Reed-Solomon Encoder 9.0 - 2020.2 English

This block is listed in the following Xilinx® Blockset libraries: AXI4, Communications, and Index.

Note: This block goes into the FPGA fabric and is a Licensed Core. Please visit the Xilinx web site to purchase the appropriate core license.

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:

Figure 1. Typical System

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 2^S -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.

Figure 2. Systematic Encoder

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-α^j)(x-α^j+1...(x-α^i+n-k-1)

where α is a primitive element of the finite field having n + 1 elements.

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

input_tvalid: TVALID for the input channel.
input_tdata_data_in: Presents blocks of n symbols to be decoded. This signal must have type UFIX_s_0, where s is the width in bits of each symbol.
input_tlast: 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.
input_tready: TREADY for the input channel.
input_tuser_marker: 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

output_tready: TREADY for the output channel. Added to the channel when you select Output TREADY from the Optional Pins tab.
output_tvalid: TVALID for the output channel.
output_tdata_data_out: Produces the information and parity symbols resulting from decoding. The type of data_out is the same as that for data_in.
output_tlast: Goes high when the last symbol of the last block is on tdata_data_out. output_tlast produces a signal of type UFIX_1_0.
output_tuser_maker: This pin is available when user selects "Marker Bits" from the Detailed Implementation tab.

event Channel

event_s_input_tlast_missing: This output flag indicates that the input_tlast was not asserted when expected. You should leave this pin unconnected if it is not required.
event_s_input_tlast_unexpected: This output flag indicates that the input_tlast was asserted when not expected. You should leave this pin unconnected if it is not required.
event_s_ctrl_tdata_invalid: This output flag indicates that values provided on ctrl_tdata were 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.

ctrl_tvalid: TVALID for the ctrl channel.
ctrl_tdata_n_in: This signal is only present if “Variable Block Length” is selected in the GUI. This allows the block length to be changed every block. The ctrl_tdata_n_in signal 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.
ctrl_tdata_r_in: 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_in sampled. The ctrl_tdata_r_in signal 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

aresetn: 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 Bool.

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.

aclken: Carries the clock enable signal for the encoder. The signal driving aclken must be Bool. Added to the block when you select the optional pin ACLKEN.

Block Parameters

The block parameters dialog box can be invoked by double-clicking the icon in your Simulink® model.

Attributes

Parameters specific to the Attributes tab are as follows.

Code Block Specification

Code specification

specifies the encoder type desired. The choices are:

Custom: Allows you to set all the block parameters.
DVB: Implements DVB (Digital Video Broadcasting) standard (204, 188) shortened RS code.
ATSC: Implements ATSC (Advanced Television Systems Committee) standard (207, 187) shortened RS code
G_709: Implements G.709 Optical Transport Network standard.
ETSI_BRAN: Implements the ETSI Project standard for Broadband Radio Access Networks (BRAN).
CCSDS: Implements CCSDS (Consultative Committee for Space Data Systems) standard (255, 223) full length RS code.
ITU_J_83_Annex_B: 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 2^S - 1 where s is the symbol width. The value must be chosen so that α ^h is primitive. That is, h must be relatively prime to 2^S - 1.

Generator Start

Specifies the first root r of the generator polynomial. The generator polynomial g(x), is given by:

where α is 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 2^S -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

Implementation

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.
Area: The check symbol generator implementation is optimized for area and speed efficiency. The range of input, ctrl_tdata_n_in, is reduced.
Flexibility: 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

ACLKEN

Adds a aclken pin to the block. This signal carries the clock enable and must be of type Bool.

Output TREADY

When selected, the output channels will have a TREADY and hence support the AXI4handshake protocol with inherent back-pressure.

ARESETn

Adds a aresetn pin to the block. This signal resets the block and must be of type Bool. 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.

Info bit

Adds the output_tdata_info pin. Marks the last information symbol of a block on tdata_data_out.

Marker Bits

Adds the following pins to the block:

input_tuser_user: Carries marker bits for tagging data on input_tdata_ data_in.
output_tuser_user: mark_in tagging 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.

LogiCORE™ Documentation

LogiCORE IP Reed-Solomon Encoder v9.0