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Hamming iteration and interpretation method based on sum and product algorithm

An iterative decoding, Hamming code technology, applied in the direction of error correction/detection using linear codes, error correction/detection using block codes, data representation error detection/correction, etc., which can solve decoding complexity and performance tradeoffs, etc. question

Inactive Publication Date: 2004-12-29
王琳
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Problems solved by technology

[0011] The present invention is based on the understanding of the superior performance of the iterative decoding of the sum-product algorithm, and the purpose is to introduce the iterative decoding based on the sum-product algorithm into the Hamming code, effectively solving the problem of decoding complexity and performance compromise

Method used

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  • Hamming iteration and interpretation method based on sum and product algorithm
  • Hamming iteration and interpretation method based on sum and product algorithm
  • Hamming iteration and interpretation method based on sum and product algorithm

Examples

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Embodiment Construction

[0045] A concrete example of realizing the sum-product algorithm under the AWGN channel with the (7,4) Hamming code modulated by BPSK is given below.

[0046] 1. Encoding of (7,4) Hamming code.

[0047] Convert the parity check matrix H of the (7,4) Hamming code into a generator matrix G. Put the information source through the generating matrix G

[0048] put m i encode into c i .

[0049] 2. BPSK modulation

[0050] put c i (0 or) modulated to ±1 by BPSK, ie x i .

[0051] 3. Channel

[0052] Modulated baseband signal x i Through the AWGN channel, add Gaussian noise.

[0053] 4. Receive

[0054] received y i Thereafter, iterative decoding using the sum-product algorithm of the Hamming code is performed.

[0055] 5. Decoding steps

[0056] Given the bilateral graph of (7,4) Hamming code as Figure 5 , where f refers to the checkpoint and x refers to the variable point. Received codeword y i =x i +n i , where n i ~N(0,σ 2 ), satisfying a Gaussian distributi...

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Abstract

The invention relates to the field of communication system technology, in particular a Hamming code iterated interpretation method based on sum of products algorism, which can be applied to bluetooth systems, computer memory systems, mobile memory systems and DVD system, wherein iterated code translation based on sum of products algorism is introduced into Hamming code to solve the problem of code interpreting complexity and performance.

Description

technical field [0001] The invention belongs to the technical field of communication systems, and in particular relates to a Hamming code iterative decoding method based on a sum-product algorithm, which is applied to a bluetooth system, a computer storage system, a mobile storage system, a DVD system, and the like. Background technique [0002] In 1948, Shannon first proposed the famous channel coding theory in his groundbreaking paper "Mathematical Principles of Communication": For any communication channel with a channel capacity of C, if the transmission rate R required by the communication system is less than C, then there is A coding method, when the code length n is sufficiently large and maximum likelihood decoding is applied, the error rate of the system can be arbitrarily small. He applied three basic conditions in the theorem: [0003] 1) Use random coding; [0004] 2) The code length n→∞, that is, the code length tends to be infinite; [0005] 3) Decoding adop...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): H03M13/19
Inventor 王琳王丹徐位凯
Owner 王琳
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