4.4 Channel Coding

Channel coding is adding some extra codes to a digital sequence M by definite rules so that irregular information sequence M becomes a regular digital sequence Y (code sequence). That is to say, in code sequence, every code of information sequence is related to extra code. At the receiving end, the channel encoder encodes with this prescient coding rules, or verifies that the received digital sequence R conforms to the set rule to find out errors in R and then corrects them. That is the basic idea of channel coding, namely, verifying and correcting the errors during transmission based on correlativity.

Generally, digital sequence M is transmitted with K codes as a group. We call the one with K-code block an information code block. Channel encoder adds some extra codes to each information code block by definite rules, and so the code block with n-code is constituted. Such n codes are mutually related, that is, the extra n-k codes are called the supervising codes of this code block. In terms of information transmission, supervising codes are redundant, as it carries no information. However, such redundancy gives the codes some error detection and correction capability, so the reliability of transmission is increased and error rate is reduced. On the other hand, if we require the speed of information transmission to remain constant, after supervising codes are added, the duration of each code in the code block should be reduced. For a binary code, pulse width should be also reduced. If the normalized width of each code pulse is 1 before coding, it should be k/n after coding, so channel bandwidth should be spread by n/k times. In this case, bandwidth redundancy substitutes for reliability of channel transmission. If the speed of information transmission is allowed to be slower, the duration of each code after coding can remain the same. In this case, bandwidth redundancy substitutes for reliability of channel transmission.

As shown in Table 4-1, there are great gaps between coding gains from different coding methods and the ideal coding gain (up to Shannon limit).

Table 4-1 BPSK or QPSK Coding Gain

Coding Adopted	Coding Gain (dB@BER = 10-3)	Coding Gain (dB@BER = 10-5)	Data Speed
Ideal Coding	11.2	13.6
Cascaded Code (RS and Convolution Code Viterbi Coding)	6.5 ~ 7.5	8.5 ~ 9.5	moderate
Convolution Code Sequence Coding (Soft Decision)	6.0 ~ 7.0	8.0 ~ 9.0	moderate
Cascaded Code (RS and Group Code)	4.5 ~ 5.5	6.5 ~ 7.5	Very High
Convolution Code Viterbi Coding	4.0 ~ 5.5	5.0 ~ 6.5	High
Convolution Code Sequence Coding (Hard Decision)	4.0 ~ 5.0	6.0 ~ 7.0	High
Group Code (Hard Decision)	3.0 ~ 4.0	4.5 ~ 5.5	High
Convolution Code Threshold Coding	1.5 ~ 3.0	2.5 ~ 4.0	Very High

It is observed that, for the same modulating, coding gains vary with different coding schemes. The coding schemes we usually adopt are convolution code, Reed-Solomon code, BCH code and Turbo code, etc. Convolution code is used for voice and low-speed signaling in WCDMA, while Turbo code is used for data encoding.

4.4.1  Convolution Code

The n codes generated by the convolution coder during any definite time is dependent on K information bits during this period and the number of information bits during the former N-1 period of time. At this moment, supervising code monitors the information during the N period of time when the number of codes nN is called constraint length.

The decoding schemes of convolution code are as follows: threshold decoding, hard decision Viterbi decoding and soft decision Viterbi decoding. Among these decoding schemes, the best one is soft decision Viterbi decoding, which is usually adopted. Compared with hard decision Viterbi decoding, it is not much more complex, but its performance is better by 1.5 ~ 2 dB.

4.4.2  Turbo Code

We are striving to approach Shannon limit in coding field, where Turbo code is an innovation milestone. Grid code is close to Shannon limit in case of bandwidth-limited channels, while Turbo code is especially applicable to bandwidth-unlimited channels, such as deep space communication and satellite communication. Theory emulation shows that, in the AWGN channel with 0.7dB Eb/N0, Turbo code with 1/2 code rate has bit error rate of 10^-5.

Two or more basic coders are cascaded in parallel via one or more interweavers, and so Turbo code is constituted. Turbo code is based on the correction of the algorithm and structure of the traditional cascade code. The positive feedback of iterative decoding is cancelled thanks to the introduction of internal-interweaver. The algorithm of Turbo iterative decoding involves SOVA (soft output Viterbi algorithm) and MAP (maximum posterior probability algorithm) and so on. Thanks to each iterative performance of MAP algorithm excels Viterbi algorithm, iterative decoding of MAP algorithm can get more coding gains.