The Reed-Solomon (RS) codes are block-based error correcting codes with a wide range of applications in digital communications and storage. This block adheres to the AMBA® AXI4-StreamAXI4-Stream standard.
They are used to correct errors in many systems such as digital storage devices, wireless or mobile communications, and digital video broadcasting.
The Reed-Solomon encoder augments data blocks with redundant symbols so that errors introduced during transmission can be corrected. Errors can occur for a number of reasons (noise or interference, scratches on a CD, etc.). The Reed-Solomon decoder attempts to correct errors and recover the original data. The number and type of errors that can be corrected depends on the characteristics of the code.
A typical system is shown below:
Reed-Solomon codes are Bose-Chaudhuri-Hocquenghem (BCH) codes, which in turn are linear block codes. An (n, k) linear block code is a k-dimensional sub space of an n-dimensional vector space over a finite field. Elements of the field are called symbols. For a Reed-Solomon code, n ordinarily is 2S -1, where s is the width in bits of each symbol. When the code is shortened, n is smaller. The encoder handles both full length and shortened codes.
The encoder is systematic. This means it constructs code blocks of length n from information blocks of length k by adjoining n-k parity symbols.
A Reed-Solomon code is characterized by its field and generator polynomials. The field polynomial is used to construct the symbol field, and the generator polynomial is used to calculate parity symbols. The encoder allows both polynomials to be configured. The generator polynomial has the form:g(x)=(x-αj)(x-αj+1...(x-αi+n-k-1)
α is a primitive element of the finite field having n +
Block Interface Channels and Pins
The Xilinx Reed-Solomon Decoder 8.0 block is AXI4 compliant. The following describes the standard AXI channels and pins on the interface:
- input Channel
- TVALID for the input channel.
- Presents blocks of
nsymbols to be decoded. This signal must have type
sis the width in bits of each symbol.
- Marks the last symbol of the input block. Only used to generate event outputs. Can be tied low or high if event outputs are not used.
- TREADY for the input channel.
- Marker bits for tagging data on
input_tdata_data_in. Added to the channel when you select Marker Bits from the Detailed Implementation tab.
- output Channel
- TREADY for the output channel. Added to the channel when you select Output TREADY from the Optional Pins tab.
- TVALID for the output channel.
- Produces the information and parity symbols
resulting from decoding. The type of
data_outis the same as that for
- Goes high when the last symbol of the last
block is on
output_tlastproduces a signal of type
- This pin is available when user selects "Marker Bits" from the Detailed Implementation tab.
- event Channel
- This output flag indicates that the
input_tlastwas not asserted when expected. You should leave this pin unconnected if it is not required.
- This output flag indicates that the
input_tlastwas asserted when not expected. You should leave this pin unconnected if it is not required.
- This output flag indicates that values provided
ctrl_tdatawere illegal. This pin is available when "Variable Block Length" or "Variable Number of Check Symbols" are selected on the GUI.
- ctrl Channel
- This channel is only present when variable block length or
number of check symbols is selected as a block parameter.
- TVALID for the ctrl channel.
- This signal is only present if
Length” is selected in the GUI. This
allows the block length to be changed every block. The
ctrl_tdata_n_insignal must have type UFIX_s_0, where s is the width in bits of each symbol. Unless there is an R_IN field, the number of check symbols is fixed, so varying n automatically varies k.
- This field is only present if
“Variable Number of Check
Symbols” is selected in the GUI. It
allows the number of check symbols to be changed every block.
The new block's length, r_block, is set to
ctrl_tdata_r_insignal must have type UFIX_p_0, where p is the number of bits required to represent the parity bits (n-k) in the default code word, n being the "Symbols Per Block" and k being "Data Symbols". Selecting this input significantly increases the size of the core.
Other Optional Pins
- Resets the encoder. This pin is added to the block when you
specify ARESETn on the
Detailed Implementation tab.
The signal driving
aresetn must be asserted low for at
least 2 clock periods and at least 1 sample period before the decoder can start
decoding code symbols.
- Carries the clock enable signal for the encoder. The signal
Bool. Added to the block when you select the optional pin ACLKEN.
The Block Parameters dialog box can be invoked by double-clicking the icon in your Simulink® model.
- Parameters specific to the
Attributes tab are as follows.
- Code Block Specification
- Code specification
- specifies the encoder type desired.
The choices are:
- Allows you to set all the block parameters.
- Implements DVB (Digital Video Broadcasting) standard (204, 188) shortened RS code.
