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This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.IEEE TRANSACTIONS ON BROADCASTING 1

Design of LDPC Coded BICM in DVB BroadcastingSystems With Block Permutations

Min Jang, Hyunjae Lee, Sang-Hyo Kim, Member, IEEE, Seho Myung, Hongsil Jeong, and Jaeyeol Kim

AbstractA new simplified structure of bit-interleaved coded modu-lation (BICM) for second generation digital video broadcasting (DVB)standards, such as DVB-T2, DVB-C2, and DVB-NGH is proposed. In theBICM of the DVB standards, parity and column-twist interleavers areemployed in order to avoid possible performance degradation due to thestructural weaknesses of the BICM scheme. In this paper, a new methodis proposed of finding permutation-equivalent low-density parity-checkcodes that eliminate the BICM weaknesses without the column-twist inter-leaver, thereby simplifying the BICM structure of the DVB standards.The new code descriptions are found by applying a column permutationto the parity check matrices of the original codes in the DVB standards.The codes generated by these new descriptions have the same error cor-recting capability individually for a binary memoryless channel. However,the resulting BICM has a different structure that is free of weakness,called the less-capable check node.

Index TermsDigital video broadcasting (DVB), low-densityparity-check (LDPC) codes, bit-interleaved codedmodulation (BICM), column-twist interleaving, less-capablecheck node (LCN), block permutation.

I. INTRODUCTION

FROM the early 2000s, European Telecommunications StandardsInstitute (ETSI) has been developing second generation standardsfor digital video broadcasting (DVB) transmission: DVB-S2 for satel-lite services [1], DVB-T2 for terrestrial broadcasting systems [2][4],and DVB-C2 for cable systems [5]. In addition, the standardizationof DVB-NGH for mobile handheld broadcasting services is now inprogress and is expected to be finished in the near future [6]. Themain goal of these systems is to increase the spectral efficiency. Toachieve this goal, new physical layer techniques such as orthogonalfrequency division multiplex (OFDM) modulation and an advancednew bit-interleaved coded modulation (BICM) scheme are included.

All the second generation DVB standards share a similar BICMstructure. The BICM consists of forward error correction (FEC)coding, modulation, and bit interleaving. First, message bits areencoded by outer BCH codes and inner low-density parity-check(LDPC) codes. The LDPC codes provide excellent error-correctingperformance [7], and residual errors are eliminated by the BCH codesin order to achieve an extremely low bit error rate. Since the error-correcting performance is improved compared to previous standards,it becomes possible to employ higher order modulation schemes toincrease the spectral efficiency and the maximum data rate. To thisend, DVB-T2 and DVB-NGH introduce high-order modulations up to256-QAM, and DVB-C2 exploits even 1024-QAM and 4096-QAM.

Manuscript received August 2, 2014; revised October 27, 2014; acceptedOctober 28, 2014. This work was supported by Samsung Electronics.

M. Jang, H. Lee, and S.-H. Kim are with the College of Informationand Communication Engineering, Sungkyunkwan University, Suwon 440-746,Republic of Korea (e-mail: [email protected]).

S. Myung, H. Jeong, and J. Kim are with the DMC Research andDevelopment Center, Samsung Electronics, Suwon 443-742, Republic ofKorea.

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TBC.2015.2400815

Bit interleavers in the DVB-T2, DVB-C2, and DVB-NGHstandards are realized as a serial concatenation of several components,and they are designed to optimize the structure of the BICM,incorporating the employed FEC codes and modulations. When high-order modulations are used, bits sent over a single symbol canexperience several different virtual bit channels derived from the sametransmission channel. Some codeword bits are transmitted on goodchannels and others are sent on poor channels; a way to allocate code-word bits to modulation symbols thus needs to be considered. A bitinterleaver is placed between the FEC encoder and the modulator toappropriately reorder codeword bits to guarantee good performanceof BICM systems. In DVB-T2, DVB-C2, and DVB-NGH, the bitinterleaver is composed of the parity interleaver, the column-twistinterleaver, and the block interleaver, while the demultiplexer alsorearranges a bit sequence as an interleaver.

