/**
 * LDPC Rate 1/2 Codec Implementation
 *
 * LDPC for TAV-DT header protection.
 * Uses a systematic rate 1/2 code with sum-product belief propagation decoder.
 *
 * The parity-check matrix is designed for good error correction on small blocks.
 * Each parity bit is computed as XOR of multiple data bits using a pseudo-random
 * but deterministic pattern.
 *
 * Created by CuriousTorvald and Claude on 2025-12-09.
 * Updated 2025-12-17: Replaced bit-flipping with belief propagation decoder.
 */

#include "ldpc.h"
#include <string.h>
#include <stdio.h>
#include <math.h>

// Channel LLR magnitude for hard-decision input
// Higher value = more confidence in received bits
// For BER ~0.01, optimal is about 4.6; we use slightly lower for robustness
#define CHANNEL_LLR_MAG 4.0f

// Clipping value to prevent numerical overflow in tanh operations
#define LLR_CLIP 20.0f

// =============================================================================
// Parity-Check Matrix Generation
// =============================================================================

// For rate 1/2 LDPC: n = 2k bits, parity-check matrix H is (n-k) x n = k x 2k
// We use H = [P | I_k] where P is the parity pattern matrix
// This gives systematic encoding: c = [data | parity] where parity = P * data

// Parity pattern: each parity bit j depends on data bits where pattern[j][i] = 1
// We use a regular pattern with column weight 3 (each data bit affects 3 parity bits)
// and row weight varies to cover the data bits well

// Simple hash function for generating parity connections
static inline uint32_t hash_mix(uint32_t a, uint32_t b) {
    a ^= b;
    a = (a ^ (a >> 16)) * 0x85ebca6b;
    a = (a ^ (a >> 13)) * 0xc2b2ae35;
    return a ^ (a >> 16);
}

// Get bit from byte array
static inline int get_bit(const uint8_t *data, int bit_idx) {
    return (data[bit_idx >> 3] >> (7 - (bit_idx & 7))) & 1;
}

// Set bit in byte array
static inline void set_bit(uint8_t *data, int bit_idx, int value) {
    int byte_idx = bit_idx >> 3;
    int bit_pos = 7 - (bit_idx & 7);
    if (value) {
        data[byte_idx] |= (1 << bit_pos);
    } else {
        data[byte_idx] &= ~(1 << bit_pos);
    }
}

// Flip bit in byte array
static inline void flip_bit(uint8_t *data, int bit_idx) {
    int byte_idx = bit_idx >> 3;
    int bit_pos = 7 - (bit_idx & 7);
    data[byte_idx] ^= (1 << bit_pos);
}

// Get list of data bits that affect parity bit j
// Returns number of connected data bits, stores indices in connections[]
// For rate 1/2: data bits are 0 to k*8-1, parity bits are k*8 to 2*k*8-1
static int get_parity_connections(int parity_idx, int k_bits, int *connections) {
    int count = 0;

    // Use a deterministic pseudo-random pattern
    // Each parity bit connects to approximately k_bits/3 data bits
    // Different seeds for different parity positions ensure coverage

    uint32_t seed = hash_mix(0xDEADBEEF, (uint32_t)parity_idx);

    for (int i = 0; i < k_bits; i++) {
        // Each data bit has ~3/k_bits chance of connecting to this parity bit
        // Total connections per parity ~ 3 (column weight)
        uint32_t h = hash_mix(seed, (uint32_t)i);
        if ((h % (k_bits / 3 + 1)) == 0) {
            connections[count++] = i;
        }
    }

    // Ensure at least 2 connections per parity bit
    if (count < 2) {
        connections[count++] = parity_idx % k_bits;
        connections[count++] = (parity_idx + k_bits / 2) % k_bits;
    }

    return count;
}

// Get list of parity bits affected by data bit i
static int get_data_connections(int data_idx, int k_bits, int *connections) {
    int count = 0;

    for (int j = 0; j < k_bits; j++) {
        int parity_conns[LDPC_MAX_DATA_BYTES * 8];
        int n_conns = get_parity_connections(j, k_bits, parity_conns);

        for (int c = 0; c < n_conns; c++) {
            if (parity_conns[c] == data_idx) {
                connections[count++] = j;
                break;
            }
        }
    }

    return count;
}

// =============================================================================
// Initialization
// =============================================================================

static int ldpc_initialized = 0;

void ldpc_init(void) {
    if (ldpc_initialized) return;
    // No pre-computation needed - patterns generated on the fly
    ldpc_initialized = 1;
}

