Turbo Codes

This module supports encoding and decoding of Turbo codes[Berrou], e.g., asused in the LTE wireless standard. The convolutional component encoders anddecoders are composed of theConvEncoder andBCJRDecoder layers, respectively.

Please note that various notations are used in literature to represent thegenerator polynomials for the underlying convolutional codes. For simplicity,TurboEncoder only accepts the binaryformat, i.e.,10011, for the generator polynomial which corresponds to thepolynomial\(1 + D^3 + D^4\).

The following code snippet shows how to set-up a rate-1/3, constraint-length-4TurboEncoder and the correspondingTurboDecoder.You can find further examples in theChannel Coding Tutorial Notebook.

Setting-up:

encoder=TurboEncoder(constraint_length=4,# Desired constraint length of the polynomialsrate=1/3,# Desired rate of Turbo codeterminate=True)# Terminate the constituent convolutional encoders to all-zero state# orencoder=TurboEncoder(gen_poly=gen_poly,# Generator polynomials to use in the underlying convolutional encodersrate=1/3,# Rate of the desired Turbo codeterminate=False)# Do not terminate the constituent convolutional encoders# the decoder can be initialized with a reference to the encoderdecoder=TurboDecoder(encoder,num_iter=6,# Number of iterations between component BCJR decodersalgorithm="map",# can be also "maxlog"hard_out=True)# hard_decide output

Running the encoder / decoder:

# --- encoder ---# u contains the information bits to be encoded and has shape [...,k].# c contains the turbo encoded codewords and has shape [...,n], where n=k/rate when terminate is False.c=encoder(u)# --- decoder ---# llr contains the log-likelihood ratio values from the de-mapper and has shape [...,n].# u_hat contains the estimated information bits and has shape [...,k].u_hat=decoder(llr)

classsionna.phy.fec.turbo.TurboEncoder(gen_poly=None,constraint_length=3,rate=0.3333333333333333,terminate=False,interleaver_type='3GPP',precision=None,**kwargs)[source]

Performs encoding of information bits to a Turbo code codeword

Implements the standard Turbo code framework[Berrou]: Two identicalrate-1/2 convolutional encodersConvEncoder are combined to produce arate-1/3 Turbo code. Further, puncturing to attain a rate-1/2 Turbo code issupported.

Parameters:

• gen_poly (tuple |None (default)) – Tuple of strings with each string being a 0,1 sequence. IfNone,constraint_length must be provided.

• constraint_length (int,3...6) – Valid values are between 3 and 6 inclusive. Only required ifgen_poly isNone.

• rate (float,1/2 |1/3) – Valid values are 1/3 and 1/2. Note thatrate here denotesthedesign rate of the Turbo code. Ifterminate isTrue, asmall rate-loss occurs.

• terminate (bool, (defaultFalse)) – Underlying convolutional encoders are terminated to all zero stateifTrue. If terminated, the true rate of the code is slightly lowerthanrate.

• interleaver_type (str,"3GPP" |"random") – Valid values are“3GPP” or“random”. Determines the choice ofthe interleaver to interleave the message bits before input to thesecond convolutional encoder. If“3GPP”, the Turbo code interleaverfrom the 3GPP LTE standard[3GPPTS36212_Turbo] is used. If“random”,a random interleaver is used.

• precision (None (default) | ‘single’ | ‘double’) – Precision used for internal calculations and outputs.If set toNone,precision is used.

Input:

inputs ([…,k], tf.float32) – Tensor of information bits wherek is the information length

Output:

[…,k/rate], tf.float32 – Tensor whererate is provided as input parameter. The output is theencoded codeword for the input information tensor. WhenterminateisTrue, the effective rate of the Turbo code is slightly less thanrate.

Note

Various notations are used in literature to represent the generatorpolynomials for convolutional codes. For simplicityTurboEncoder onlyaccepts the binary format, i.e.,10011, for thegen_poly argumentwhich corresponds to the polynomial\(1 + D^3 + D^4\).

Note that Turbo codes require the underlying convolutional encodersto be recursive systematic encoders. Only then the channel outputfrom the systematic part of the first encoder can be used to decodethe second encoder.

Also note thatconstraint_length andmemory are two differentterms often used to denote the strength of the convolutional code. Inthis sub-package we useconstraint_length. For example, the polynomial10011 has aconstraint_length of 5, however itsmemory isonly 4.

