Near-Capacity Variable-Length Coding: Regular and EXIT-Chart-Aided Irregular Designs

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}^N_n=1 having a variety of coding rates {R(VLECⁿ)}^N_n=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)

(9.2)

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] I_eⁱ(I_a) 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 I_a^o(I_e). As described in Section 5.5, ...