- Implements ATSC (Advanced Television Systems Committee) standard (207, 187) shortened RS code
- Implements G.709 Optical Transport Network standard.
- Implements the ETSI Project standard for Broadband Radio Access Networks (BRAN).
- Implements CCSDS (Consultative Committee for Space Data Systems) standard (255, 223) full length RS code.
- Implements International Telecommunication Union(ITU)-J.83 Annex B specification (128, 122) extended RS code.
- IESS-308 (126)
- Implements IESS-308 (INTELSAT Earth Station Standard) specification (126, 112) shortened RS code.
- IESS-308 (194)
- Implements IESS-308 specification (194, 178) shortened RS code.
- IESS-308 (208)
- Implements IESS-308 specification (208, 192) shortened RS code.
- IESS-308 (219)
- Implements IESS-308 specification (219, 201) shortened RS code.
- IESS-308 (225)
- Implements IESS-308 specification (225, 205) shortened RS code.
- Variable Number of Check Symbols (r)
- False, true. When checked, the ctrl_tdata_r_in and ctrl_tdata_n_in pins become available on the block.
- Variable Block Length
- False, true. When checked, the ctrl_tdata_n_in pin becomes available on the block.
- Symbol width
- Tells the width in bits for symbols in the code. The encoder support widths from 3 to 12 and the default value is 8.
- Field polynomial
- specifies the polynomial from which
the symbol field is derived. It must be specified as
a decimal number. This polynomial must be primitive.
A value of zero indicates the default polynomial
should be used. Default polynomials are listed in
the table below.
Table 1. Field Polynomials Symbol Width Default Polynomials Array Representation 3 x3 + x + 1 11 4 x4 + x + 1 19 5 x5 + x2 + 1 37 6 x6 + x + 1 67 7 x7 + x3 + 1 137 8 x8 + x4 + x3 + x2 + 1 285 9 x9 + x4+ 1 529 10 x10 + x3 + 1 1033 11 x11 + x2 + 1 2053 12 x12 + x6 + x4 + x + 1 4179
- Scaling Factor (h)
- (represented in the previous
formula as h) specifies the scaling factor for the
code. Ordinarily, h is 1, but can be as large as
2S - 1 where s is the
symbol width. The value must be chosen so that
αh is primitive. That is, h must be relatively prime to 2S - 1.
- Generator Start
- Specifies the first root r of the
generator polynomial. The generator polynomial g(x),
is given by:
αis a primitive element of the symbol field, and the scaling factor is described below.
- Symbols Per Block(n)
- Tells the number of symbols in the blocks the encoder produces. Acceptable numbers range from 3 to 2S -1, where s denotes the symbol width.
- Data Symbols(k)
- Tells the number of information symbols each block contains. Acceptable values range from max(n - 256, 1) to n - 2.
- Detailed Implementation tab
- Check Symbol Generator Optimization
- This option is available when
"Variable Number of Check Symbols" option is
selected on the GUI.
- Fixed Architecture
- The check symbol generator is implemented using a highly efficient fixed architecture.
- The check symbol generator
implementation is optimized for area and speed
efficiency. The range of input,
ctrl_tdata_n_in, is reduced.
- The check symbol generator implementation is optimized to maximize the range of input of ctrl_tdata_n_in.
- Memory Style
- Select between Distributed, Block and Automatic memory choices. This option is available only for CCSDS codes.
- Number Of Channels
- Specifies the number of separate time division multiplexed channels to be processed by the encoder. The encoder supports up to 128 channels.
- Optional Pins
- Adds a aclken pin to the block. This signal
carries the clock enable and must be of type
- Output TREADY
- When selected, the output channels will have a TREADY and hence support the AXI4handshake protocol with inherent back-pressure.
- Adds a aresetn pin to the block. This signal
resets the block and must be of type
aresetnmust be asserted low for at least 2 clock periods and at least 1 sample period before the decoder can start decoding code symbols.
- Info bit
- Adds the output_tdata_info
pin. Marks the last information symbol of a block on
- Marker Bits
- Adds the following pins to the block:
- Carries marker bits for
tagging data on
mark_intagging bits delayed by the latency of the LogiCORE.
- Number of Marker Bits
- Specifies the number of marker bits.
Other parameters used by this block are explained in the topic Common Options in Block Parameter Dialog Boxes.
Reed-Solomon Encoder LogiCORE IP Product Guide (PG025)