Part II
Irregular Concatenated VLCs and Their Design
List of Symbols in Part II
Schematics
| fn | Current video frame. |
 |
Quantized current video frame. |
 |
Reconstructed current video frame. |
 |
Quantized previous video frame. |
 |
Reconstructed previous video frame. |
| e | Source sample frame. |
| ê | Quantized source sample frame. |
 |
Reconstructed source sample frame. |
| s | Source symbol frame. |
 |
Reconstructed source symbol frame. |
| u | Transmission frame. |
| û | Received transmission frame. |
 |
Reconstructed transmission frame. |
| π | Interleaving. |
| π−1 | De-interleaving. |
| u′ | Interleaved transmission frame. |
| v | Encoded frame. |
| v′ | Interleaved encoded frame. |
| La(·) | A priori Logarithmic Likelihood Ratios (LLRs) pertaining to the specified bits. |
| Lp(·) | A posteriori LLRs/logarithmic A Posteriori Probabilities (log-APPs) pertaining to the specified bits/symbols. |
| Le(·) | Extrinsic LLRs pertaining to the specified bits/symbols. |
| x | Channel’s input symbols. |
| y | Channel’s output symbols. |
Channel
| η | Effective throughput. |
| Ec/N0 | Channel Signal-to-Noise Ratio (SNR). |
| Eb/N0 | Channel SNR per bit of source information. |
Video blocks(VBs)
| JxMB | Number of VB columns in each Macro-Block (MB). |
| JyMB | Number of VB rows in each MB. |
| JMB | Number of VBs in each MB. |
Sub-frames
| M | Number of sub-frames. |
| m | Sub-frame index. |
| em | Source sample sub-frame. |
| êm | Quantized source sample sub-frame. |
| m |
Reconstructed source sample sub-frame. |
| um | Transmission sub-frame. |
| m |
Reconstructed transmission sub-frame. |
| sm | Source symbol sub-frame. |
| m |
Reconstructed source symbol sub-frame. |
Source samplesub-frames
| J | Number of source samples comprising each source sample sub-frame. |
| Jsum | Number of source samples comprising each source sample frame. |
| j | Source sample index. |
| emj | Source sample. |
| êmj | Quantized source sample. |
| mj |
Reconstructed source sample. |
Transmission sub-frames
| I | Number of bits comprising each transmission sub-frame. |
| Isum | Number of bits comprising each transmission frame. |
| Imin | Minimum number of bits that may comprise each transmission sub-frame. |
| Imax | Maximum number of bits that may comprise each transmission sub-frame. |
| i | Transmission sub-frame bit index. |
| umi | Transmission sub-frame bit. |
| b | Binary value. |
Codebooks
| K | Number of entries in the codebook. |
| k | Codebook entry index. |
VQ codebook
| VQ | Vector Quantization (VQ) codebook. |
| VQk | VQ tile. |
| Jk | Number of VBs that comprise the VQ tile VQk. |
| jk | VQ tile VB index. |
 |
VQ tile VB. |
VL-coding codebook
| VLC | Variable-length coding (VL-coding) codebook. |
| VLCk | Variable-length codeword. |
| Ik | Number of bits that comprise the variable-length codeword VLCk |
| Ikb | Number of bits in the variable-length codeword VLCk assuming a value b ∈ {0, 1}. |
| ik | Variable-length codeword bit index. |
 |
Variable-length codeword bit. |
VL-coding codebook parameters
| E | Entropy. |
| L(VLC) | Variable-length codebook average codeword length. |
| R(VLC) | Variable-length coding rate. |
| E(VLC) | Variable-length-encoded bit entropy. |
| T(VLC) | VL-coding trellis complexity. |
| OAPP(VLC) | Average number of Add, Compare and Select (ACS) operations performed per source symbol during A Posteriori Probability (APP) Soft-Input Soft-Output (SISO) variable-length decoding. |
| OMAP(VLC) | Average number of Add, Compare and Select (ACS) operations performed per source symbol during Maximum A posteriori Probability (MAP) VL-coding sequence estimation. |
| dfree(VLC) | Variable-length codebook free distance. |
| dbmin(VLC) | Variable-length codebook minimum block distance. |
| ddmin(VLC) | Variable-length codebook minimum divergence distance. |
| dcmin(VLC) | Variable-length codebook minimum convergence distance. |
 |
Variable-length codebook free distance lower bound. |
| D(VLC) | Variable-length codebook Real-Valued Free Distance Metric (RV-FDM) |
Irregular Variable-Length Codes(IrVLCs)
| N | Component variable-length codebook count. |
| n | Component variable-length codebook index. |
| un | Transmission sub-frame. |
| sn | Source symbol sub-frame. |
| Cn | Component variable-length codebook source symbol frame fraction. |
| αn | Component variable-length codebook transmission frame fraction. |
IrVLC codebooks
| VLCn | Component variable-length codebook. |
| VLCn,k | Component variable-length codeword. |
| In,k | Number of bits that comprise the component variable-length codeword VLCn,k. |
| in,k | Component variable-length codeword bit index. |
 |
Component variable-length codeword bit. |
