Channel coding for the physical layer of LTE--Data information coding: Turbo coded __lte

The Turbo code skillfully constructs the long code with pseudo random character by the parallel cascade of two simple component codes through pseudo random interleaving, and realizes pseudo random decoding by multiple iterations between two soft/soft out (SISO) decoders. His performance is far more than other coding methods, and has received wide attention and development.

Turbo Coding Principle

The coding aspect mainly includes the analysis of parallel cascade coding and serial cascaded coding, and the research of hybrid cascade mode.

the structure of Turbo encoder

The typical structure block diagram of the Turbo Code encoder is shown in Figure 1: A two-feedback encoder (called a member encoder) is connected by a interleaving i parallel. If necessary, the sequence that is output by the member encoder is deleted, which can produce a series of codes with different code rates. For example, for a (2,1,2) convolutional code that generates a matrix of g=[g1,g2], the encoded output sequence with a code rate of 1/2 is obtained if it is deleted, and the code rate is 1/3 if not deleted. In general, the Turbo code member encoder is a RSC encoder. The reason is that the recursive encoder can improve bit BER performance of code.

Turbo Code

The turbo code used in the 3GPP LTE protocol is a parallel cascaded code with a 1/3-bit rate, and its encoder consists of two RSC encoders with the same code rate of 1/2 and a interleaving, as shown in Figure 2.

Since recursive convolutional codes produce more code weight than non recursive convolutional codes, two identical system recursive convolutional codes (RSC) are used here. The information sequence is divided into the same two routes, the first path passes through the RSC encoder 1, the output system code and the check code. The other way first through the interlaced weaving, the information sequence is rearranged in 1 frames, then the system code and the corresponding check code are obtained through the RSC Encoder 2, because the system code and in fact are original information sequences, but the arrangement order is different, and the receiving end can be interleaved by the Therefore, in the transmission process can be omitted, but only the corresponding check bit.

Since the RSC encoder cannot reset the encoder (grid termination) by entering the "0" sequence as a non-recursive encoder, so by designing the switch between A and B as shown in Fig. 8 to control the encoder termination (AB connection, the data is 0 when the same feedback is found to vary or feed into the memory), when the end of a frame Switch from A to B, then after m time, encoder reset, you can encode the next frame of data. Here m=2. Only the RSC Encoder 1 (external encoder) has a network termination, and the RSC Encoder 2 remains open.

Example of Turbo Code Working principle

Suppose the input sequence is: U = (1 0 1 0 1 1 0 1)

The checksum sequence for the first child code is V1 = (1 1 0 0 0 1 1 1)

Suppose the input sequence of the second substring after interleaving is: U ' = (1 1 0 1 1 0 0 1)

The checksum sequence for the second child code is: V2 = (1 0 0 1 1 0 1 1)

The output sequence of the turbo code is: V = (111,010,100,001,101,110,011,111)

Turbo the interleaving device in the code

The relationship between the input and output bit of the interleaved device in the protocol:

The values of F1 and F2 are related to K value, and the relationship is table5.1.3-3 in protocol TS36.212.

Turbo decoding

Decoding mainly includes iterative decoding, decoding algorithm (maximum posteriori probability algorithm map, modified map algorithm max-log-map, soft output Viterbi algorithm Sova, etc.) research.

Standard Turbo Decoder structure

The iterative decoding scheme of turbo code, combined with its parallel cascaded coding scheme, regards the turbo code as a whole long random code from both the coding structure and the decoding idea, thus greatly improving the decoding performance.

Iterative decoding gives the output of the external code decoder a feedback back to the internal decoder, so that two independent decoders make full use of each other's information, so that each code is connected to a real long code.

Turbo decoding algorithm

Standard map Algorithm

It is the algorithm to eliminate the positive feedback by dividing the prior distribution after the Bahl soft output algorithm is modified. For a convolutional code with a constraint length of M 1, the computation is 6x3^m multiplication and 5x2^m addition of each bit. Because of the large number of multiplication operations, the size and speed of decoding are limited.

Log-map Algorithm

In fact, the likelihood of the standard map algorithm is all expressed by logarithmic likelihood, so that the multiplication operation becomes the addition operation. The total computation becomes 6x2^m addition, 5x2^m the maximum operation and 5x2^m look-up table.

Max-log-map Algorithm

In the above log-domain algorithm, the logarithmic component in the likelihood value addition expression is ignored, and the likelihood addition is completely converted to the maximum operation, so that, in addition to omitting most of the addition operation, the biggest advantage is that it eliminates the estimation of SNR and makes the algorithm more robust.