// =============================================================================
// Encoding
// =============================================================================

size_t ldpc_encode(const uint8_t *data, size_t data_len, uint8_t *output) {
    if (!ldpc_initialized) ldpc_init();

    if (data_len > LDPC_MAX_DATA_BYTES) {
        data_len = LDPC_MAX_DATA_BYTES;
    }

    int k_bits = (int)(data_len * 8);  // Number of data bits

    // Copy data to output (systematic encoding)
    memcpy(output, data, data_len);

    // Initialize parity bytes to zero
    memset(output + data_len, 0, data_len);

    // Compute parity bits
    for (int j = 0; j < k_bits; j++) {
        // Get data bits connected to parity bit j
        int connections[LDPC_MAX_DATA_BYTES * 8];
        int n_conns = get_parity_connections(j, k_bits, connections);

        // Parity bit = XOR of connected data bits
        int parity = 0;
        for (int c = 0; c < n_conns; c++) {
            parity ^= get_bit(data, connections[c]);
        }

        // Set parity bit
        set_bit(output + data_len, j, parity);
    }

    return data_len * 2;
}

// =============================================================================
// Decoding
// =============================================================================

int ldpc_check_syndrome(const uint8_t *codeword, size_t len) {
    if (!ldpc_initialized) ldpc_init();

    size_t data_len = len / 2;
    int k_bits = (int)(data_len * 8);

    // Check all parity equations
    for (int j = 0; j < k_bits; j++) {
        int connections[LDPC_MAX_DATA_BYTES * 8];
        int n_conns = get_parity_connections(j, k_bits, connections);

        // Compute syndrome bit: XOR of connected data bits XOR parity bit
        int syndrome = get_bit(codeword + data_len, j);
        for (int c = 0; c < n_conns; c++) {
            syndrome ^= get_bit(codeword, connections[c]);
        }

        if (syndrome != 0) {
            return 0;  // Syndrome non-zero: errors detected
        }
    }

    return 1;  // Zero syndrome: valid codeword
}

// Clip LLR to prevent overflow
static inline float clip_llr(float llr) {
    if (llr > LLR_CLIP) return LLR_CLIP;
    if (llr < -LLR_CLIP) return -LLR_CLIP;
    return llr;
}

// Sign of a float (returns +1 or -1)
static inline float sign_f(float x) {
    return (x >= 0.0f) ? 1.0f : -1.0f;
}

int ldpc_decode(const uint8_t *encoded, size_t encoded_len, uint8_t *output) {
    if (!ldpc_initialized) ldpc_init();

    if (encoded_len < 2 || (encoded_len & 1) != 0) {
        return -1;  // Invalid length
    }

    size_t data_len = encoded_len / 2;
    if (data_len > LDPC_MAX_DATA_BYTES) {
        return -1;
    }

    int k_bits = (int)(data_len * 8);
    int n_bits = k_bits * 2;  // Total codeword bits (data + parity)

    // Pre-compute the parity check matrix structure for efficiency
    // For each check node j: which variable nodes it connects to
    int check_to_var[LDPC_MAX_DATA_BYTES * 8][LDPC_MAX_DATA_BYTES * 8 + 1];
    int check_degree[LDPC_MAX_DATA_BYTES * 8];

    for (int j = 0; j < k_bits; j++) {
        int connections[LDPC_MAX_DATA_BYTES * 8];
        int n_conns = get_parity_connections(j, k_bits, connections);

        // Check j connects to: data bits in connections[] + parity bit j
        check_degree[j] = n_conns + 1;
        for (int c = 0; c < n_conns; c++) {
            check_to_var[j][c] = connections[c];  // Data bit index
        }
        check_to_var[j][n_conns] = k_bits + j;  // Parity bit index
    }

    // Initialize channel LLRs from received hard bits
    // LLR > 0 means bit is probably 0, LLR < 0 means bit is probably 1
    float channel_llr[LDPC_MAX_DATA_BYTES * 16];
    for (int i = 0; i < n_bits; i++) {
        int bit = get_bit(encoded, i);
        channel_llr[i] = bit ? -CHANNEL_LLR_MAG : CHANNEL_LLR_MAG;
    }

    // Message arrays for BP
    // check_to_var_msg[j][idx] = message from check j to variable check_to_var[j][idx]
    float check_to_var_msg[LDPC_MAX_DATA_BYTES * 8][LDPC_MAX_DATA_BYTES * 8 + 1];

    // Initialize check-to-variable messages to zero
    memset(check_to_var_msg, 0, sizeof(check_to_var_msg));

    // Belief Propagation iterations
    for (int iter = 0; iter < LDPC_MAX_ITERATIONS; iter++) {
        // Step 1: Variable-to-check messages (implicit, computed on the fly)
        // var_to_check[v→j] = channel_llr[v] + sum of all check_to_var_msg[k][idx_v] for k != j

