Reed-Solomon Decoder 9.0 - 2020.2 English

This block is listed in the following Xilinx® Blockset libraries: AXI4, Communication, 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.

They are used to correct errors in many systems such as digital storage devices, wireless/ mobile communications, and digital video broadcasting.

The Reed-Solomon decoder processes blocks generated by a Reed-Solomon encoder, attempting to correct errors, and recover information symbols. The number and type of errors that can be corrected depend on the characteristics of the code.

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 decoder handles both full length and shortened codes. It is also able to handle erasures, that is, symbols that are known with high probability to contain errors.

When the decoder processes a block, there are three possibilities:

The information symbols are recovered. This is the case provided 2p+r <= n-k, where p is the number of errors, and r is the number of erasures.
The decoder reports it is unable to recover the information symbols.
The decoder fails to recover the information symbols but does not report an error.

The probability of each possibility depends on the code and the nature of the communications channel. Simulink® provides excellent tools for modeling channels and estimating these probabilities.

Block Interface Channels and Pins

This Xilinx Reed-Solomon Decoder 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_erase: Added to the channel when you select Erase on the Optional Pins tab. It indicates the symbol currently presented on data_in should be treated as an erasure. The signal driving this pin must be Bool.
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_mark_in: marker bits for tagging data on data_in. Added to the channel when you select Marker Bits from the Optional Pins tab.

output Channel

output_tready: TREADY for the output channel.
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_mark_out: mark_in tagging bits delayed by the latency of the LogiCORE™ . Added to the channel when you select Marker Bits on the Optional Pins tab.
output_tdata_info: Added to the channel when you select Info on the Optional Pins tab. The signal marks the last information symbol of a block on tdata_data_out.
output_tdata_data_del: Added to the channel when you select Original Delayed Data on the Optional Pins tab. The signal marks the last information symbol of a block on tdata_data_out.

stat Channel

stat_tready: TREADY for the stat channel.
stat_tvalid: TVALID for the stat channel. You should tie this signal high if the downstream slave is always able to accept data or if the stat channel is not used.
stat_tdata_err_cnt: Presents a value at the time data_out presents the last symbol of the block. The value is the number of errors that were corrected. err_cnt must have type UFIX_b_0 where b is the number of bits needed to represent n-k.
stat_tdata_err_found: presents a value at the time output_tdata_data_out presents the last symbol of the block. The value 1 if the decoder detected any errors or erasures during decoding. err_found must have type UFIX_1_0.
stat_tdata_fail: Presents a value at the time output_tdata_data_out presents the last symbol of the block. The value is 1 if the decoder was unable to recover the information symbols, and 0 otherwise. This signal must be of type UFIX_1_0.
stat_tdata_erase_cnt: Only available when erasure decoding is enabled. Presents a value at the time dout presents the last symbol of the block. The value is the number of erasures that were corrected This signal must be of type UFIX_b_0 where b is the number of bits needed to represent n. Added to the channel when you select Erase from the Optional Pins tab.
stat_tdata_bit_err_1_to_0: Number of bits received as 1 but corrected to 0. Added to the channel when you select Error Statistics from the Optional Pins tab. The element width is the number of binary bits required to represent ((n-k) * Symbol_Width).
stat_tdata_bit_err_0_to_1: Number of bits received as 0 but corrected to 1. Added to the channel when you select Error Statistics from the Optional Pins tab. The element width is the number of binary bits required to represent ((n-k) * Symbol_Width).
stat_tlast: Added when Number of Channels parameter is greater than 1. Indicates that status information for the last channel is present on output_tdata.

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. The block must be reset if this is asserted.You should leave this pin unconnected if it is not required.

ctrl Channel

This channel is only present when variable block length, number of check symbols or puncture is selected as a block parameter.

ctrl_tready: TREADY for the ctrl channel.
ctrl_tvalid_r_in: TVALID for the ctrl channel.
ctrl_tdata: This input contains the block length, the number of check symbols and puncture select, if applicable.

Other Optional Pins

aresetn

Resets the decoder. This pin is added to the block when you specify Synchronous Reset on the Optional Pins tab. The signal driving rst must be Bool.

aresetn must be asserted high for at least 1 sample period before the decoder can start decoding code symbols.

aclken

Carries the clock enable signal for the decoder. The signal driving aclken must be Bool. Added to the block when you select the optional pin Clock Enable.

Block Parameters

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

Attributes 1 tab

Parameters specific to the Attributes 1 tab are as follows.

Code Block Specification

Code specification

Specifies the type of RS Decoder desired. The choices are as follows.

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.

CCSDS

Implements CCSDS (Consultative Committee for Space Data Systems) standard (255, 223) full length RS code.

IESS-308 (All)

Implements IESS-308 (INTELSAT Earth Station Standard) specification (all) shortened 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.

IEEE-802.16

Implements IEEE-802.16 specification (255, 239) full length RS code.

Symbol width

Tells the width in bits for symbols in the code. The encoder support widths from 3 to 12 (default 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.

Variable Block Length: When checked, the block is given a ctrl input channel.
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.

Variable Check Symbol Options

Variable Number of Check Symbols (r)
Define Supported R_IN Values: If only a subset of the possible values that could be sampled on R_IN is actually required, then it is possible to reduce the size of the core slightly. For example, for the Intelsat standard, the R_IN input is 5 bits wide but only requires r values of 14, 16, 18, and 20. The core size can be slightly reduced by defining only these four values to be supported. If any other value is sampled on R_IN, the core will not decode the data correctly.
Number of Supported R_IN Values: Specify the number of supported R_IN values.
Supported R_IN Definition File: This is a COE file that defines the R values to be supported. It has the following format: radix=10; legal_r_vector=14,16,18,20; The number of elements in the legal_r_vector must equal the specified Number of Supported R_IN Values.

Attributes 2 tab

Implementation

State Machine

Self Recovering: When checked, the block synchronously resets itself if it enters an illegal state.

Memory Style

Select between Distributed, Block and Automatic memory choices.

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.

Output check symbols

If selected, then the entire n symbols of each block are output on the output channel. If not selected, then only the k information symbols are output.

Puncture Options

Number of Puncture Patterns: Specifies how many puncture patterns the LogiCORE needs to handle. It is set to 0 if puncturing is not required.
Puncture Definition File: Specifies the pathname of the puncture definition file that is used to define the puncture patterns.
A relative pathname can be specified for a COE file in the current working directory. For example, the syntax is [cwd ‘/ieee802_16d_puncturing.coe’].

Optional pins tab

Clock Enable

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

Info

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

Synchronous Reset

Adds a aresetn pin to the block. This signal resets the block and must be of type Bool. The signal must be asserted for at least 2 clock cycles, however, it does not have to be asserted before the decoder can start decoding.

Original Delayed Data

When checked, the block is given a tdata_data_del output. Indicates that a DAT_DEL field is in the output_tdata output.

Erase

When checked, the block is given an input_tdata_erase input pin.

Error Statistics

adds the following error statistics outputs:

bit_err_0_to_1: Number of bits received as 1 but corrected to 0.
bit_err_1_to_0: Number of bits received as 0 but corrected to 1.

Marker Bits

Adds the following pins to the block:

input_tuser_mark_in: Carries marker bits for tagging data on input_tdata_ data_in.
output_tuser_mark_out: 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 Decoder v9.0