Among the component interleavers, the parity interleaver and thecolumn-twist interleaver are specially introduced to avoid a certainweakness in the BICM structure with regard to the graph of theLDPC code used [8]. When encoded bits are modulated by a high-order scheme, several bits, which are constrained by a single linearequation in the LDPC code structure, may be sent over a single QAMsymbol. The bits will then together experience a channel response,thereby being highly correlated after demapping at the receiver. Ifa BICM structure has many such QAM symbols, the performancecan be degraded in channels with deep fades or erasures - even ifthey seldom occur - which is typical in terrestrial and cable broad-casting environments [9], [10]. Parity and column-twist interleaverswere carefully designed in [8], such that the codeword bits with acommon constraint in the LDPC code structure are sent over dif-ferent QAM symbols. It was shown that these interleavers provide asignificant performance gain in faded erasure channels by eliminatingthe weaknesses of the BICM structure. The column-twist interleaveris studied in more detail in [11].

Although the column-twist interleaving effectively avoids perfor-mance degradation for the BICM scheme, it requires additionalstorage and operations. In this paper, by exploiting the permuta-tion equivalence property of linear codes, we propose permutationmethods called block permutation for designing an LDPC codedBICM system without the column-twist interleaver, which preventspossible performance degradation in fading or erasure channels. Wefind new LDPC code descriptions equivalent to the original codesof current DVB standards using the block permutation such thatthe codeword bits are previously desirably rearranged immediatelyafter LDPC encoding. Because the block permutation is a sim-ple column permutation for a parity check matrix, the permutedcodes retain the same error correcting capability as that of theoriginal code in binary input memoryless channels. When com-bined with high-order modulation in BICM schemes, the codesgenerated by the block permutation can remain detached fromthe problem in which multiple dependent bits are sent on a sin-gle symbol. We are thus able to solve the problem without thecolumn-twist interleaver, and this leads to a simpler DVB BICMstructure.

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Fig. 1. Block diagrams of (a) conventional BICM scheme in the DVB-T2,DVB-C2, and DVB-NGH standards and (b) new BICM scheme designed usingblock permutations.

Fig. 2. Example of (a) parity check matrix H and (b) corresponding bipartitegraph.

The remainder of this paper is organized as follows. Section IIintroduces the elements of BICM in the second generation DVBbroadcasting standards. In Section III, we propose the employment ofpermutation equivalent LDPC codes as an alternative to the column-twist interleaver to simplify the BICM structure. An example is thenshown in Section IV demonstrating that the proposed method canreplace the column-twist interleaver. Finally, Section V presents theconclusions.

II. PRELIMINARIES: BICM SCHEME IN DVB-T2/C2/NGHSecond generation DVB transmission standards such as DVB-T2,

DVB-C2, and DVB-NGH share a similar BICM structure as shownin Fig. 1. The BICM scheme consists of an FEC code, a bit inter-leaver, and a modulation scheme. The combination of the BCH andLDPC codes provides a supreme error correcting performance, andhigh-order modulations support high data rate communications forHD broadcasting services. The bit interleaver is composed of sev-eral components and is designed so as to eliminate the dependencyof the channels experienced by the adjacent codeword bits so thatthe effective binary channel for transmitting codeword bits becomesmemoryless.

LDPC codes are a good choice for practical communication sys-tems due to their capacity-approaching performance and possible highparallelism in implementation [7]. Binary LDPC codes are (n, k) lin-ear block codes with k information bits and n codeword bits, andeach LDPC code is defined as the null space of a sparse parity checkmatrix H {0, 1}(nk)n. Given a codeword vector x {0, 1}n,Hx = 0. The matrix H is represented by a bipartite graph with nvariable nodes and (n k) check nodes. Fig. 2 shows an example ofH and its corresponding bipartite graph. The i-th column and the j-th

TABLE INUMBER OF COLUMNS Nc ACCORDING TO THE STANDARD,

BLOCK LENGTH n, AND MODULATION ORDER M

row of H correspond to the i-th variable node and the j-th check node,respectively, and they are connected if hji equals one. In the graph,the variable nodes correspond to codeword bits, and the check nodesare linear binary constraints. For example, in Fig. 2(b), a check nodec2 is connected with four variable nodes v1, v3, v6, and vn, demon-strating that the modulo-2 sum of the corresponding codeword bitsx1, x3, x6, and xn must be zero. The iterative belief-propagation (BP)decoding operates for error correction under such constraints.