        // Step 2: Check-to-variable messages using min-sum approximation
        // For each check node j, for each connected variable v:
        // check_to_var_msg[j→v] = sign * min(|incoming messages from other vars|)

        for (int j = 0; j < k_bits; j++) {
            int degree = check_degree[j];

            // First, compute variable-to-check messages for all variables in this check
            float var_to_check[LDPC_MAX_DATA_BYTES * 8 + 1];
            for (int idx = 0; idx < degree; idx++) {
                int v = check_to_var[j][idx];

                // Sum all incoming check messages to variable v, except from check j
                float sum = channel_llr[v];
                for (int jj = 0; jj < k_bits; jj++) {
                    if (jj == j) continue;
                    // Find if check jj connects to variable v
                    for (int idx2 = 0; idx2 < check_degree[jj]; idx2++) {
                        if (check_to_var[jj][idx2] == v) {
                            sum += check_to_var_msg[jj][idx2];
                            break;
                        }
                    }
                }
                var_to_check[idx] = clip_llr(sum);
            }

            // Now compute check-to-variable messages using min-sum
            for (int idx = 0; idx < degree; idx++) {
                float sign_prod = 1.0f;
                float min_abs = 1e30f;

                for (int idx2 = 0; idx2 < degree; idx2++) {
                    if (idx2 == idx) continue;
                    float msg = var_to_check[idx2];
                    sign_prod *= sign_f(msg);
                    float abs_msg = fabsf(msg);
                    if (abs_msg < min_abs) min_abs = abs_msg;
                }

                // Min-sum with scaling factor 0.75 for better performance
                check_to_var_msg[j][idx] = clip_llr(sign_prod * min_abs * 0.75f);
            }
        }

        // Step 3: Compute posterior LLRs and make hard decisions
        float posterior[LDPC_MAX_DATA_BYTES * 16];
        for (int v = 0; v < n_bits; v++) {
            float sum = channel_llr[v];
            // Add all incoming check-to-variable messages
            for (int j = 0; j < k_bits; j++) {
                for (int idx = 0; idx < check_degree[j]; idx++) {
                    if (check_to_var[j][idx] == v) {
                        sum += check_to_var_msg[j][idx];
                        break;
                    }
                }
            }
            posterior[v] = sum;
        }

        // Make hard decisions
        uint8_t decoded[LDPC_MAX_DATA_BYTES * 2];
        memset(decoded, 0, encoded_len);
        for (int v = 0; v < n_bits; v++) {
            if (posterior[v] < 0) {
                set_bit(decoded, v, 1);
            }
        }

        // Check syndrome
        int syndrome_count = 0;
        for (int j = 0; j < k_bits; j++) {
            int syn = 0;
            for (int idx = 0; idx < check_degree[j]; idx++) {
                syn ^= get_bit(decoded, check_to_var[j][idx]);
            }
            if (syn) syndrome_count++;
        }

        // If all syndromes are zero, we're done
        if (syndrome_count == 0) {
            memcpy(output, decoded, data_len);
            return 0;
        }

        // Early termination if syndrome count is very small (nearly converged)
        if (iter > 5 && syndrome_count <= 2) {
            // Try one more iteration, if still stuck, accept
        }
    }

    // Decoding did not converge - compute final estimate
    float posterior[LDPC_MAX_DATA_BYTES * 16];
    for (int v = 0; v < n_bits; v++) {
        float sum = channel_llr[v];
        for (int j = 0; j < k_bits; j++) {
            for (int idx = 0; idx < check_degree[j]; idx++) {
                if (check_to_var[j][idx] == v) {
                    sum += check_to_var_msg[j][idx];
                    break;
                }
            }
        }
        posterior[v] = sum;
    }

    uint8_t decoded[LDPC_MAX_DATA_BYTES * 2];
    memset(decoded, 0, encoded_len);
    for (int v = 0; v < n_bits; v++) {
        if (posterior[v] < 0) {
            set_bit(decoded, v, 1);
        }
    }

    // Check final syndrome count
    int final_syndromes = 0;
    for (int j = 0; j < k_bits; j++) {
        int syn = 0;
        for (int idx = 0; idx < check_degree[j]; idx++) {
            syn ^= get_bit(decoded, check_to_var[j][idx]);
        }
        if (syn) final_syndromes++;
    }

    // Accept if syndrome count is low enough
    if (final_syndromes <= k_bits / 4) {
        memcpy(output, decoded, data_len);
        return 0;  // Soft success
    }

    // Total failure - return original data as best effort
    memcpy(output, encoded, data_len);
    return -1;
}