基于Huffman信源编码和LDPC信道编码的联合译码算法

Joint Source-Channel Decoding of Huffman Codes with

LDPC Codes

Zhonghui Mei and Lenan Wu

Abstract In this paper, we present a joint source-channel decoding algorithm (JSCD) for

LDPC codes by exploiting the redundancy of the Huffman coded sources.When the number

of Huffman codes increases, just a moderate complexity is added for our algorithm by

increasing the size of the lookup table, which is used to estimate the information bit

probability based on the source redundancy.

Key words － LDPC, Variable length codes (VLC), Huffman code, sum-product algorithm

(SPA), joint source-channel decoding (JSCD)

I. INTRODUCTION

Recently in [1]-[4] several joint source-channel decoding algorithms for variable length codes

(VLC) have been proposed. All of these algorithms consider the overall sequence of variable

length codeword to exploit the source redundancy. The drawback is that the symbols have to be

synchronized in order to limit error propagating. Furthermore, when the number of VLC

increases, the decoding complexity of these algorithms explodes.

In this paper we present a JSCD algorithm for LDPC codes in combination with Huffman

coded sources. The error correcting property of our JSCD algorithm mainly depends on channel

codes rather than source redundancy. In order to exploit the source redundancy, we estimate the

information bit probability with just some corresponding bits before it, which simplifies the

decoding algorithm significantly.

The rest of the paper is organized as follows. Section II presents the Huffman coded source

model. The JSCD algorithm for LDPC codes is described in section III. Section IV provides the

simulation results. Section V concludes this paper.

II. HUFFNAN CODED SOURCE MODEL

Let denotes a sequence of information bits coded by VLC (e.g. a

Huffman code). In [1], [3] and [4], they consider the overall sequence and express the source

redundancy with . In order to compute , [3] and [4] design a

trellis to illustrate statistics of the source sequence. When the number of the trellis states

increases, the computational complexity of will rise explosively.

],......,,,[321n s s s s S =),......,,,()(21n s s s s p S p =)(S p )(S p In this paper, we make use of the source redundancy with , as is

illustrated in Fig.1 and table 1. k is chose to be larger than the maximum length of Huffman

codes. When the number of VLC increases, we only need to expand the lookup table. In addition,

for we just estimate one bit probability with a small part bit of the information sequence every

time, the error propagation phenomenon has been avoided successfully.

]),......,,[|(11−+−−i k i k i i s s s s p