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Section 6.3.  Long-Term  Memory Motion-Compensated Prediction   151


                where D INTRA  is the SSD between the current macroblock and its INTRA
                encoded reconstruction and R INTRA  is the number of bits used to INTRA
                encode the current macroblock. Similar de)nitions also apply for D INTER
                and R INTER , but they are calculated by INTERencoding the current mac-
                roblock. In both equations,   MODE  is a Lagrange multiplier related to the
                quantization parameter QP using

                                      MODE  =0:85 × QP :                 (6.8)
                                                   2
                The  mode  with  the  minimum  cost  function  is  chosen  as  the  mode  of
                the  current  macroblock.  Note  that,  in  this  case,  a  macroblock  needs  to
                be  encoded  twice  before  being  able  to  decide  its  mode.  This  increases
                the  complexity  of  the  encoder.  A  more  detailed  description  of  this  rate-
                constrained  motion  estimation  and  mode  decision  method  can  be  found
                in Ref. 143.

            MR  This  is  a  multiple-reference  encoder  with  no  rate  constraints.  Thus,  it
                is  the  same  as  SR,  but  it  uses  long-term  memory  motion-compensated
                prediction.

            MR-RC  This is a multiple-reference rate-constrained encoder. Thus, it is the
                same as SR-RC, but it uses long-term memory motion-compensated pre-
                diction.
               The  preceding  encoders  were  tested  using  the  three  QSIF  test  sequences
            AKIYO,FOREMAN,  and  TABLE  TENNIS.  The  frame  skip  parameter  was  set  to  3
            to  achieve  low  bit  rates.  To  generate  a  range  of  bit  rates,  the  quantization
            parameter  QP  was  varied  over  the  range  5–30  in  steps  of  5.  This  means  that
            each encoder was used to encode a given sequence six times. Each time, QP
            was  held  constant  over  the  whole  sequence  (i.e.,  no  rate  control  was  used).
            The )rst frame was always INTRA encoded. The INTRA bits of the )rst frame
            were  included  in  the  bit-rate  calculations,  and  no  header  bits  were  generated.
            All  quoted  results  refer  to  the  luma  components  of  sequences.  For  MRand
            MR-RC, sliding-window control was used to maintain a long-term memory of
            size  M = 50  frames.  The  VLC  codewords  in  Table  6.1  were  used  to  encode 1
            the temporal components  d t  of  the long-term motion vectors.
               Figures  6.6,  6.7,  and  6.8  show  the  R-D  performance  of  the  preceding
            encoders  for  the  three  test  sequences.  Note  that  both  single-reference  and



              1 For example, since d t  = 4 is in the range (3:6), then according to Table 6.1 it will be encoded
            using  a  5-bit  codeword.  This  codeword  is  derived  as  follows.  With  reference  to  the  start  of  its
            range, d t  = 4 is represented by d t  − 3=4  − 3 = 1. Thus, x 1 x 0  = 01 and the codeword is given by
            0x 1 1x 0 0 = 00110.
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