All LDPC codes in the second generation DVB standards have aquasi-cyclic (QC) structure for a decoder with high parallelism [12],and parity bits are simply generated by irregular repeat accumulate(IRA) structures [13]. The submatrix for the message part is com-posed of QQ circulant permutation matrices with a size of Q = 360.Let Sn,r be called a code description for a code with length n andrate r, which is provided in [2], [5], and [6]. There are = kQ linesin Sn,r , and let Sin,r be the i-th line of the description. We assumethat all indices with respect to the LDPC code structure begin from0, so Sn,r is composed of lines S0n,r, S1n,r, . . . , S1n,r . The line Sin,rdetermines the (n k) Q submatrix, of which the starting columnindex is iQ, and we call the submatrix a block. Each block is a verticalstack of q = nkQ circulant permutation matrices.

At the modulator, the encoded bits are mapped to uniform M-QAMsymbols, where M is the modulation order (i.e., number of points onthe constellation). Each M-QAM symbol contains log2 M codewordbits. Before the modulation mapping, the bit sequence is rearrangedby the block interleaver, which has a block memory with Nc columnsand Nr = n/Nc rows. The number of columns is determined as aninteger multiple of log2 M; that is, Nc = K log2 M, where K is thenumber of QAM symbols that obtained from a single column ofthe block interleaver. In the DVB standards, K equals one or two,and Table I presents the values of Nc for the DVB systems underconsideration, n and M. The codeword bits are sequentially writtencolumn-wise and read out row-wise on the block memory. The out-put bits of the block interleaver are grouped at the demultiplexer, andthe Nc bits in each group are mapped to a sequence of the constella-tion points for K symbols. Since the demultiplexing determines themapping from the Nc bits to one or two QAM symbols, this can beregarded as a component interleaver.

In BP decoding over a LDPC graph, if more than two variablenodes connected to a check node are largely corrupted by deep fading,erasures, or strong noise, then the check node becomes less efficientin correcting errors. This problem can be mitigated by the diversityderived from the presumable independence of the channels experi-enced by neighbor variable nodes. However, in the BICM structure,the structural weakness can be exposed if the neighbor variable nodesof a check node are connected to a modulation symbol. In such a case,since the neighbor variable nodes are sent over the same QAM sym-bol, the channel diversity for the check node is reduced and the overallperformance can be degraded. This situation causes inefficiency of


TABLE IIOCCURRENCES OF LCNS IN LDPC CODED BICM IN

DVB-T2 LEFT: (n = 16 200. RIGHT: n = 64 800)

TABLE IIIOCCURRENCES OF LCNS IN LDPC CODED BICM IN

DVB-C2 (LEFT: n = 16 200. RIGHT: n = 64 800)

TABLE IVOCCURRENCES OF LCNS IN 16 K LDPC CODED

BICM IN DVB-NGH

the check node, and leads to a delay in decoding convergence and tothe performance degradation.

Actually, in broadcasting environments, we should take account ofevents in which some symbols are erased or corrupted by strong noiseor interference. For example, 0-dB echo channels and symbol erasurechannels are considered as reference channel models for DVB-T2 sin-gle frequency networks [9]. In addition, a reference channel studiedfor DVB-C2 is composed of several elements: thermal noise, impulsenoise, burst noise, and narrow-band interference [10]. In these typesof channels, some symbols suffer from exceptionally worse channelsthan average.