Whenterminate isTrue, the true rate of the Turbo code isslightly lower thanrate. It can be computed as\(\frac{k}{\frac{k}{r}+\frac{4\mu}{3r}}\) wherer denotesrate and\(\mu\) is theconstraint_length - 1. For example, in3GPP,constraint_length = 4,terminate =True, forrate = 1/3, true rate is equal to\(\frac{k}{3k+12}\).

propertycoderate

Rate of the code used in the encoder

propertyconstraint_length

Constraint length of the encoder

propertygen_poly

Generator polynomial used by the encoder

propertyk

Number of information bits per codeword

propertyn

Number of codeword bits

propertypunct_pattern

Puncturing pattern for the Turbo codeword

propertyterminate

Indicates if the convolutional encoders are terminated

propertytrellis

Trellis object used during encoding

classsionna.phy.fec.turbo.TurboDecoder(encoder=None,gen_poly=None,rate=0.3333333333333333,constraint_length=None,interleaver='3GPP',terminate=False,num_iter=6,hard_out=True,algorithm='map',precision=None,**kwargs)[source]

Turbo code decoder based on BCJR component decoders[Berrou].

Takes as input LLRs and returns LLRs or hard decided bits, i.e., anestimate of the information tensor.

This decoder is based on theBCJRDecoder and, thus, internallyinstantiates twoBCJRDecoder blocks.

Parameters:

• encoder (TurboEncoder) – Ifencoder is provided as input, the following input parametersare not required and will be ignored:gen_poly,rate,constraint_length,terminate,interleaver. They will be inferredfrom theencoder object itself.Ifencoder isNone, the above parameters must be providedexplicitly.

• gen_poly (tuple orNone) – Tuple of strings with each string being a 0, 1 sequence. IfNone,rate andconstraint_length must be provided.

• rate (float,1/3 |1/2) – Rate of the Turbo code. Valid values are 1/3 and 1/2. Note thatgen_poly, if provided, is used to encode the underlyingconvolutional code, which traditionally has rate 1/2.

• constraint_length (int,3...6) – Valid values are between 3 and 6 inclusive. Only required ifencoder andgen_poly areNone.

• interleaver (str,None (default) | “3GPP” | “Random”) –“3GPP” or“Random”. If“3GPP”, the internal interleaver for Turbocodes as specified in[3GPPTS36212_Turbo] will be used. Only requiredifencoder isNone.

• terminate (bool, (defaultFalse)) – IfTrue, the two underlying convolutional encoders are assumedto have terminated to all zero state.

• num_iter (int) – Number of iterations for the Turbo decoding to run. Each iteration ofTurbo decoding entails one BCJR decoder for each of the underlyingconvolutional code components.

• hard_out (bool, (defaultTrue)) – Indicates whether to output hard or softdecisions on the decoded information vector.True implies a hard-decoded information vector of 0/1’s is output.False impliesdecoded LLRs of the information is output.

• algorithm (str,"map" (default)|"log" |"maxlog") – Indicates the implemented BCJR algorithm,wheremap denotes the exact MAP algorithm,log indicates theexact MAP implementation, but in log-domain, andmaxlog indicates the approximated MAP implementation in log-domain,where\(\log(e^{a}+e^{b}) \sim \max(a,b)\).

• precision (None (default) | ‘single’ | ‘double’) – Precision used for internal calculations and outputs.If set toNone,precision is used.

Input:

llr_ch (tf.float) – Tensor of shape[…,n] containing the (noisy) channeloutput symbols wheren is the codeword length.

Output:

tf.float – Tensor of shape[…, coderate * n] containing the estimates of theinformation bit tensor.

Note

For decoding, inputlogits defined as\(\operatorname{log} \frac{p(x=1)}{p(x=0)}\) are assumed forcompatibility with the rest of Sionna. Internally,log-likelihood ratios (LLRs) with definition\(\operatorname{log} \frac{p(x=0)}{p(x=1)}\) are used.

propertycoderate

Rate of the code used in the encoder

propertyconstraint_length

Constraint length of the encoder

depuncture(y)[source]

Given a tensory of shape[batch, n], depuncture() scattersyelements into shape[batch, 3*rate*n] where theextra elements are filled with 0.

For e.g., if input isy, rate is 1/2 andpunct_pattern is [1, 1, 0, 1, 0, 1], then theoutput is [y[0], y[1], 0., y[2], 0., y[3], y[4], y[5], 0., … ,].

propertygen_poly

Generator polynomial used by the encoder

propertyk

Number of information bits per codeword

propertyn

Number of codeword bits

propertytrellis

Trellis object used during encoding