Documentation 
The BinaryOutput RS Decoder block recovers a binary message vector from a binary ReedSolomon codeword vector. For proper decoding, the parameter values in this block should match those in the corresponding BinaryInput RS Encoder block.
The ReedSolomon code has message length, K, and codeword length, (N  number of punctures). You specify both N and K directly in the dialog box. The symbols for the code are binary sequences of length M, corresponding to elements of the Galois field GF(2^{M}), where the first bit in each sequence is the most significant bit. Restrictions on M and N are described in Restrictions on the M and the Codeword Length N.
This block can output shortened codewords when N and K are appropriately specified. To specify output codewords that are shortened by a length S, N and K must be specified in the dialog box as N_{full} – S and K_{full} – S, where N_{full} and K_{full} are the N and K of an unshortened code. If $$\text{S}<({\text{N}}_{\text{full}}+1)/2$$, the encoder can automatically determine the value of N_{full} and K_{full}. However, if $$\text{S}\ge ({\text{N}}_{\text{full}}+1)/2$$, Primitive polynomial must be specified in order to properly define the extension field for the code.
The input and output are binaryvalued signals that represent codewords and messages, respectively. This block accepts a column vector input signal with a length that is an integer multiple of M * (N  number of punctures). This block outputs a column vector with a length that is the same integer multiple of M*K. The output signal inherits its data type from the input signal. For information about the data types each block port supports, see the Supported Data Type table on this page.
For more information on representing data for ReedSolomon codes, see Integer Format (ReedSolomon Only) in Communications System Toolbox™ User's Guide.
If the decoder is processing multiple codewords per frame, then the same puncture pattern holds for all codewords.
The default value of M is ceil(log2(N+1)), that is, the smallest integer greater than or equal to log2(N+1). You can change the value of M from the default by specifying the primitive polynomial for GF(2^{M}), as described in Specifying the Primitive Polynomial below. If N is less than 2^{M}1, the block uses a shortened ReedSolomon code.
You can also specify the generator polynomial for the ReedSolomon code, as described in Specifying the Generator Polynomial.
Each M*K input bits represent K integers between 0 and 2^{M}1. Similarly, each M*(N  number of punctures) output bits represent N integers between 0 and 2^{M}1. These integers in turn represent elements of the Galois field GF(2^{M}).
The second output is a vector of the number of errors detected during decoding of the codeword. A 1 indicates that the block detected more errors than it could correct using the coding scheme. An (N,K) ReedSolomon code can correct up to floor((NK)/2) symbol errors (not bit errors) in each codeword.
You can disable the second output by deselecting Output port for number of corrected errors. This removes the block's second output port.
This block supports puncturing when you select the Punctured code parameter. This selection enables the Puncture vector parameter, which takes in a binary vector to specify the puncturing pattern. For a puncture vector, 1 represents that the data symbol passes unaltered, and 0 represents that the data symbol gets punctured, or removed, from the data stream. This convention is carried for both the encoder and the decoder. For more information, see Shortening, Puncturing, and Erasures.
The codeword length. The input has vector length NC*M*(N  NP), where NC is the number of codewords being output, and NP is the number of punctures per codeword.
The message length. The first output has vector length NM*M*K, where NM is the number of messages per frame being output.
Selecting this check box enables the Primitive polynomial field.
Binary row vector representing the primitive polynomial in descending order of powers. When you provide a Primitive polynomial, the number of input bits must be an integer multiple of K times the order of the Primitive polynomial instead.
This parameter applies only when you select Specify primitive polynomial.
Selecting this check box enables the Generator polynomial field.
Integer row vector, whose entries are in the range from 0 to 2^{M}1, representing the generator polynomial in descending order of powers. Each coefficient is an element of the Galois field defined by the primitive polynomial.
This parameter applies only when you select Specify generator polynomial.
Selecting this check box enables the Puncture vector field.
A column vector of length NK. For a puncture vector, 1 represents an Mbit symbol that passes unaltered, and 0 represents an Mbit symbol that gets punctured, or removed, from the data stream.
The default value is [ones(2,1); zeros(2,1)].
This parameter applies only when you select Punctured code.
Select this check to open the erasures port, Era.
Through the port, you can input a binary column vector that is 1/M times as long as the codeword input.
Erasure values of 1 correspond to erased symbols in the same position in the bitpacked codeword, and values of 0 correspond to nonerased symbols.
When you select this box, the block outputs the number of corrected errors in each word through a second output port. A decoding failure occurs when a certain received word in the input contains more than (NK)/2 symbol errors. The value 1 indicates the corresponding position in the second output vector.
The output type of the block can be specified as Same as input, boolean, or double. By default, the block sets this to Same as input.
Port  Supported Data Types 

In 

Out 

Era 

Err 

This block uses the BerlekampMassey decoding algorithm. For information about this algorithm, see the references listed below.
[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, McGrawHill, 1968.
[3] Clark, George C., Jr., and J. Bibb Cain, ErrorCorrection Coding for Digital Communications, New York, Plenum Press, 1981.