short forward error-correcting codes

8/4/2019 Short Forward Error-Correcting Codes

1/19

Short Forward Error-CorrectingCodes for

Wireless Communication Systems

By Sheng Tong, Dengsheng Lin, Aleksandar Kavi,

Baoming Bai, and Li Ping

Presented by Ashish Lohana


2/19

Introduction

Wireless communication mainly consistsof Real time traffic.

The factor that effects the real time trafficmost is Latency (delay)

Thus there comes a need to use codeswhich have a smaller block size.

These smaller sized block codes derivedfrom the standard FEC codes are calledShort Forward Error-Correcting Codes


3/19

Introduction cont..

Example:

Standard Reed Soloman(RS) code is(255,223)

But such a large sized code cannot beused in wireless communications.

Thus NASA uses a modified RS code of(N, N-32) for Data transmission.

It has been proved that if N>180 thesystem can work at a BER of 10-6


4/19

Effect of Reduction in Block Size

It increases the over all speed of the

system.

It increases the BER. The reduction in block size reduces the

amount of energy per symbol or per bit

(Eb/N

0) transmitted.

Thus increase in BER.

Still we use carefully designed Short FEC.


5/19

Going ahead with the paper:

In this paper we study the performance of

short FEC codes.

We will compare the performance of ShortRS codes and Short Low Density Parity-

Check (LDPC) codes based on the art of

encoding and decoding techniques.

The reference code chosen is Random

Binary Linear (RBL) codes.


6/19

For more practical codes, we examine Reed-Solomon (RS) and LDPC codes that representthe classical algebraic codes and moderniterative decodable codes respectively.

Among the various options for LDPC codes, wefocus on the concatenated zigzag (CZ) codesthat can offer good performance with very low-cost encoder and decoder structures.

We show that with carefully designed linearinterleavers, such simple codes can performvery well at short coding lengths.


7/19

We will see Soft decision decoding techniquesthat offer near maximum likelihood (ML)performance at short block lengths.

Recently, an enhanced hybrid soft decodingalgorithm for linear block codes is presentedwhich combines a reliability-based decodingalgorithm (e.g., ordered statistics decoding(OSD)) and adaptive belief propagation (ABP),denoted as ABP-OSD. This algorithm provides

improved soft decision decoding performance.For short block lengths, this algorithm can evenapproach the ML decoding performance.


8/19

In this The basic idea is to use the soft

output provided by ABP in each iteration

as the input for OSD.

This will provide improved estimation.

Consequently the errors among the most

reliable basis (MRB) will reduce and so

OSD become more efficient.


9/19

Ordered statistics decoding (OSD)

OSD can be briefly outlined as follows:

For an (N, K) linear block code, the decoding process of OSD(i)has 2 stages:

The first stage is to determine the Kmost reliable bits (MRB)

which should be chosen to be linearly independent by applyingGaussian elimination on the generator matrix and transformingthe Kcolumns corresponding to the Kmost reliable bits into anidentity matrix.

The second stage is to flip at most ibits in the MRB to construct a

codeword list and choose the most likely codeword from the listbased on minimum distance between the chosen codeword andreceived bit.


10/19

Adaptive belief propagation (ABP) ABP is a modified version of

belief propagation.

Its novelty lies in adaptively

modifying the parity-check sub-

matrix corresponding to the

least reliable bits in the parity-check matrix to an identity

matrix using a Gaussian

elimination in each decoding

iteration.

OSD and ABP both requireGauss elimination. But now

only one is needed.


11/19

PERFORMANCE COMPARISON

OF SHORT CODES Using ABP-OSD we can achievenear ML decoding performance.

High-rate short RS codes are as

good as random binary linear

codes.

Fig.s 2 and 3 show the FER

performance of RS(31,25),

RS(63,55), respectively.


12/19


13/19

This means that there is significant room for potentialperformance improvement for short RS codes if anefficient soft decoding algorithm is available.

Another interesting observation is that short RS codes

perform similarly to RBL codes, which suggests thatshort RS codes have good error-correcting performance.Moreover, due to their algebraic structure, hardwareimplementations of short RS codes are preferred forpractical applications.


14/19

Carefully designed LDPC codes perform

close to random binary linear codes

we consider CZ codes [8,9] that is a special case of LDPC codes.

carefully designed CZ codes can achieve performance close to

RBL codes under ML decoding.

Denote the code length and information block length of a CZ code

as Nand K, respectively. c=[pT,dT]

H=[Hp, Hd]

Choose M such that:

(i) Mdivides N-K

ii) N-Kdivides KM.


15/19

We construct Hp in the following block diagonal form with Mnon-zero

blocks (each denoted by L) on its diagonal line as

where each L is of size ((N-K)/M)((N-K)/M) with the following dual

diagonal structure,

Partition Hdandp (both having N-Krows) into Mequal sub-blocks as

Hdm,pm and L have the same number, (N-K)/M, of rows.


16/19

pm={pm(i)} (m=1,2,,M,) i=1,2,,(NK)/M) can be easily

calculated from d={di} as follows:

when Mis large

CZ code has a

similar weight

distribution as an

RBL code.


17/19

The gap between the CZ

(8,10,10) code and the(160,80) RBL code

performance is only a

fraction of a dB, which

further verifies the

observation in Fig. thatthe near ML decoding

performance of CZ codes

improves when K

increases.


18/19

An interesting observation can be made from Fig. that

opposite conclusions can be made for the performance

comparison of two codes when different decoding methods are

used. This suggests that code design should carefully take into

consideration the potential decoding capability.


19/19

Thank you

short forward error-correcting codes

Documents