In this respect, we define the less-capable check node (LCN) asa check node of which two or more neighbor codeword bits areconveyed over a single modulation symbol. For example, if two ormore codeword bits among x1, x3, x6, and xn in Fig. 2(b) are mappedonto a single 16-QAM symbol, then their common neighbor checknode c2 becomes an LCN.

Many LDPC codes in DVB standards generate LCNs when theencoded bits are modulated immediately after block interleaving anddemultiplexing. Tables IIIV present LCN occurrences in the LDPCcoded BICM in DVB-T2, DVB-C2, and DVB-NGH, respectively.The results in the tables are obtained under the BICM structurein Fig. 1(a) without the parity interleaver and the column-twist

interleaver. For example, in DVB-C2, all codes with n = 64800combined with 256-QAM (i.e., Nc = 16) result in many LCNs dueto QC structures. Thus, an additional operation was required for DVBstandards to eliminate LCNs.

Parity and column-twist interleavers were introduced in [8] toeliminate LCNs, and these interleavers were adopted in DVB-T2,DVB-C2, and DVB-NGH. First, the parity interleaver transforms thesubmatrix of the parity part into the same QC structure as that of thepreparing step for LCN elimination, and the column-twist interleaverapplies an appropriate offset to the start position for each columnof the block interleaver. The column-twisting is equivalent to cir-cular shifts in the submatrices of H. The size of each submatrix isn/Nc. Fig. 3(a) shows an example of the column-twist interleavingfor the case of Nc = 4 and M = 16, and three submatrices includingthe parity part are circular-shifted according to predetermined offsets.The offsets are carefully determined in order to avoid LCNs [8], [11].Note that the column-twist interleaving and de-interleaving are imple-mented as component operations, and the sets of twisting offsets arespecified for different n and M in the DVB standards.

III. NEW BICM DESIGN WITH BLOCK PERMUTATIONIn this section, methods to avoid LCNs that are more efficient

and economical are introduced. First, a graphical representation ofthe LDPC coded BICM structure is introduced, and the behaviorof conventional schemes over this graph is discussed. We then pro-pose another method, block permutation, for designing new BICMschemes that replaces the column-twist interleaver.

A. LDPC Coded BICM GraphAs shown in Fig. 2, an LDPC code structure is represented by a

bipartite graph. Similarly, we illustrate an entire LDPC coded BICMstructure using a tripartite graph as depicted in Fig. 4. We refer tothe tripartite graph as an LDPC coded BICM graph. This graph con-sists of a conventional LDPC bipartite graph, symbol nodes (roundedsquares), and additional edges. The new edges connect a variablenode and a symbol node, and there is no connection between checknodes and symbol nodes. A symbol node indicates each QAM sym-bol, and neighbor codeword bits of a symbol node are sent on a singlesymbol through the channels. Fig. 4 shows the case of 16-QAM, andthe degree (number of edges connected to a node) of all symbolnodes is 4.

In the LDPC coded BICM graph, the left-hand side edge connec-tions of variable nodes are described by the LDPC code structure.Especially, Fig. 4 depicts a QC-LDPC code structure with Q = 4 inthe left-hand side. As shown in Fig. 2, edge connections between vari-able nodes and check nodes describe codeword bits and their linearconstraints, respectively. On the other hand, the right-side edge con-nections of the variable nodes are determined by the bit interleaver ofthe BICM. Every variable node has only one neighbor symbol node,which means that the codeword bits are merely permuted and thenmapped to the symbols.

According to our definition, if a check node share two or moreneighbor variable nodes with any symbol node, then the checknode becomes an LCN. In other words, an LCN contributes tomake a length-4 cycle accompanying any symbol node. To eliminateLCNs, edge connections in the LDPC coded BICM graph shouldbe carefully determined so that any combination of a check nodeand a symbol node does not have more than one common neigh-bor variable node. We define the LCN-free graph as a graph inwhich there is no length-4 cycle that includes a check node and asymbol node.


