Chapter 9

Joint EXIT-Chart Matching of Irregular Variable-Length Coding and Irregular Unity-Rate Coding1

9.1 Introduction

In Chapters 7 and 8 we characterized the serial concatenation [275] of an irregular outer codec with a regular inner codec, as proposed in [149]. Whilst Chapters 7 and 8 employed different regular inner codecs, they both employed Irregular Variable-Length Coding (IrVLC) as their irregular outer codec. This scheme comprises N component Variable-Length Error-Correction (VLEC) codebooks [179] {VLECn}Nn=1 having a variety of coding rates {R(VLECn)}Nn=1, as described in Section 5.5. At the transmitter, each component VLEC codebook VLECn is invoked to generate a specific fraction of the transmission frame, given by the component’s weight αn, where we have

(9.1)c09e001

(9.2)c09e002

At the receiver, an inner A Posteriori Probability (APP) Soft-Input Soft-Output (SISO) decoder [292] iteratively exchanges extrinsic information with the APP SISO IrVLC decoder [278], as described in Section 4.1. As usual, the EXtrinsic Information Transfer (EXIT) function [294] Iei(Ia) of the inner APP SISO decoder may be employed to characterize its operation. Similarly, the operation of the APP SISO IrVLC decoder may be characterized by its inverted EXIT function Iao(Ie). As described in Section 5.5, ...

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