IrregularUnity-RateCodes (IrURCs)
| R | Component Unity-Rate Code (URC) count. |
| r | Component URC index. |
| u′r | Interleaved transmission sub-frame. |
| vr | Encoded sub-frame. |
| URCr | Component URC. |
Code parameters
| R(·) | Coding rate. |
| M(·) | Number of modulation constellation points. |
| L(·) | Coding memory. |
EXtrinsic Information Transfer (EXIT) chart
| Ia | A priori mutual information. |
| Ie | Extrinsic mutual information. |
| y | Importance of seeking a reduced computational complexity during EXIT-chart matching. |
Trellises
| ï | Bit state index. |
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Symbol state index. |
 |
Node state index. |
| S(ï,) |
Symbol-based trellis state. |
| S(ï,) |
Bit-based trellis state. |
Trellis transitions
| T | Trellis transition. |
| kT | Codebook entry index associated with the symbol-based trellis transition T. |
| bT | Bit value represented by the bit-based trellis transition T. |
| iT | Index of bit considered by the bit-based trellis transition T. |
| ïT | Bit state index of the trellis state from which the symbol-based trellis transition T emerges. |
| T |
Symbol state index of the trellis state from which the symbol-based trellis transition T emerges. |
| T |
Node state index of the trellis state from which the bit-based trellis transition T emerges. |
Trellis sets
| en(umi) | The set of all trellis transitions that encompasses the transmission sub-frame bit umi |
| en(umi = b) | The subset of en(umi) that maps the binary value b to the transmission sub-frame bit umi. |
en( ) |
The set of all trellis transitions that encompasses the VB . |
 |
The subset of en() that maps the VQ tile VQkjk. |
| fr(S) | The set of all transitions that emerge from the trellis state S. |
| to(S) | The set of all transitions that merge to the trellis state S. |
| fr(T) | The state from which the transition T emerges. |
| to(T) | The state to which the transition T merges. |
| nr() |
The set of all VBs that immediately surround the VB. |
Viterbi algorithm
| d(T) | The distortion of the trellis transition T. |
| D(T) | The minimum cumulative distortion of all trellis paths between the trellis state S(0,0) and the trellis transition T. |
| D(S) | The minimum cumulative distortion of all trellis paths to the state S. |
| m(T) | The Viterbi algorithm metric of the trellis transition T. |
| M(T) | The maximum cumulative Viterbi algorithm metric of all trellis paths between the trellis state S(0,0) and the trellis transition T. |
| M(S) | The maximum cumulative Viterbi algorithm metric of all trellis paths to the state S. |
Bahl–Cocke–Jelinek–Raviv (BCJR) algorithm
| Pa(umi = b) | A priori probability of the transmission sub-frame bit umi taking the value b. |
| P(k) | Probability of occurrence of the codebook entry with index k. |
| P(S) | Probability of occurrence of the trellis state S. |
| P(T|fr(T)) | Conditional probability of the occurrence of the trellis transition T given the occurrence of the trellis state from which it emerges. |
| Pp(T) | A posteriori trellis transition probability. |
| C1 | A posteriori trellis transition probability normalization factor. |
| γ(T) | A priori trellis transition probability. |
| γ′(T) | Weighted a priori trellis transition probability. |
| C2(S) | A priori trellis transition probability normalization factor used for all trellis transitions that emerge from the trellis state S. |
| α(S) | Alpha value obtained for the trellis state S. |
| β(S) | Beta value obtained for the trellis state S. |
| CLa | BCJR algorithm LLR pruning threshold. |
| Cγ | BCJR algorithm a priori probability pruning threshold. |
| Cα | BCJR algorithm forward recursion pruning threshold. |
| Cβ | BCJR algorithm backwards recursion pruning threshold. |
Genetic Algorithm (GA) for VL-coding codebook design
| L | List of candidate VL-coding codebooks. |
| Ltar | Target GA list length. |
| M(VLC) | GA VL-coding quality metric. |
| Dlim | GA VL-coding RV-FDM limit. |
| Rlim | GA VL-coding coding rate limit. |
| αD | GA VL-coding RV-FDM importance. |
| αR | GA VL-coding coding rate importance. |
| αE | GA VL-coding bit entropy importance. |
| αT | GA VL-coding trellis complexity importance. |
| βD | GA VL-coding RV-FDM increase/decrease constant. |
| βR | GA VL-coding coding rate increase/decrease constant. |
| Dbest | Most desirable RV-FDM of VL-coding codebooks admitted to the GA list. |
| Rbest | Most desirable coding rate of VL-coding codebooks admitted to the GA list. |
| Ebest | Most desirable bit entropy of VL-coding codebooks admitted to the GA list. |
| Tbest | Most desirable trellis complexity of VL-coding codebooks admitted to the GA list. |
| Pmax | Maximum number of GA mutations. |