Fig. 3. Illustrations of (a) column-twist interleaving in conventional DVB standards, (b) interblock permutations, and (c) intrablock permutations on a paritycheck matrix in the DVB-T2/C2 standards (n = 64 800, r = 3/4, Q = 360, q = 45, = 145). While the column-twist interleaving is an actual operationperformed at the transmitter and the receiver, the interblock permutation and the intrablock permutations are design procedures used to obtain new encodingdescriptions of LDPC codes.

B. LCN Avoidance on LDPC Coded BICM GraphThe LCN avoidance method in conventional DVB standards is a

careful design of the right-hand side edge connections with a givenfixed left-hand side subgraph. This is used to have the entire graphbe LCN-free, i.e., cycle-4 free. In this design, LCNs are avoidedby revising the edge connections derived by concatenating the par-ity interleaver and the column-twist interleaver to the existing blockinterleaver and demultiplexer. As a result, every combination ofmodulation and coding scheme in the DVB standards results in anLCN-free graph using a proper column-twist interleaver setting.

Our goal is to propose a new method for avoiding LCNs. Thismethod replaces the column-twist interleaver and provides a simplerimplementation. We will briefly describe our approach in terms ofthe tripartite graph in Fig. 4 and then give further details later.

Let us assume that the right-hand side subgraph is formed by thebit-interleaver composed of all components except the column-twistinterleaver and that the left-hand side subgraph is determined by theLDPC code in use. Some LCNs may exist in the entire graph. Insteadof modifying the right-hand side graph by applying the column-twistinterleaver in order to avoid the LCNs, the code will only be re-described by applying a coordinate permutation to avoid the LCNs.

First, we unplug the right-hand side edges from the variable nodesockets. The terminated right-hand side subgraph is kept intact.

The variable nodes untied from the right-hand side are reordered bya certain permutation maintaining the left-side socket connections.Note that this operation will provide a new permutation-equivalentLDPC code of which the error correcting property is identical tothe original since the LDPC graph structure is unchanged. Then,the edges of the intact right-hand side subgraph are plugged in thesockets of the reordered variable nodes, and we check whether ornot the new LDPC coded BICM graph is LCN-free. This seriesof operations is iteratively performed until an LCN-free graph isfound.

A new BICM graph is obtained, of which the structure differs fromthat of the former structure. If the reordering of the variable nodes isadequately performed, the entire set of LCNs can be removed. Thebenefit of the new structure is that the variable node reordering canbe realized by only modifying the code description without changingthe encoder implementation.

The reordering of variable nodes needs to be carefully designed sothat it effectively removes the existing LCNs. Furthermore, we wantto find a single good reordering pattern that has LCN-free combina-tions with all possible modulation schemes. We develop the methodunder the following two design constraints.

Reuse of individually well-designed LDPC codes. Retention of the QC and IRA structures for the LDPC code.


Fig. 4. QC-LDPC coded BICM graph showing a set of variable nodes(circles), a set of check nodes (squares), a set of symbol nodes (roundedsquares), and a set of edges. The left-hand side edge connections of vari-able nodes show the LDPC code structure, while the right-hand side edgeconnections depict bit interleaving.

First, for a fair comparison of the structures, we need to use thecode with the same error-correcting capability as that of the codedefined in the standards. Second, our aim is to take advantage of theimplementation-friendly structures, QC and IRA. Our approach auto-matically satisfies the first constraint since the variable node orderingwill not change the algebraic properties of the code. A reordering orpermutation method which also satisfies the second condition needs tobe devised. We introduce permutation methods called block permu-tations which make BICM graphs satisfying the second constraint inthe following subsection. Note that the block permutation is distin-guished from the block interleaving, which is an actual componentof the BICM structure.

C. LCN Avoidance Via Block PermutationThe block permutations are permutation methods applied to the

blocks of the parity check matrix with the QC structure. Note thata block permutation is equivalent to a variable node permutation.We propose two types of block permutations for avoiding LCNs:inter-block and intra-block. The inter-block permutation reorders theblocks of the message part of the parity check matrix where therelative order of the columns within a block is not changed, whilethe intra-block permutation applies a circular shift to each block inthe message part.

