in the present invention, such invalid errors are known as false errors. To maximize the efficiency of FEC, the present invention provides a method to detect such false errors. By ensuring that the BCH codewords are shortened from one or more substantially larger parent codewords(s), the presence of any errors detected beyond the parameters of the shortened codeword, i.e. within the set of data constants, signify that all detected errors are invalid; therefore the decoder is prevented from correcting such false errors.

The present invention discloses a 2D product code for FEC in high-speed data transmission systems. The present invention is comprised of two interleaved BCH codes, concatenated to provide a high-performance, efficient algorithm. FIG. 1 illustrates the conceptual view of the data matrix utilized by the present invention, as is known in the art; as shown, the frame comprises x row codes and y column codes. Each bit located within the frame, such as within bit location 1, is subject to both the x row code and the y column code.

As further illustrated by FIG. 1(a) the data matrix is comprised of row and column codewords; each codeword n contains k data bits and r parity bits. The 2D data matrix is constructed as a row encoder processes and encodes the k data bits, appending the r parity bits to the data rows. Likewise, a column encoder processes and encodes the k data bits, appending the r parity bits to the data columns. It should be noted that the encoding process can be performed with the rows encoded, followed by the columns encoded, or the encoding process can be performed with the columns encoded, followed by the rows encoded. As illustrated, a section of the data matrix exists where the row parity bits and the column parity bits intersect; here, the row encoder can compute the column parity and append the information into the parity intersection position, or, similarly, the column encoder can compute the row parity and append the information into the parity intersection position. Due to orthogonal mapping the parity value calculated over the row parity is equal to the parity value calculated over the column parity.

The error correction process is shown in FIG. 1(b), which illustrates the 2D product code as decoded using an iterative approach. Data is transmitted row by row to ensure the transmitted data is bit-wise interleaved when data is input (1) into decoder (8). As shown, the data is written into syndrome (2), which processes each code and determines whether or not an error exists in each code. The data is then transmitted from syndrome (2) to row decoder (3), which decodes the data and subsequently transmits the data to column decoder (4), which continues to decode the data. It should be noted that the decoding process can begin with either set of codes—row codes decoded, followed by column codes decoded, or with column codes decoded, followed by row codes decoded—provided that one group of codes follows the other group of codes. The data may be passed back and forth between row decoder (3) and column decoder (4) until all the data is decoded or a stop condition occurs. Once each of the codes has been fully decoded, or the row decoder (3) and/or the column decoder (4) have been stopped, the detected errors and the data from the buffer (6) are passed to the error correction element (5). The error correction element (5) corrects the data using the supplied error information and the data is subsequently transmitted out of the system (7).

The present invention operates with a large GF, such that m is large enough to ensure the maximum code length of the parent code (2m−1) is sufficiently larger than the shortened codeword length. For example, FIG. 4 illustrates a codeword operating on a GF with 0 to m elements. As shown, beyond the shortened codeword and parity bits, a series of data constants, i.e., a series of 0 values, are used to occupy the remaining elements within the 0 to m elements. For explanatory purposes the shortened codeword illustrated is subject to an m value large enough to cover 30% of the codeword and operates with a t=3 value, where t=the number of errors that can be corrected within a row code or a column code. It should be noted that this example is provided for illustrative purposes only and is not meant to limit the scope of the invention, as other m values and t values may be accommodated. As illustrated in FIG. 4, three errors are detected; while one of these errors is located within the range of the shortened codeword, two of the errors are located outside this range, thus the errors are determined to be false errors. As further illustrated in FIG. 5, where all three errors are located outside the shortened codeword range, they are similarly determined to be false errors. For legitimate errors to occur, all three errors must be located within the range of the shortened codeword, as illustrated in FIG. 6. By providing a large m value the present invention ensures the maximum parent code length of (2m−1) is sufficiently larger than the shortened codeword length; thus the decoders are able to detect and ignore false errors, thereby increasing the code's error correction and error detection capability.

An illustrative embodiment of the present invention, as illustrated in FIG. 2, employs a 2D product code comprising 1280 row codes and 1020 column codes. In the illustrative embodiment, the present invention employs a GF with m=12 and operates with the polynomial p(x)=x¹²+x⁶+x⁴+x+1. The row codes are implemented as BCH (1280, 1244) and the column codes are implemented as BCH (1020, 984). Both the row codes and the column codes are shortened from a BCH (4095, 4059) parent code. The illustrative embodiment operates with t=3, allowing for three errors to be corrected within each codeword. The BCH (1280, 1244) row codes and BCH (1020, 984) column codes are interleaved to produce the 2D product code, and the 2D product code is transmitted row by row as illustrated in FIG. 3, with the column codes bit-interleaved within. As illustrated in FIG. 7, the codeword elements range from 0 to 4095, as the GF operates with m=12, i.e., GF (2^m), which contains 4096 elements. As t=3, up to three errors may be corrected per codeword. The BCH (1280, 1244) row code covers approximately 30% of the codeword length and the decoder corrects the three legitimate errors found in this area. As illustrated in FIG. 8, if any errors are detected outside the codeword's shortened BCH (1280, 1244) length, all errors, both outside the range of the shortened codeword and inside the range of the shortened codeword are determined to be false errors. Where any errors are detected within the codeword but outside the range of the shortened codeword length, the errors are determined to be false errors, as the product code is only valid for the parameter of the shortened code length. In the present invention, an algorithm will detect any errors occurring outside the valid codeword parameter, but the decoder will recognize these errors as false errors, for legitimate errors cannot occur within the range of constant values, i.e., outside the range of the shortened codeword.