10.4 Concatenated Coeds

Convolutional and block codes are far from the theoretical limit of the channel capacity after Shannon. With increasing performance, the decoding effort increases exponentially for these codes, therefore they are only limited operational in practice.

The concatenation of these codes to a more powerful overall code with better decodability is one possible solution. Therefore, codes are concatenated either
  • serial, i.e. the complete data stream including redundancy bits first is coded by an outer and then by an inner code or
  • parallel, i.e. every coder only gets the information bit but not the redundancy bits of the other codes; the resulting data stream is formed by a parallel to serial converter.
One possibility to increase the efficiency of codes is the serial concatenation of different codes. The first code (with code rate CR1) is called outer code, the second (with code rate CR2) inner code. For a transmission code rate CRt the total data rate is Rd =CRt/(CR1 CR2). If the outer code e.g. is a block code and the inner code is a convolutional code the inner code can correct single bit errors and the outer code smaller burst errors.

The block diagram starts with an arrow crt that moves step by step from one block to the other, starting as input to an external encoder with code rate cr1, leading to data rate crt/cr1 into the internal encoder with code rate cr2 leading to data rate crt/product of cr1and cr2 as input of the channel as well as the output. Thereafter the internal decoder produces data rate crt/cr1 and finally the external decoder recovers crt.
Figure 10-14: Concatenation of codes with corresponding data rates.

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