Since the QC and IRA structures are maintained, we can continueto use the same encoder for generating the codewords correspondingto the new modified code. Let Sn,r be a new encoding descriptiondesigned by applying the proper block permutations to the existingencoding description Sn,r . The identical encoding is applied to Sn,rbecause the QC structure in the message part and the IRA structurein the parity part have been retained.

As previously mentioned, our main goal is to find a single newLDPC code description that is free of LCNs in combination with allmodulation schemes. We will now explain how to remove the LCNs

with the block permutations. First, we start with the parity checkmatrix Hn,r of an original encoding description Sn,r , as providedin [2], [5], and [6]. Parity interleaving needs to be applied since themessage and parity parts must have the same QC structure to easethe design for LCN avoidance. Let Hn,r denote a parity check matrixof which the submatrix of the parity part is rearranged by parityinterleaving. We then reorder the columns in Hn,r so that no LCNoccurs for all modulation schemes with different Nc (see Table I)considered. The parity part should be protected unchanged. Afterfinding a modified parity check matrix that does not create LCNs,a corresponding encoding description Sn,r is derived from the matrix.

1) LCN Avoidance Via Inter-Block Permutation: As depicted inFig. 3(b), the inter-block permutation is a block-wise permutationthat blocks of the size (n k) Q are exchanged. Let (i) be theinter-block permutation order of the i-th block, and the reordering ofblocks of the parity check matrix are determined by (i). Let hj andhj denote the j-th column vector of an original parity check matrixH and that of a resulting block permuted parity check matrix H,respectively. Then,

h(p)Q+r = hj, (1)where p = jQ and r = j mod Q. Only the blocks in the messagepart are permuted, and for the parity part, i , (i) = i. We willthen obtain a new encoding description Sn,r , where S(i)n,r = Sin,r .

We place a design constraint such that the variable node degreeprofile of the resulting code should be the same as that of the originalcode, because the demultiplexer has been designed considering thedegree profile and because any change in the degree profile mayrequire a modification of the demultiplexer. A good reordering patterncan be found by even a simple trial and error approach.

Table V shows an example of an inter-block permutation descrip-tion S16200,1/2 for DVB-T2/C2 is given. As shown in the table, thelines are simply reordered compared to the original description, andthis description results in LCN-free BICM structures for all modula-tion schemes considered. While proper inter-block permutations forshort codes with n = 16200 are easy to find in all DVB standards,for some long codes with n = 64800, a suitable pattern of inter-blockpermutations is not easily obtained by a simple brute-force search.

2) LCN Avoidance Via Intra-Block Permutation: Intra-block per-mutation is a more effective method than inter-block permutation.Within each block in the message part, columns (variable nodes) arecircularly shifted according to a proper offset as depicted in Fig. 3(c).Let ti be an intra-block permutation offset for the i-th block; the Qcolumns of the i-th block are then circular-shifted to the right by tiunits. Therefore,

hpQ+u = hj, (2)where p = jQ and u = (j mod Q + tp) mod Q.

The intra-block permutation is equivalent to the additions of con-stant offset values to each line of Sn,r . According to the propertyof the encoding in the DVB standards, if we cyclically shift col-umn vectors in the i-th block to the right by ti units, then tiq isadded to all elements in Sin,r . Here, the additions are operated undermodulo (n k). Using the derived encoding description directly, wefind the intra-block permutation offsets by a simple search algorithm.Pseudo-codes in Algorithm 1 describe the design of a new encodingdescription Sn,r from Sn,r with intra-block permutations.

