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BCH Decoder - Decode BCH code to recover binary vector data

Library

Block sublibrary of Channel Coding

Description

The BCH Decoder block recovers a binary message vector from a binary BCH codeword vector. For proper decoding, the first two parameter values in this block should match the parameters in the corresponding BCH Encoder block.

This block supports punctures and erasures (Shortening, Puncturing, and Erasures provides a tutorial).

Note 1s and 0s have precisely opposite meanings for the puncture and erasure vectors. For a puncture vector, a 1 means that the data symbol is passed unaltered, and a 0 means that the data symbol is punctured (i.e., removed) from the data stream. For an erasure vector, a 1 means that the data symbol is to be replaced with an erasure symbol, and a 0 means that the data symbol is passed unaltered. These conventions are carried for both the encoder and the decoder.

The input must be a frame-based column vector with an integer multiple of (N - the number of punctures) elements. Each group of N input elements represents one codeword to be decoded. The values of (N + shortening length) and (K + shortening length) must produce a valid narrow-sense BCH code.

If the decoder is processing multiple codewords per frame, then the same puncture pattern holds for all codewords.

For a given codeword length N, only specific message lengths K are valid for a BCH code. For a full length BCH code, N must be of the form 2^M-1, where . If N is less than 2^M-1, the block assumes that the code has been shortened by length 2^{M -
1} - N. However, if N is greater than or equal to 2^M-1, Primitive polynomial must be specified to appropriately set the value of M.

No known analytic formula describes the relationship among the codeword length, message length, and error-correction capability. For a list of some valid values of K corresponding to values of N up to 511, see the bchenc reference page in the Communications Toolbox documentation.

The primitive and generator polynomials may be specified in their respective fields, which appear after selecting their corresponding check boxes.

To have the block output error information, select Output number of corrected errors. Selecting this option causes a second output port to appear. The second output is the number of errors detected during decoding of the codeword. A negative integer indicates that the block detected more errors than it could correct using the coding scheme.

In the case of a decoder failure, the message portion of the decoder input is returned unchanged as the decoder output.

The sample times of all input and output signals are equal.

This block supports double and boolean data types.

Dialog Box

Codeword length, N

The codeword length.

Message length, K

The message length.

Specify primitive polynomial

Selecting this check box enables the field Primitive polynomial.

Primitive polynomial

A row vector that represents the binary coefficients of the primitive polynomial in order of descending powers.

This field defaults to de2bi(primpoly(4, 'nodisplay'), 'left-msb'), corresponding to a (15,5) code.

This field appears only when you select Specify primitive polynomial.

Specify generator polynomial

Selecting this check box enables the field Generator polynomial.

Generator polynomial

A row vector that represents the binary coefficients of the generator polynomial in order of descending powers.

The length of the Generator polynomial must be N-K+1.

This field defaults to bchgenpoly(15,5).

This field appears only when you select Specify generator polynomial.

Disable generator polynomial checking

This check box appears only when you select Specify generator polynomial.

Each time a model initializes, the block performs a polynomial check. This check verifies that X ^N + 1 is divisible by the user-defined generator polynomial, where N represents the full code word length. Selecting this check box disables the polynomial check. For larger codes, disabling the check speeds up the simulation process. You should always run the check at least once before disabling this feature.

Puncture code

Selecting this check box enables the field Puncture vector.

Puncture vector

This field is available only when Puncture code is selected.

A column vector of length N-K. A value of 1 in the Puncture vector corresponds to a bit that is not punctured, and a 0 corresponds to a bit that is punctured.

The default value is [ones(8,1); zeros(2,1)].

Enable erasures input port

Selecting this check box will open the ports, Era and Err.

Through the Era port, you can input a frame-based binary column vector the same size as the codeword input. The number of errors corrected is output through the Err port.

Erasure values of 1 correspond to erased bits in the same position in the codeword, and values of 0 correspond to nonerased bits.

Output number of corrected errors

Selecting this check box gives the block an additional output port, which indicates the number of errors the block detected in the input codeword.

Pair Block

BCH Encoder

References

[1] Wicker, Stephen B., Error Control Systems for Digital Communication and Storage, Upper Saddle River, N.J., Prentice Hall, 1995.

[2] Berlekamp, Elwyn R., Algebraic Coding Theory, New York, McGraw-Hill, 1968.

[3] Clark, George C., Jr., and J. Bibb Cain, Error-Correction Coding for Digital Communications, New York, Plenum Press, 1981.