Evaluating and optimizing error-correcting codes using projective analysis

An error-correcting code and optimization technology, applied in the field of error-correcting codes, can solve problems such as poor real performance

Inactive Publication Date: 2007-04-25
MITSUBISHI ELECTRIC CORP
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  • Description
  • Claims
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Problems solved by technology

However, it is known that the real performance of regular Gallager codes with finite block length is better than that obtained by such natural (na ve) method predicts considerably poorly

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  • Evaluating and optimizing error-correcting codes using projective analysis
  • Evaluating and optimizing error-correcting codes using projective analysis
  • Evaluating and optimizing error-correcting codes using projective analysis

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Embodiment Construction

[0110] The present invention evaluates the performance of error correcting codes (ECCs) that are decoded by a message passing decoding process where each message can be in a finite number of different discrete states. At each iteration of the decoding process, the method keeps track of the probability that each message sent by the decoding process is in any of its possible states. In contrast to prior art density evolution methods, the present method is accurate for any code represented by a parity check matrix, including bipartite graph representations containing cycles (loops).

[0111] In contrast to prior art density evolution methods which use real numbers to represent probabilities, the present method represents each probability of interest with a "projective polynomial". By projecting polynomials, we have x i to represent polynomials in the form of , where no term of the polynomial has an exponent of order greater than one.

[0112] Also, operations on projective poly...

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Abstract

A method evaluates and optimizes an error-correcting code to be transmitted through a noisy channel and to be decoded by an iterative message-passing decoder. The error-correcting code is represented by a parity check matrix which is modeled as a bipartite graph having variable nodes and check nodes. A set of message passing rules is provided for the decoder. The decoder is analyzed to obtain a set of density evolution rules including operators and operands which are then transformed to projective operators and projected operands to generate a set of projective message passing rules. The projective message passing rules are applied iteratively to the error-correcting code modeled by the bipartite graph until a termination condition is reached. Error rates of selected bits of the error-correcting code are then determined by evaluating the corresponding operands. The error rates can be passed to an optimizer to optimize the error-correcting code.

Description

technical field [0001] The present invention relates generally to the field of error correcting codes for data storage and data transmission, and more particularly to evaluating and optimizing error correcting codes. Background technique [0002] A fundamental problem in the field of data storage and communication is the evaluation of error-correcting codes (ECC). The general framework for the problem addressed by the present invention is shown in FIG. 1 . Source 110 intends to transmit to target 150 a block of k bits represented by vector u111. Source 110 adds redundant bits to the source symbols by passing them through encoder 120 . The output of the encoder is a block of N bits represented by vector x121. A block of N bits passes through the channel 130, experiencing noise 135, where the block may be doped with another block of N output symbols 131 represented by the vector y. The output of the channel is then decoded 140 into a received block represented by a k-bit v...

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): H03M13/00H03M13/39G06F11/10H03M13/01H03M13/09H03M13/11
CPCH03M13/01H03M13/1191H03M13/1102
Inventor J·S·耶迪达E·B·苏德斯J·-P·布朝德
Owner MITSUBISHI ELECTRIC CORP
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