Table V also shows intra-block permuted encoding description ofour running example, and the offset tiq = 25ti is added to all ele-ments in some lines. The resulting code leads to LCN-free BICMstructures for all modulation schemes. As a matter of course, thisblock permutation does not break the QC and the IRA structure of


TABLE VEXAMPLES OF ENCODING DESCRIPTIONS OBTAINED BY INTERBLOCK AND INTRABLOCK PERMUTATIONS (DVB-T2/C2, n = 16 200, r = 1/2)

Algorithm 1 Intrablock Permutation Designfor i = 1 to do

Sin,r (Sin,r tiq + (n k)) mod (n k)(ti is a circular shift offset, and 0 ti < Q)

end forConstruct a parity check matrix H with Sin,r , i = 1, 2, . . . , qRearrange H by parity interleaving, and then obtain Hfor all Nc considered do

Divide H into Nc submatrices H1, H2, . . . , HNcCalculate Q = H1 + H2 + + HNcif there is a value greater than 1 in Q then

Go back to the beginning of the algorithmend if

end forObtain Sin,r for i = 1, . . . , as a new encoding description

the parity check matrices, and the column-twist interleaver can beomitted.

The main advantage of the intra-block permutation compared tothe inter-block permutation is a greater degree of freedom in design.While the number of all possible inter-block permutations is less than()!, we may consider Q patterns of intra-block permutations tochoose a proper permutation. Furthermore, the aim of the inter-blockpermutation search is to find a solution to a complex combinatorialproblem of blocks, whereas the aim of the intra-block permuta-tion search is to solve a set of independent problems within eachindividual block. Therefore, it is easier to find appropriate encod-ing descriptions by using intra-block permutations than by usinginter-block permutations. As a result, for all codes in the DVB-T2,DVB-C2, and DVB-NGH standards, we have found modified encod-ing descriptions that do not generate any LCN in the BICM graph incombination with the subsequent block interleavers, demuliplexers,and QAMs.

IV. NUMERICAL RESULTSIn this section, we show that the new BICM schemes do not cause

performance degradation compared to conventional DVB standards.We consider the Rayleigh faded erasure channel modeled in [8],

Fig. 5. BER curves of a DVB-T2/C2 LDPC code (n = 64 800, r = 3/4) overRayleigh faded erasure channel with erasure probability = 0.18.

where the harmful effect of LCNs is noticeable. Given n code-word bits, n/log2 M QAM symbols are generated at the encoder.Let xi be the i-th transmitted symbol through the channel with whiteGaussian noise power 2, and the corresponding received symbol isthen given as

yi = hieixi + zi, (3)where hi CN (0, 1), zi CN (0, 2), and ei is a discrete ran-dom variable with probability mass function (pmf) pE(0) = andpE(1/

1 ) = 1 . For each symbol, hi, zi, and ei are indepen-

dently generated from the respective distributions. We assume thatperfect channel state information is available at the receiver, i.e., thereceiver knows the exact values of hiei for all i.

Bit error rates (BERs) of three different schemes for an LDPC code(n = 64800, r = 3/4) in DVB-T2/C2 are compared. In the first scheme,a code is constructed based on the conventional encoding descrip-tion in [2] and [5], but parity and column-twist interleavers are notemployed. The second scheme is the conventional DVB-T2/C2 BICM


with the parity and column-twist interleaver corresponding to thecurrent standards. The third scheme is a new BICM with an encod-ing description obtained by intra-block permutations and without thecolumn-twist interleaver.

The resulting BER curves are shown in Fig. 5. For the three mod-ulation schemes (16-QAM, 64-QAM, and 256-QAM), it is verifiedthat the new BICM with the LDPC code designed by block permuta-tions achieves the same gain although the column-twist interleaver isnot exploited. Therefore, with new encoding descriptions, the BICMsystem structure in the DVB standards is simplified, and it is not nec-essary to store the sets of twisting parameters for different modulationand coding schemes.

V. CONCLUSIONSFor QC-LDPC codes in second generation DVB standards, a new

code description via block permutation methods was proposed toachieve the same BICM gain as that of column-twist interleaving.Two different block permutations, inter-block and intra-block permu-tations, were introduced, and it was demonstrated that the intra-blockpermutation is an effective way to design LCN-free BICM graphs. Byusing intra-block permutations, proper modification of LDPC paritycheck matrices was achieved for all codes, modulation and codingschemes in the DVB-T2, DVB-C2, and DVB-NGH standards. Thisenabled a simplification of the BICM structure with no performancedegradation compared to the conventional schemes.

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